REPORTS IN METEOROLOGY AND OCEANOGRAPHY

UNIVERSITY OF BERGEN, 1 - 2010

Ocean near-surface boundary layer: processes and turbulence measurements

MOSTAFA BAKHODAY PASKYABI

and

ILKER FER

Geophysical Institute University of Bergen

December, 2010

2

«REPORTS IN METEOROLOGY AND OCEANOGRAPHY»

utgis av Geofysisk Institutt ved Universitetet I Bergen.

Formålet med rapportserien er å publisere arbeider av personer som er tilknyttet avdelingen.

Redaksjonsutvalg:

Peter M. Haugan, Frank Cleveland, Arvid Skartveit og Endre Skaar.

Redaksjonens adresse er : «Reports in Meteorology and Oceanography»,

Geophysical Institute.

Allégaten 70

N-5007 Bergen, Norway

RAPPORT NR: 1- 2010

ISBN 82-8116-016-0

1

CONTENT

1. INTRODUCTION ................................................................................................2

2. NEAR SURFACE BOUNDARY LAYER AND TURBULENCE MIXING .............3

2.1. Structure of Upper Ocean Turbulence ........................................................................................ 5

2.2. Governing Equations......................................................................................................................... 6 2.2.1. Turbulent Kinetic Energy and Temperature Variance .................................................................. 6 2.2.2. Relevant Length Scales ..................................................................................................................... 8 2.2.3. Relevant non-dimensional numbers................................................................................................ 8 2.2.4. Turbulence Spectra ........................................................................................................................... 9

2.3. Atmospheric Forcing ....................................................................................................................... 10 2.3.1. Wind Stress....................................................................................................................................... 10 2.3.2. Bulk Heat Fluxes .............................................................................................................................. 11 2.3.3. Solar Radiation Fluxes..................................................................................................................... 12 2.3.4. Precipitation...................................................................................................................................... 13 2.3.5. Surface Buoyancy Flux.................................................................................................................... 13 2.3.6. Gas Fluxes......................................................................................................................................... 14

3. OCEAN TURBULENCE MEASUREMENT.........................................................14

3.1. Measurement systems ................................................................................................................... 14

3.2. Sensor Features ................................................................................................................................ 21 3.2.1. Temperature..................................................................................................................................... 21 3.2.2. Conductivity ...................................................................................................................................... 21 3.2.3. Shear ................................................................................................................................................. 22

3.3. Parameter Estimation..................................................................................................................... 23 3.3.1. Turbulence Dissipation Rate .......................................................................................................... 23 3.3.2. Vertical Eddy Diffusivity for Mass .................................................................................................. 24 3.3.3. Dissipation Rate of Temperature Variance and Eddy Diffusivity for Heat ............................... 24 3.3.4. Vertical Overturns ............................................................................................................................ 25

3.4. Measurement Limitations and Platform Motion ................................................................... 26 3.4.1. Platform Motion and Vibration Correction Procedures ............................................................... 26 3.4.2. Despiking and Denoising ................................................................................................................ 30

4. TURBULENCE NUMERICAL MODELING .......................................................30

4.1. Direct Numerical Simulation ........................................................................................................ 30

4.2. Large Eddy Simulation ................................................................................................................... 30

4.3. Statistical Turbulence Modeling ................................................................................................. 31

4.4. Empirical Turbulence Modeling................................................................................................... 31

5. SUMMARY ........................................................................................................31

6. REFERENCES....................................................................................................32

2

Abstract

Exchange of mass, momentum and heat by turbulent processes is crucial in the air-sea interactions. In this report, state-of-the-art of turbulent kinetic energy dynamics in the upper ocean boundary layer is reviewed. Particular attention is given to the structure of the upper mixed layer, main turbulent processes in this layer, different methodology of near surface turbulence measurements, and complementary turbulence numerical models.

1. Introduction

The complex air-sea interface sets the boundary conditions for physical and biogeochemical processes and plays a key role in the global atmosphere-ocean heat balance. Fluxes across this interface influence the weather, climate and spatial distribution and evolution of greenhouse gases. The upper water column below the air-sea interface comprises of an actively entraining upper ocean mixed layer, the upper 10-50 m well-mixed in temperature and salinity, bounded at its base by a sharp density discontinuity separating the layer from a stable, essentially non-turbulent pycnocline. The thermal and mechanical energy received from the atmosphere in the upper layer not only control the local dynamics, but the layer itself modulates the flux of this energy to the deeper water masses (Garwood 1976). This mixing process plays a major role for the dynamics of marine ecosystems. It provides food web, light and nutrients for phytoplankton population (Gargett 1997). The first classical study of the surface mixed layer and shelf sea waters was done by Sverdrup (1953) about the development of spring phytoplankton blooms as a function of light supply and the depth of vertical mixing. Blooming can occur only when the depth of the mixed layer is less than a compensation depth at which gain and loss of the population balance each other.

Sverdrup’s theory thus necessitated a better understanding of the complex upper ocean dynamics, of erosion of the pycnocline, and especially of the turbulent mixing processes which control the exchange and variability of properties such as momentum, heat, mass and gases in the upper ocean. Furthermore, understanding turbulence and its role in ocean mixing is key in critical ocean processes (Nihoul 1980), and needed even in the studies of ocean circulations and the coupled ocean-atmosphere climate.

Upper ocean turbulence has a broad spectrum of time and spatial scales, forced by surface fluxes of buoyancy, momentum and surface waves. The buoyancy loss at the surface due to surface cooling and evaporation (and due to ice freezing at high latitudes, which is not considered in this report) results in convection due to unstable surface density stratification. The overturning eddies will lead to entrainment of water from below the pycnocline. The mean shear due to loss of mean flow kinetic energy generated by wind stress over sea surface (and its associated currents) can lead to instability of Kelvin–Helmholtz billows with their axes oriented roughly at right angles to the shear (Li et al. 2005). The interaction between the wind-driven Stokes drift of surface waves and the mean shear generates counter-rotating vortices aligned with the wind direction, so-called the Langmuir circulation (Thorpe 2004, 2007). Langmuir circulation is a means of efficient energy transfer from the surface wave energy to turbulence mixing (Grant and Belcher 2009; Teixeira and Belcher 2010). Therefore, the upper ocean turbulence and associated mixing are sensitive to and dependent on the properties of the surface gravity waves (Ardhuin and Jenkins 2006). Deeper in the water column, internal wave breaking, dynamical Kelvin-Helmholtz instabilities at the pycnocline

3

and local frictional drag against the topography are other typical trigger mechanisms which contribute significantly to the vertical redistribution of both momentum and scalars in the ocean interior (Thorpe 2004, 2007).

Understanding of the aforementioned processes at the sea surface and the structure of the boundary layers requires careful observations and measurements of turbulence mixing. Direct measurements of turbulence are very limited and difficult. Surface wave orbital velocity fluctuations are often about 1 m s-1, whereas the velocity scale of turbulent velocity fluctuations in the near surface is about 1 cm s-1, illustrating the measurement complexity. Thus, the surface wave orbital velocity fluctuations are two orders of magnitude larger than the turbulence velocity fluctuations, so they represent a large signal that must be separated from the less energetic turbulent signal in order to compute turbulent variances, co-variances, and dissipation rates (Soloviev et al. 1999). Indirect methods are often used to study ocean turbulence mixing by using appropriate measurement techniques, sensors, and theoretical approximations (Burchard et al. 2008b). A useful parameter for characterizing the turbulence field is the viscous dissipation rate of turbulent kinetic energy per unit mass, . Different approaches to measure ocean turbulence include profiling or towed microstructure measurements, time series from fixed sensors, as well as particle image velocitimeter (Section 3). The vertical fluxes of heat and buoyancy are usually obtained by assuming a balance between turbulent production, buoyancy flux and dissipation (Osborn 1980) and a constant mixing efficiency. For the past 40 years, the standard technique of measuring turbulent quantities in the ocean has been the use of vertical microstructure profilers, pioneered by Osborn (1974) and Gregg et al. (1973).

In this report, we review the current understanding of the processes at the sea surface and in the near surface boundary layer, including theory and observational techniques. Recently, numerical modeling has been extensively applied to analyze the dynamics of turbulent mixing. For completeness, a brief description of typical numerical tools for turbulent mixed layer modeling (direct numerical simulation, large eddy simulation, statistical and empirical models) is also presented. The report is organized as follows. Near surface structure and dynamics with the state-of-the-art in turbulence mixing are presented in Section 2.1. The governing equations and relevant non-dimensional numbers are reviewed in Section 2.2. Important components of the atmospheric forcing are summarized in Section 2.3. Turbulence measurement and instrumentations are reviewed in Section 3. Subsequently, in Section 4 numerical models of turbulence in the mixed layer are introduced briefly, followed by the concluding remarks.

2. Near Surface Boundary Layer and Turbulence Mixing

The near surface boundary layer is the upper part of ocean that is dominantly (directly or indirectly) influenced by the surface fluxes such as heat, moisture, momentum, wind stress and surface waves (Anis and Moum 1995). It comprises the interface between the ocean and atmosphere where many processes occur, such as breaking waves (upper few meters), molecular transport (upper few millimeters), diurnal and seasonal convection, and Langmuir circulation (Soloviev and Lukas 2006). Turbulence acts to remove the vertical gradients of oceanic tracers (temperature, salinity and density) above the pycnocline leading to a quasi-homogenous layer: the upper ocean mixed layer. While the profiles of turbulent dissipation in the upper layer define the mixing layer depth, the mixed layer depth and its evolution is

4

shaped by an integral of mixing events (Brainerd and Gregg 1995; Fer and Sundfjord 2007). At instances when the mixing layer penetrates deeper than the mixed layer, turbulent motions work against the stratification and a part of the energy input is used to increase the potential energy of the water column. At the base of the mixed layer is a transitional region with strong density gradient where the density increases with depth (pycnocline). Typically this layer corresponds to the thermocline where the temperature decreases with depth. Generation and propagation of internal waves and formation of strong velocity gradient can occur in the pycnocline (not covered in this report).

The near surface boundary layer, including the mixed layer, is a key component in the study of climate, biological productivity and marine pollution (Thorpe 2007). Transfer of momentum, heat, gases across the ocean surface, and the turbulent motions within the relatively uniform mixed layer of the ocean are largely controlled by waves, especially breaking waves (Thorpe 2004, 2007), local source of shear and convective instabilities or nonlocal source by convection and advection (Soloviev and Lukas 2003b, 2006). Figure 1 illustrates some of the processes in the upper ocean. Diurnal cycle of solar radiation (heating) reduces the density of the upper water column, thereby suppressing the near surface turbulence. Cooling of the upper surface due to evaporation and long wave radiation leads to convection (positive buoyancy flux) into the interior of water column and develop turbulence. Breaking waves are the main source of turbulent kinetic energy (TKE) in the top meters of the ocean. This production of TKE is believed to occur mostly through the large shear at the forward face of breaking waves (Ardhuin and Jenkins 2006). Ocean-atmosphere interface is a two phase boundary with air bubbles in water and sea spray in air. The near surface processes are sensitive to the appropriate conditions in this two phase boundary. Bubbles from breaking waves change the density stratification and affect the near-surface thermohaline stratification.

Understanding of the small-scale turbulence depends on understanding of the multiple interactions between the turbulence, currents, and surface waves. In this section, a brief description of the upper ocean structure is given in section 2.1, followed by the governing equations (section 2.2). Finally, basic components of the atmospheric surface forcing are presented in section 2.3.

Figure 1. An illustrated view of the most important processes shaping the upper ocean boundary

layer. The scales of the drawing are arbitrary (http://www.us-solas.org:8080/Plone).

5

2.1. Structure of Upper Ocean Turbulence

Wind waves supply energy for turbulence through breaking and impact strongly the air-sea system on all scales. Due to breaking and vortex instabilities at the ocean surface, waves release TKE and generate a source of turbulence at the ocean surface. Thus, turbulent vertical mixing is intensified within the near surface layer (Qun et al. 2007). Furthermore, exchange of atmospheric gases such as oxygen and carbon dioxide occurs by diffusion across the sea surface and across the surfaces of bubbles created by the breaking waves (Garrett 1996). Phenomena such as surface waves (especially breaking waves), bubbles, shear instabilities, surface heating and cooling influence TKE and its dissipation rate in the water column. Ignoring stratification and rotation effects, the upper ocean turbulent boundary layer can be conveniently divided into four sublayers as illustrated in figure 2 (Soloviev and Lukas 2006):

1- the wave-stirred layer where the TKE production by wave breaking significantly exceeds the mean shear effect, and the turbulent diffusion of the wave kinetic energy dominates in the range of depths where the wave motion continues to be vigorous,

2- the turbulent diffusion layer where the turbulent diffusion of TKE exceeds the wave (as well as the mean shear) effect in the TKE budget,

3- the wall layer where the mean shear production of turbulent energy dominates, and

4- the viscous sublayer. Viscous sublayers develop at both the water- and air-side of the air-sea interface due to the suppression of the normal component of turbulent velocity fluctuations near the density interface. This sublayer is controlled by the tangential wind stress.

The most significant characteristic of the ocean mixed layer, in contrast to the atmospheric boundary layer, is the presence of wave breaking and the Langmuir circulation at the free surface. Breaking of surface waves generates large amounts of small-scale turbulence near the sea surface, and the interaction between the wind-driven surface shear and the Stokes drift of surface waves generates Langmuir circulations that are large circulation cells aligned in the wind direction (Noh and Min 2004). Measurements revealed that in the presence of wave breaking, the dissipation rate of TKE near the sea surface is several orders of magnitude larger than that expected from the law of the wall (section 2.3.1) (Anis and Moum 1995). Furthermore, wave breaking increases the roughness length scale, z0, at the sea surface to 0.1–8 m, much larger than that of the atmospheric boundary layer. The first numerical attempt to model the wave-enhanced turbulence near the surface was done by Craig and Banner (1994), who used the level 2.5 turbulence closure scheme of Mellor and Yamada (1982) with a simple model of the oceanic boundary layer to successfully reproduce the observations from a number of datasets. Their model predicts significantly enhanced surface turbulence relative to the law of the wall (Thorpe 2007). They suggest that z0 in the oceanic boundary layer is of the order of the surface wave amplitude, much larger than that in the atmospheric side of the air–sea interface. Craig (1996) notes that z0 is a significant scaling parameter for the dynamics in the boundary layer affected by waves, but that the dissipation measurements in the ocean or lakes are not yet precise enough to enable an accurate estimation of its magnitude. Clearly, z0

is an important length scale but it is as yet hard to quantify (Stacey 1999).

The large-scale Langmuir circulations as a source of convective motions in the ocean surface layer are another result of wind-induced flow in presence of surface gravity waves (Li,

6

2009). Skyllingstad and Denbo (1995) used a large eddy simulation model to simulate the Langmuir circulation and convection in the surface mixed layer and carried out numerical experiments with different combinations of wind stress, wave forcing, and convective forcing. In these simulations the Langmuir circulations were found to dominate the vertical mixing, leading to enhanced dissipation rates that were consistent with observations of Lombardo and Gregg (1989). McWilliams et. al. (1997) introduced the turbulent Langmuir number,

5005 .

* sat uuL , where *u is the surface friction velocity in the water and 0su is the surface

Stokes drift. atL is now recognized as an important parameter describing the Langmuir

turbulence (Grant and Belcher 2009). Furthermore, recent work suggests that high-frequency internal waves generated by Langmuir circulation over stratified water may be an important source of turbulent mixing below the surface mixed layer (Polton et al. 2008).

Figure 2. Diagram of the upper ocean turbulent boundary layer. Here hW-S is the wave stirred

layer depth, and hTD is the turbulent diffusion layer depth (Soloviev and Lukas 2006).

2.2. Governing Equations

The well-known Navier-Stokes equations for the analysis of Newtonian fluid dynamics include conservation laws for mass (continuity equation), momentum, heat, energy, salt, humidity, and the equation of state. Presentation and derivation of the basic equations can be found in e.g., Tennekes and Lumley (1972), Gill (1982) and Pond and Pickard (1983). The next section presents the budget equations for TKE and the temperature variance. To provide a framework for near surface turbulence, we then present a brief summary of different length scales, characteristic non-dimensional numbers, parameters and universal spectral forms.

2.2.1. Turbulent Kinetic Energy and Temperature Variance

The TKE budget equation is

7

0

1 12 2

2i

j i i j j i j i ij i j i ij ijj j j C D

A B

UU e U u u e p u u s u u b u s s

t x x x

(1)

where the primes and the overbar denote fluctuations and averaging, respectively. Here jU is

the mean field velocity vector, is the kinematic viscosity, 0 is a constant reference

density, 0/b g is the buoyancy anomaly, g is the gravitational acceleration,

321 ,, uuu is the velocity in the standard orthogonal coordinate system where directions

21 , xx and 3x are positive to the east, north and upwards, respectively. The strain rate tensor

ijs is given by

i

j

j

iij x

u

x

us

2

1 (2)

The products in equation (1) are taken over repeated suffices 3,2,1, ji . The first term in

equation (1) expresses the local storage of variance or TKE. The other terms are

Term A: Transport terms containing energy transported by the mean flow and turbulence respectively (first and second terms), the pressure correlation term (third one) and the viscous transport term (last term).

Term B: Shear production term, the rate at which TKE is produced by the interaction

of the Reynold’s stress, jiuu , with the mean velocity shear.

Term C: Buoyancy flux (B). In the case of an unstable density stratification, the buoyancy flux is positive; it will be a TKE production term. In stable stratification, turbulent mixing induces a negative buoyancy flux by displacing the dense water upward, hence B becomes a sink in equation (1).

Term D: Dissipation rate, . It is the loss of kinetic energy of turbulent motion per unit mass through viscosity to heat.

By Reynolds averaging of the heat equation, the temperature variance equation can be derived as

E

jj

D

jT

C

jj

B

jT

j

A

jj x

TuT

x

TkuT

xT

xk

xT

xu

t

2

222

2

1

2

1

2

1 (3)

where Tk is molecular diffusivity for heat, T is temperature fluctuation. The terms are

Term A: Storage term. Term B: Molecular transport. Term C: Turbulent transport. Term D: Dissipation rate of temperature variance. Term E: Gradient production.

8

2.2.2. Relevant Length Scales

The following length scales are descriptive of mixing in a turbulent flow.

Kolmogorov length scale: It is defined as Kk/1 with the Kolmogorov

wavenumber Kk (cyclic units)

413 / Kk (4)

It represents the scale at which viscous forces equal the inertial forces, and represents the lower end of TKE at the dissipation subrange of the spectrum. The relation between a cyclic wavenumber, k, and a radian wavenumber, , is k = /2.

Batchelor length scale: It is defined as Bk/1 where Bk is the Batchelor

wavenumber

412 /

TB kk (5)

expressed in cyclic units, and Tk is molecular diffusivity for heat. It is the length

scale at which temperature fluctuations disappear. An equivalent Batchelor length scale for salinity can be written by replacing the diffusivity of heat with the diffusivity of salt.

Ozmidov length scale: It is defined as the length scale at which buoyancy forces balance the inertial forces, expressed as

213NLO (6)

where N is the buoyancy frequency,

dz

dg

dz

d

dz

dgN

adiabatic

2

where is the potential density anomaly.

Corrsin length scale: It is the smallest scale at which eddies are strongly deformed by the mean shear, estimated as

1 23CL S (7)

where 2 22S du dz dv dz , and u and v are the orthogonal components of

the mean horizontal velocity. Corrsin length scale represents the upper limit of eddy sizes when the background shear is more restrictive than the background stratification.

2.2.3. Relevant non-dimensional numbers

Gradient Richardson number: It is defined as the ratio of squared buoyancy frequency and squared mean shear

2 2Ri N S . (8)

Flux Richardson number: It is defined as the ratio of buoyancy production/consumption term in equation (1) (i.e., negative of the buoyancy flux, B) to shear production term. For stable stratification, Rif is the efficiency of

9

mixing. When the mean flow u is aligned with the x-axis, the flux Richardson number is given as

z

uwu

bwRi f

(9)

Mixing Efficiency factor: It is given as

1f fR R , (10)

and a typical upper limit of 20% is often used (Moum 1996).

Buoyancy Reynolds number: It is a non-dimensional number which characterises the vigour of turbulence. It is also called the turbulence activity index, and is also indicative of the likelihood of local isotropy (see section 3.3.1). It is defined as

2NI (11)

2.2.4. Turbulence Spectra

Spectral analysis is a widely-used approach in turbulence studies since the wavenumber or frequency domain distribution of velocity, or scalar variance can be readily related to scale and evolution of eddies, and the rate of their dissipation. A theoretical form of the spectrum of TKE was hypothesized by Kolmogorov that covers the broad range of wavenumbers up to a cut-off wavenumber limited by the effect of viscosity (the Kolmogorov wavenumber, Eq. 4). According to Kolmogorov’s hypothesis, there exists an inertial subrange where the three-dimensional velocity wavenumber spectrum of a high Reynolds number flow has a universal form that depends only on the energy dissipation. Assuming isotropic turbulence, Kolmogorov’s spectrum is given by following functional relationship

3532 kCkSK (12)

where k is the radian wavenumber and 50.C is the universal Kolmogorov constant. This simple relationship between energy dissipation and the wavenumber spectra allows the estimation of using the inertial-dissipation method.

The Batchelor spectrum, here given for the temperature gradient, in one dimension can be written as (Dillon and Caldwell 1980)

fkkqkS TBTB11212 (13)

where q is a universal constant, T is the temperature variance dissipation rate due to

turbulence. Assuming isotropy

2

066

z

TkdkkSk TBTT (14)

where Tk is the molecular diffusivity for heat, /T z is the small scale vertical temperature

gradient. In equation (13), is a non-dimensional wavenumber equal to 212qkkB . The non-

dimensional shape of the spectrum is given by

10

0

22 22

dxeef x (15)

The universal constant q has been estimated as 52.167.3 q (Oakey 1982).

2.3. Atmospheric Forcing

2.3.1. Wind Stress

The wind stress, or momentum flux, is a driving force for surface gravity waves and oceanic currents (Garrett 1996). This momentum exchange between air and sea is determined to a large extent by the aerodynamic roughness at the air–sea interface since it determines the turbulence level near the interface, and thereby the wind stress. Stress is nearly constant with height in the surface layer; the mechanisms, however, vary with height. In a wave boundary layer, much less than a wavelength in height, part of the stress is carried by the wave-coupled motion, while away from it nearly all the stress is due to the turbulent momentum flux. In a viscous sublayer, generally less than 1 mm thick, the turbulent momentum flux gives way to viscous shear stress (Smith et al. 1995). At the sea-air interface this stress is expressed as

2*ua

where a is the density of air and *u is the friction velocity which can be thought of as a

proxy for the surface wave. One of the difficulties in the turbulent near surface layer is the formulation of the aerodynamic roughness, 0z , and its relationship to *u . On dimensional

grounds

g

uz

2*

0

(16)

where 01850. is the Charnock constant (Toba and Kunish 1970; WOM 1998). The wind velocity develops a logarithmic form (Wu 1983)

0

* lnz

zuzu

(17)

where zu is the velocity profile, z is the height, and 4.0 is the von-Karman constant. A

common reference level for turbulence in boundary layers in the absence of buoyancy forces is the constant stress layer scaling, also called the law of the wall (Tennekes and Lumley 1972). For a mixed layer of depth h , the dissipation rate, , profile in the near surface layer can be divided into inner ( hz 1.00 ) and outer hzh 10. parts. In the inner part, the

dissipation profile is closely related to the wind stress production and decays with depth following

0

3*

zz

uz

. (18)

The velocity profile given by equation (17) can be rewritten as (Taylor 1972)

0

0* lnz

zzuzu

(19)

11

Dissipation in the outer part is influenced by other environmental parameters such as rotation and stratification. However, both the inner and the outer parts are affected by the depth of the mixed layer which evolves in response to heat fluxes, wind stress and the Earth’s rotation (Soloviev and Lukas 2006). It is common to express wind stress, , through the following bulk transfer relation

zuzCDa2

where zCD is the drag coefficient and zu is given in equation (17). If the boundary is in a

state of neutral stratification, the drag coefficient can be expressed as

2

zu

uzCD

* (20)

However, the boundary layer over the ocean is not necessarily neutral. A stability dependence is derived using the Monin-Obukhov similarity theory as

1

0

lnDMO

z zC z

z L

(21)

The function (Stull 1988) is given for stable and unstable conditions according to the

Monin-Obukhov length

0

3

b

MOJ

uL

* (22)

where 0bJ is the surface buoyancy flux. Further, the logarithmic velocity profile (Eq. 17), can

be revised as

MOL

z

z

zuzu

0

ln*

At the air–water interface the energy input equals the sum of the surface stress, , per unit mass times an effective phase speed, effc , of waves acquiring energy from the wind and the

input to the surface drift, su , i.e.,

2*

2* uuucE seffin

(Wu 1975). The second term is generally small (Gemmrich 2010). In a fully developed wave

field, the total energy dissipation, hdzE , balances the energy input, i.e., inEE . Thus,

the dissipation rate plays an important role in the energy balance, especially if it is affected by breaking waves. However, it is typically difficult to measure the dissipation rate of TKE near the ocean surface, especially in the presence of wave-induced motions (Zhang and Chan 2003; Weller et al. 2004).

2.3.2. Bulk Heat Fluxes

Turbulent and radiative processes exchange heat between the atmosphere and the sea, and together with evaporation and precipitation, modify air and water masses at the surface

12

(Smith et al. 1995). The turbulent fluxes of the sensible, TQ , and latent, EQ , heat and the net

long wave radiation LQ are defined by the standard bulk formulae

awswL

asEVaVaE

asTpaapaaT

ETQ

qqUCLqwLQ

TTUCcTwcQ

4

10

10

(23)

where pac is the specific heat capacity of air at constant pressure, and Tw , and q are the

fluctuations of vertical velocity, temperature and specific humidity, respectively. VL is the

specific latent heat of vaporization, TC and EC are the drag coefficients or bulk transfer

coefficients for sensible and latent heat, sT is the sea surface temperature, aT is the air

temperature at 10 m height, sq is the water vapor ratio (saturation specific humidity) at the

ocean surface level, aq is the specific humidity of air at the standard level of 10 m above sea

surface, 428 KWm10675 . is the Stefan-Boltzmann constant, 97.0w is the infrared

emissivity of water, and aE is the long wave irradiance from sky. The drag coefficients in

equation (23) can be calculated as (Rodriguez 2005)

1

0

2/1 ln

z

zCC DT

1

1/2

0

lnE T

zC C

z

and DC is given by equation (20) or (21) according to the stability conditions. Alternatively,

empirical formulae can be used: CE = 1.510-3 and CT = 1.110-3 for unstable and 0.8310-3 for stable conditions (Soloviev and Lukas 2006). Furthermore, the aerodynamic roughness length includes a correction term to equation (16),

*

2*

0 ug

uz

(24)

Where = 0.11. The second term in equation (24) has negligible influence for wind speeds above about 6 m s-1. The value of z0 in equation (24) is determined by an iterative process (Smith et al. 1995).

2.3.3. Solar Radiation Fluxes

The incoming solar radiation at the top of the atmosphere is determined by the solar elevation and also by the orbital variations in distance between the Earth and the Sun. In the atmosphere, clouds and aerosols reflect and absorb a fraction of the incoming radiation. The albedo (fraction of solar energy reflected at the surface) depends on solar elevation, sea state, ice cover, and cloud cover. The incoming energy is absorbed in the top few meters, depending on the clarity of the water which in turn depends on the plankton and sediment present in the water. The net long-wave radiation is usually, but not always, upward. The loss is nearly all from the top few mm and is responsible (together with the latent heat flux) for a “cool skin” that is often a few tenths, or even a degree, cooler than the bulk of the near-surface water

13

temperature. The upward component depends on the sea temperature and on the emissivity of sea water. The downward long-wave radiation from the overlying air is more complex, depending on profiles of air temperature and humidity and on the presence of fog and cloud.

The net long-wave radiation is given as

faawasawB cTeTTTTQ )05.039.0()(4 43 (25)

where e is water vapor pressure, Cc f 72.01 , and C is a cloud correction factor, or the

fractional cloud cover.

The short–wave net radiation based on latitude, longitude, time, fractional cloud cover and albedo is (Payne 1972)

30 6.011 CQQ ssS (26)

where s is the mean albedo over a period of time, often a month, and 0sQ is the short-wave

radiation reaching the surface under clear sky.

2.3.4. Precipitation

The evaporation and precipitation imbalance is a major branch of the hydrological cycle. The measurement of precipitation at sea remains a problem. Data exist mainly from a few atolls and small islands (Smith et al. 1995). Large and variable flow distortion makes it extremely difficult to measure precipitation from moving ships, and there are no valid data from the Voluntary Observing Ships that otherwise provide the bulk of the marine meteorological data (Li 1998).

2.3.5. Surface Buoyancy Flux

The surface buoyancy flux is given by

0 0b S

P

gJ Q J

c

(27)

where, 0SJ is the surface salinity flux due to evaporation-precipitation imbalance or ice

freezing, Pc is the specific heat of water, T /1 is the thermal expansion

coefficient of seawater at the surface, 1 / S is the corresponding coefficient for salinity (Gill 1982), and Q is the net surface heat flux expressed as

SBTLE QQQQQQ

The net surface heat flux affects the near surface turbulence by inducing a buoyancy flux. The distance from the surface where the wind stress and buoyancy are equally effective at producing turbulence is scaled by the Monin-Obukhov length (Eq. 22), and in the absence of salt fluxes, can be rewritten as (Lombardo and Gregg 1989).

33**

0

pMO

b

c uuL

J gQ

(28)

The similarity scaling works well when the near surface boundary layer is controlled vertically by horizontally uniform fluxes at the surface. MOL is used to separate the two

14

asymptotic regimes: when 1MOLz / the wind stress dominates the production of

turbulence, and when 1MOLz / , the buoyancy controls the production.

2.3.6. Gas Fluxes

The flow of inert gases between the atmosphere and ocean is controlled on a planetary scale by heat fluxes across the air-sea interface. Since the solubility of gases in water is temperature dependent, with cold water being able to dissolve more gas, areas of net heat input to the ocean degas to the atmosphere, while areas of net ocean cooling absorb the atmospheric gases (Schudlich and Emerson 1996). The gas flux across the air-sea interface is typically expressed as the product of a gas transfer velocity, k , and the difference between the gas concentration in air and water. In low and moderate wind speed, micro-scale wave breaking (or micro-breaking1) plays more significant role in the air-sea exchange. This micro-scale wave breaking on gas transfer can be modeled as

21*

cSuk

where is the fractional surface area covered by intense wave-induced surface divergence

generated during the breaking process, is a dimensionless constant, *u is the friction

velocity, and DSc is the Schmidt number (the ratio of the kinematic viscosity of water to

the gas diffusivity in water). For detailed information about the effect of microscale breaking wave on the air-water gas exchange the reader is referred to Zappa et al. (2001). Larger breaking waves cause whitecaps that inject air bubbles into the water and inversely, water drops and sprays into the air.

3. Ocean Turbulence Measurement

3.1. Measurement systems

Ocean near-surface boundary layer dynamics is dominated by high-frequency, intermittent phenomena that can only be described by turbulence statistics. Direct measurement of turbulent microstructure2 in the ocean has proven elusive. Precise estimation of vertical fluxes of mass, heat, and momentum requires eddy correlation sensor packages comprising a current meter measuring the three components of small-scale velocity, and temperature and conductivity sensors sampling the same measurement volume. Indirect measurements, typically sampling the dissipation range of turbulence, are more typical. Some examples of indirect measurements and their applications are tethered or loosely tethered vertical microstructure profilers equipped with shear probes, thermistors, microstructure sensor packages installed on towed bodies etc.. In the following we give a categorized summary of turbulent measurement approaches. A detailed review on ocean microstructure measurements is given by Luek et al. (2002) and Thorpe (2007).

None of the measurement systems exemplified below is able to cover the full range of spatial scales from the smallest dissipative eddies (typically on the order of a centimetre) to the largest energy-containing eddies (typically on the order of several meters). Thus, to

1 Breaking of steep, wind-forced waves without air entrainment, which occurs at wind speeds well below the level at which whitecaps appear. 2 The term microstructure is used for fluctuations associated with small-scale turbulence. The term fine structure is used for inhomogeneities related to stratification.

15

quantify statistics of turbulence, additional assumptions have to be made. The extrapolation to the four-dimensional space usually assumes local isotropy (that is, the turbulence has no preferred direction), at least for the smallest scales. To overcome the problem of sampling only a part of the turbulence spectrum, it is assumed that larger scales do not significantly contribute to the microstructure turbulence (for observations of the dissipation of TKE into heat) and that the smaller scales do not contribute to the energy-containing scales (for observations of Reynolds stress and kinetic energy). Taylor’s frozen turbulence hypothesis is often invoked, using a mean translation speed (e.g., an instrument’s profiling speed or the mean flow) to transform time series of turbulent fluctuations into spatial profiles. These assumptions are all only partly justified. Turbulence observations never have the accuracy achievable for mean properties such as temperature or currents (Burchard et al. 2008b).

The technology has matured considerably during the past 40 years of oceanic turbulence profiling. Many profilers have been developed and their use has revealed numerous unexpected features of oceanic processes. However, a complete review of all these instruments would be impossible from the scope and the frame of this report. However, we provided ample references in this section to give the reader the opportunity to examine the many details for the sake of brevity.

Point measurement at spatially fixed positions: The most widely used method to sample velocity fluctuations in the water column uses the acoustic Doppler principle, either at single point using an acoustic Doppler velocimeter (ADV) or over a limited vertical range using a high-frequency acoustic Doppler current profiler (ADCP). Such instrument is an active sonar that transmits acoustic signals (by one transmitter) and then receives their echoes (by three or more receivers) partially reflected by sound scatterers in the water, like plankton or other floating particles. The scatterers are usually passively advected by water motion. From the measured Doppler shift between emissions and echoes, the flow velocity is deduced.

An example ADV is shown in figure 3-a. An important advantage of an ADV is that it measures the flow in a small sampling volume. This enables measurement to be taken without interfering with the flow (Nikora and Goring 1998). Advantage of an ADCP is that it provides the 3D velocity profile over a limited depth range, in contrast to an ADV’s point measurement (Gargett 1997; Souza 2007). Three transducers (beams) slanted at the same angle from the horizontal are sufficient to infer the three orthogonal components of the velocity.

An additional four beam, when available, allows velocity to be inferred when one beam fails and also provides for an error velocity estimate. Recent ADCPs with five beams are particularly suited for Reynolds stress measurements since the vertical velocity can be inferred with high accuracy (for an application see Peters et al. 2007). Figure 4-a shows a conventional ADCP with four beams. A detailed outline of the procedure to calculate a three dimensional current vector based on the measured velocities of a three-beam ADCP is illustrated in figure 4-b. Reynolds stresses are measured in this instrument by the use of statistical properties of the measured in-beam velocity fluctuations which is known as the variance method (Lu and Lueck 1999).

16

Figure 3. a) Schmatic of an ADV instrument (NortekUSA 2010). b) Sketch of TAMI and the

mooring arrangement used in Cordova Channel (Lueck and Huang 1998).

Figure 4. a) Schmatic of typical 4 beam ADCP sensor head. The red circles denote the 4 transducer

faces (http://oceanexplorer.noaa.gov/technology/tools/acoust_doppler/media/adcp.html). b) Beam

geometry and calculation of the horizontal and vertical velocity components from the measured in-

beam ),,( 321 bbb for a three-beam ADCP (Lorke and Wuest 2005).

17

The Tethered Autonomous Moored Instrument (TAMI, Fig. 3b) is an example of moored turbulence measurements at a fixed point by use of airfoil shear probes (Lueck et al. 1997). The instrument measures the microstructure shear in the dissipation range of the wavenumber spectrum using shear probes, and the temperature fluctuations using fast-response thermistors. It is a convenient platform to sample the background temperature and salinity, horizontal currents, in this example using two ducted rotors and a fluxgate compass. The body motions are monitored using accelerometers and a pressure transducer. With today’s technology and data storage capacity, several months of raw data sampling is possible. TAMI, however, burst-sampled for 128 second every 5 min and stored reduced data including and band-averaged spectra and statistical parameters (Lueck et al. 1997; Lueck and Huang 1998).

Towed and free rising or falling microstructure profilers: The microstructure profilers are usually equipped with sensors to measure the fluctuation of temperature, conductivity, and velocity (current shear) in the microstructure scale range. The profilers are typically also equipped with accurate CTD (Conductivity, Temperature, Depth) sensors. Some specialized profilers are equipped with sensors for background horizontal current, oxygen concentration or fluorescence. On the Chameleon microstructure profiler a pitot tube was installed to measure vertical velocity which allowed for eddy correlation measurements from a vertical profiling instrument (Moum 1996). In their thorough review, (Lueck et al. 2002) give a historical summary of all microstructure profilers (both towed and vertical profiling). Dissipation rate profiles resulting from two sets of different profilers with different electronics and data processing schemes have been contrasted in Moum et al. (1995). for two American profilers and in Burchard et al. (2002) for two European profilers. In addition to instrumentation developed in various pioneering research institutions, a couple of microstructure profilers are commercially available: the VMP series by Rockland Scientific International, Canada (http://www.rocklandscientific.com/) and the MSS series by Sea and Sun Technology and ISW Wassermesstechnik, Germany (http://isw-wasser.com/prandke/). The latter also provides profilers for rising type measurements. For the MSS series, adjusting weights can be fixed at both ends of the profiler housing to alter the buoyancy of the profiler. For rising measurements, the microstructure profiler is given positive buoyancy. For vertical sinking measurements, the profiler is balanced with slightly negative buoyancy. For all loosely-tethered microstructure profiler systems, effects caused by cable tension (vibrations) and the ship's movement are minimized by paying out enough cable to keep it slack.

Rising profilers are needed to study the turbulence in the near-surface boundary layer. The uppermost meters are then satisfactorily resolved. A particularly relevant example is given in Ward et al. (2004). Another example is the near surface turbulence instrumentation employed in the western equatorial Pacific during the TOGA Coupled Ocean–atmosphere Response Experiment (COARE). The system consists of a free-rising profiler, bow-mounted sensors, and a dropsonde (Soloviev et al. 1999). An advantage of this method is the absence of rigid mechanical connection with the ship’s body and is an effective method for measuring the near surface turbulence. Figure 5 schematically shows deployment of the devices and includes photographs of the free-rising profiler and the bow sensors. The free-rising profiler fitted with microstructure shear, temperature, and conductivity probes is connected to a shuttle (Fig. 5-c,d) which allows the device to slide from the ship into the water. The profiler sinks a distance about 15 to 35 m far from ship’s wake. At a depth of about 20 m, the pressure-release mechanism releases the profiler from the shuttle and the profiler starts ascending at a speed

18

depending on the net buoyancy of the profiler. Due to presence of surface waves and pitching of the vessel, the bow probes are used to scan near surface boundary layer. The bow probes include high resolution probes of pressure, temperature, conductivity, and acceleration sensors which resolve the near surface turbulence as the ship steams (Fig. 5-d) (Soloviev and Lukas 2006).

Figure 5. Schematic diagram showing the near surface turbulence measurement employed by Soloviev and

Lukas. (2003a): a) deployment and d) the probe mounted on the bow. Here, 1- free-rising profiler coupled with

shuttle; 2- temperature, conductivity, and shear probes; 3- shuttle; 4- bow frame; 5- bow units (temperature,

conductivity, and pressure sensor, shear probe, and tilt sensor); 6- dropsonde; 7- temperature probe of micro-

wire type. The photographs show b) the bow sensors, c) the free-rising profiler with the shuttle, and e) the

sesnors on the profiler. (Soloviev and Lukas 2006).

19

Particle image velocimetry (PIV) in a two-dimensional plane: Turbulence energy is estimated in a backward facing step flow with three-component PIV. Estimates of turbulence energy transport equation for convection, turbulence transport, turbulence production, viscous diffusion, and viscous dissipation in addition to Reynolds stresses are computed directly from PIV data (Piirto et al. 2003). Figure 6 shows a schematic of submerged components of an oceanic PIV system. The light is delivered by a dual-head, pulsed dye laser through an optical fiber to a submerged optical probe, where the beam is expanded to a sheet that illuminates the sample area. The submersible system also contains a Seabird electronics, optical transmission and dissolved oxygen content sensors, a pressure transducer, a biaxial clinometers, and a compass. The platform is mounted on a hydraulic scissor-jack to enable acquisition of data at various elevations above the seafloor. The platform can also be rotated to align the sample area with the mean flow direction (Doron et al. 2001).

Figure 6. Schematic of oceanic PIV system: a) surface mounted laser, control and image acquisition

subsystems, b) side and top views of the submersible instrument (Doron et al. 2001).

Example field experiments: The field experiments designed to sample near surface turbulence and air-sea interaction show evidence of coupling between the surface temperature, the surface turbulent velocity fields, and the surface waves. Figure 7 shows an example of a field experiment set-up conducted from research platform (R/P) Floating Instrument Platform (FLIP), moored approximately 150 miles off the coast of southern

20

California (Veron et al. 2009). The main instruments are composed of an integrated active and passive infrared imaging, a laser altimetry system, a 6-degree-of-freedom motion package, and an eddy covariance system to acquire meteorological and atmospheric boundary layer flux data (not covered in this report).

In the presence of strong wind in the open ocean, breaking waves are an active process for generating of turbulence. For observing the turbulent velocity and bubble field as a part of air-sea fluxes, Gemmrich and Farmer (2004) conducted the Fluxes Air-Sea Interaction and Remote Sensing (FAIRS) experiment aboard the R/P FLIP 150 km offshore of Monterey, California. A surface float, tethered to the starboard boom, supported three orthogonal 2-MHz pulse-to-pulse coherent acoustic Doppler sonars and two acoustical resonators as well as an environmental package, monitoring water temperature, salinity, and float tilt and heading (Fig. 8). Three components of velocity profile are determined by Dopbeams which contains three passive sonars. A set of eight 100-kHz side-scan sonars, mounted on FLIP’s hull at depth ranging from 15 to 91.5 m, is used to estimate the directional wave field as well as the surface drift speed (Fig. 8-a).Video recording also is used to verify the occurrence and estimate the size of breaking waves at the float. The free-flooding resonators are used to determine the size distribution of microbubbles generated by breaking waves (Fig 8-b).

Figure 7. Instrumentation setup from R/P FLIP (Veron, 2009).

Figure 8. a) Schematic of the surface-following float contains two resonators and the head of the vertical Dopbeam. b) Sketch of the deployment setup. The float was tethered to the starboard boom of R/P FLIP. (Gemmrich and Farmer 2004).

21

3.2. Sensor Features

Technological advances in the last decades, including novel instrumentation, greater capacity of data recorders, faster recording rates, and more reliable and smaller sensors have increased our measurement capability, and understanding of turbulence in the ocean. Airfoil shear probes to measure velocity shear, fast-tip thermistors to measure temperature at sub-centimeter scales, and free falling (rising) instruments to carry sensors are examples of such advances.

3.2.1. Temperature

Small scale temperature fluctuations were the first to be measured to gather insight into mixing process in the near surface layer (Gregg et al. 1973; Osborn and Bilodeau 1979). Today various sensors are commercially available. The SBE 8 microstructure temperature sensor is a lightweight fast-response sensor intended for use in marine profiling applications where its high speed and spatial resolving power offer the ability to characterize small scale ocean temperature features (Fig. 9). The sensing element is a remote-cabled, probe-mounted thermistor (thermometrics type FP07). The thermistor voltage output is pre-emphasized, so the sensor's output increases as a function of the frequency components in the temperature signal. The effect of pre-emphasis is to magnify the sensor output for rapidly changing temperature, thereby overcoming the restrictions on system resolving power that would otherwise be imparted by the use of conventional (e.g., 16-bit) digitizers. The SBE 8's pre-emphasis response magnifies a 20 Hz temperature signal by a factor of 200, facilitating acquisition of signals 200 times smaller than could be characterized by conventional CTD sensors (Kanari 1991; Gregg 1999).

.

Figure 9. The SBE 8 integrated instrument probe, cabling and electronic housing.

(http://www.seabird.com/products/spec_sheets/8data.htm)

3.2.2. Conductivity

The microstructure conductivity sensor has been developed for making very rapid, high resolution measurement of electrical conductivity of water. Several versions exist, for example with dual needle or 4-electrodes. The latter contains four-electrode (platinum spheres) conductivity sensors supported by fused glass adopted for measurement of the mean conductivity profile and high frequency conductivity gradient profile (Fig. 10). The electronic circuit makes 4 terminals measurement of the conductance of the water by supplying an AC

22

Figure 10. Diagram of microstructure conductivity sensor (Nash and Moum 1999).

current between the inner electrodes of the sensor and measuring the AC voltage that develops across the outer electrodes. The ratio of this current to voltage is computed by circuit and a representative voltage supplied at the circuit output. When used in this way, the output voltage corresponds to a weighted volume average of the conductivity of the water in the vicinity of the sensor electrodes (Nash and Moum 1999).

3.2.3. Shear

An airfoil shear probe is a piezoceramic beam that generates small voltages as the turbulent velocity varies the lift and thus the bending force on an airfoil as it moves through the water (Fig. 11). It can measure velocity fluctuations on a spatial scale of about 10 mm. The general behavior and the construction principles of an airfoil sensor have been described in detail by Osborn (1974).

The basic scheme of the shear sensor operation is shown in figure 10. The cross force per unit length due to potential flow for an axially symmetric airfoil in a water jet of speed U (with horizontal, u , and vertical, w , velocity components) and an angle of attack can be expressed as

Figure 11. The piezoceramic airfoil shear probe operation in presence of cross force (Lueck 2005b).

23

2sin2

1 2

dx

dAUf p (29)

where is the density of the fluid and /dA dx is the rate of change in airfoil cross section

area in the axial direction. By integrating from the tip of the sensor to the position where / 0dA dx , and by elimination of from equation (29), the total cross force (lift force) is

obtained as

uwAF

where sinUu and cosUw are the horizontal and vertical components of the flow.

However, the speed of the probe in water also contributes to the cross-force. The constant axial velocity component w is due to falling or rising speed of profiler. The lift force, sensed by the strain-gauge, is converted to an electric voltage aE which is proportional to the lift

force. Time derivative of output aE gives the following relationship between the output

signal sE and the vertical shear of horizontal flow

dz

duwS

dt

dEE a

s2

where S is the overall sensivity of the linear response of the probe and sE is the output

voltage. Consequently, the vertical shear of horizontal flow has the following form

sEwSdz

du2

1

There are several sources of errors in this type of shear measurements, including limitations in the mathematical assumptions, determination of profiling velocity, errors in the calibration procedure, drift of the shear-probe sensitivity, temperature and pressure effects and interference from profiler vibrations (Burchard et al. 2008a). Furthermore, the wavelengths smaller than the airfoil’s spatial response length cannot be resolved (Ninnis 1984; Prandke and Stips 1998; Lueck 2005a). The shear is sensitive to the sink/rise velocity, which poses a challenge in measuring in the near surface layer influenced by wave orbital velocities.

3.3. Parameter Estimation

3.3.1. Turbulence Dissipation Rate

In the TKE balance equation (1), the major sink term is the dissipation rate, defined as

ijij ss 2 (30)

where, the second order tensor ijs is defined in equation (2). This tensor symbolizes the

deformation rate of fluid particles due to the velocity fluctuation gradients field, and is the kinematic viscosity3. For isotropic turbulence equation (30) can be expressed as (Osborn 1974)

3 Viscosity is weekly dependent on salinity and pressure but strongly dependent on temperature. For estimating it the following polynomial function is widely used 62 1000059186460051261030792471 )...( TT .

The typical value for water at 20 oC is about 10-6 m2s-1.

24

2

57

dz

ud . (31)

Isotropy can be assumed without any restriction in homogeneous flow, except close to boundaries. But in a stratified flow, like that in the thermocline, the stratification modifies the dynamics of turbulence (Rehmann and Hwang 2005). The effects of stratification can be inferred from the buoyancy Reynolds number (Eq.11), 2N (Yamazaki and Osborn 1993).

Anisotropy becomes more pronounced as diminishes relative to the stratification. The isotropic formula (Eq. 31) can be used with an error of about 35% for 202 N , and

isotropy is achieved for 2002 N (Yamazaki and Osborn 1993).

3.3.2. Vertical Eddy Diffusivity for Mass

Vertical eddy diffusivity for mass, K , relates the turbulent mass flux to the mean

density gradient , d dz ,

d

w Kdz (32)

where and w are the fluctuations of density and vertical velocity, and an overbar denotes

averaging. When turbulence is steady and homogenous, a balance is obtained between the turbulent shear production, losses to viscous dissipation and the buoyancy flux B as

u

u w Bz

(33)

By the use of equations (31), (32) and (9), equation (33) yields

2N

K

(34)

where is mixing efficiency factor defined by equation (10). This approach is called the Osborn model (Osborn 1980).

3.3.3. Dissipation Rate of Temperature Variance and Eddy Diffusivity for Heat

For steady, homogenous, and isotropic turbulence, temperature variance equation (3) can be simplified to

Tz

TwT

2 (35)

Kinematic turbulent heat flux can be written as the product of the eddy diffusivity for heat, KT, and the mean temperature gradient

z

TKTw T

From this and using equation (14), the eddy diffusivity for heat is obtained as

2

2

3zT

zTkK TT

25

where the factor 3 is valid for complete isotropy. In the absence of direct measurement of microscale velocity shear, the assumption TKK is often made to determine and

buoyancy flux. This method is called the Osborn-Cox model (Osborn and Cox 1972; Ardhuin et al. 2009).

3.3.4. Vertical Overturns

In stratified flow, turbulent mixing has manifestations on the density profile that can be used to infer the turbulent lengths scale and dissipation rate. Shear instabilities and Kelvin-Helmholtz billows lead to gravitationally unstable overturns. The characteristic of these instabilities can be obtained from the density profile relative to a reference density profile

zm computed by sorting the original density profile z (Fig. 12). From these density

profiles, the density fluctuation, mz z z and the vertical displacements (Thorpe

displacement zd ) can be computed. Thorpe displacement is the minimum distance a fluid

parcel needs to be moved from the observed profile to produce the synthetic stable profile (Thorpe 1977; Piera et al. 2002).

The Thorpe scale can be calculated as the root mean square of the Thorpe vertical displacements as

2TL d .

The Ozmidov scale (Eq. 6) is the scale at which buoyancy effects are felt strongly by the turbulent eddies. It represents the vertical scale at which buoyancy and inertial forces are equal. The Thorpe scale is found to be proportional to the Ozmidov scale ( 8.0TO LL ),

which allows for an estimate of through conventional CTD measurements of sufficient vertical resolution (Dillon 1982).

Figure 12. Schematic of different steps for deriving vertical displacement from reference potential

density, m , and original potential density, (Fernandez 2001).

26

3.4. Measurement Limitations and Platform Motion

In recent years a great deal of attention has been directed toward making high-resolution measurements of turbulence statistics at sea. The problems largely arise from three sources: undersampling, platform motion, flow distortion, and environmental factors unique to the ocean (Edson et al. 1998).

Vertical microstructure profiling has demonstrated the intermittency of ocean mixing in time, depth and intensity. Due to the logistics of vertical profiler deployment, these data sets provide sparse horizontal sampling. In spite of this intermittency, by employing sufficient sampling and averaging, relations can be found between external forcing and dissipation in the mixed layer. For example, the integral of dissipation over the mixed layer was found to account for about 2% of the energy flux from the atmospheric boundary layer (Ardhuin et al. 2009). In addition, the intensity of the dissipation was found to be well correlated with the cube of the wind speed (Greenan and Oakey 1997). In the surface layer, wave orbital velocities can dominate the turbulent fluctuations. The velocity scale of turbulent fluctuations in the near-surface layer of the ocean is about 1 cm s-1, while the typical surface wave orbital velocities are 1m s-1. The energy of the disturbance due to surface wave orbital velocities is four orders of magnitude higher than those of the turbulence signals. The additional complication is that the time scales of the surface waves and the near-surface boundary layer turbulence substantially overlap. The linear statistical filtering that has been widely used to separate linear waves and turbulence from moored or tower-based velocity measurements cannot remove the non-linear components of surface waves, which may result in an overestimation of the turbulence dissipation rate (Soloviev and Lukas 2003a). Another traditional limitation of sinking vertical profilers is the inability to sample the upper 5-8 m of the ocean mixed layer due to the fact that the profiler typically starts about 2 meter below the ocean surface and requires a few meters of free-fall before it stabilizes. Furthermore, the instrument descent starts close to the ship so the measurements near the surface are contaminated by the effect of the ship on the surrounding environment (Greenan and Oakey 1997).

The platform motion contaminates the velocity fluctuations and imposes problems when estimating the turbulence fluxes. This motion contamination must therefore be removed before computing of turbulence fluxes. The contamination arises from three sources: 1- the pitch, roll, and heading variations of the platform during measurement, 2- angular velocities at the microstructure due to rotation of the platform about its local coordinate system axes, and 3- translational velocities of the platform with respect to a fixed frame of reference. In the next section, a brief discussion about rotational frame system with 6 degrees of freedom and multivariate correction procedure with 3 degrees of freedom is given to remove vehicle motion and vibration contamination.

3.4.1. Platform Motion and Vibration Correction Procedures

A variety of approaches has been used to correct for the platform motion contamination on velocity measurements (Edson et al. 1998). One approach is to correct platform motion by carefully measuring this motion relative to a reference frame. Therefore, turbulence measuring instrumentations must be equipped with extra sensors such as accelerometers and gyros. Signals obtained from both types of instrumentations are the processed to produce corrected quantities of interest at the measurement location.

27

Assume that the turbulent momentum fluxes are measured by the eddy correlation method. The platform motion contaminates the velocity fluctuations and this motion contamination must be removed before computing the fluxes (Levine and Lueck 1999). The true velocity vector can be written as

transequipobstrue VVVV 21 TT (36)

where, trueV is the desired velocity vector in the reference coordinate system, obsV is the

measured velocity in the platform frame of reference, equipV is velocity of measurement

instrumentation in the platform frame. transV is the translational velocity vector at the center of

motion of platform to a fixed coordinate system, and 1T and 2T are rotation transformations

of velocity vector and instrument velocity from the platform frame to the reference coordinate system (Miller et al. 2008). When the motion sensors and platform have the same coordinate system, 21 TT . equipV has a linear and an angular component as

r obsequip dttaV Ω (37)

where tatatata zyx ,, is the linear acceleration (accelerometer time series output)

and zyxobs ,,Ω is the angular velocity vector of platform coordinate system that is

given as

obs

obs

obs

obs

Ω

where, the subscript “obs” denotes measurements made in the platform frame of reference, the over-dote denotes time derivative, and obsobs , and obs are roll, pitch and yaw, respectively

(Euler angles, Fig. 13). The yaw is defined positive for left-handed rotation. The negative sign

Figure 13. Location of the platform (body) and fixed coordinate frames (Linklater 2005).

28

in front of the yaw rate is required to compute the angular velocities in the standard right-handed coordinate system. The vector 21 rrr is the position vector of the velocity sensors

with respect to motion package. The vector 1r is the position vector of velocity sensors with

respect to the centre of gravity, and 2r is the correction term when motion measurement

system is not located at the centre of motion.

The rotation of coordinate system xyz into reference frame zyx is stated by

transformation matrix 21 TTT as

k

j

i

k

j

i

T

where ).(T jiji is direction cosine. The rotation matrix has six independent relations among

the nine elements. Some properties of the matrix are that its inverse is its transpose, and its determinant is unity. Meanwhile, successive rotations are not commutative (Thwaites 1995). If A and A are the roll and pitch matrices, thus

)()()()( AAAA

If rotations with respect to roll, pitch and yaw are labeled by 1, 2 and 3 respectively, there are 12 possible sets identified by the axes of rotation such as 123, 321 and etc. (Pio 1966). Therefore, the rotation transformation, T , has several forms. For example, in the 321 class of Euler angles, the rotation matrix T is given as

coscoscossinsinsincossinsincossincos

sincossinsinsinsincossinsinsin

0sincoscoscos

cossin0

sincos0

001

cos0sin

010

sin0cos

100

0cossin

0sincos

AAA

AAA

T

,,,

(38)

In the fixed frame, only yaw is measured, pitch is measured in a yaw frame, and roll is measured in a pitched and yaw frame. From equation (38), Euler angle rates can be derived as

obs

obs

obsobs

obs

obs

obstrue JAAA

0

0

0

0

0

0

)()()(TΩΩ (39)

where

cos

cos

cos

sin0

sincos0

tancosansin1 t

J

For small angles, equation (39) can be approximated as

29

obsobs

obsobs

obsobs

(40)

The above mentioned technique is based on a rotation matrix with 6 degrees of freedom. Another technique is based on removing platform motion effects and vibrations using the standard spectral signal processing techniques (Goodman et al. 2006). In this approach, the acceleration measurements are used to minimize the contamination of the shear and temperature probe measurements by vehicle motions and vibrations of the probe mounts. Let the matrix Tvuobs

,,s represent the time series of the rate of change of horizontal

velocities, and temperature measured by the shear probe, and thermistor. Furthermore, let

21 aa , and 3a are time series of accelerometer output with respect to yx, and z directions,

respectively. True signal can be represented as

jijtrueiobsi ab ,, ss (41)

where, ja is a component of acceleration, ijb is the impulse response, the operator denotes

convolution, truei ,s is uncontaminated signal related to ith component of uncontaminated

matrix trues ( 321 ,,i ). Further, assume in the equation (40), platform motions and vibrations

are statistically independent that is

jia jtruei ,,s , allfor0 (42)

For motions with scales comparable to and longer than the length of vehicle, this assumption breaks down because instrumentation response to such motion. In the Fourier transform domain, equation (40) is written as

jijtrueiobsi AB ,, SS (43)

where the capital cases represent the Fourier transform of their lower case counterparts, and fBB ijij is the frequency transfer function relating the probe signals to the accelerometer

signals. By multiplying equation (43) by its complex conjugate, ensemble average

( *,, SS obsjobsi ), and use of equation (41), it then follows that

*φφ ljklikijij 1 (44)

where, ijφ is the corrected cross-spectrum of truei ,S and *,, SSφ truejtrueiij , the *

,, SSφ obsjobsiij

is the cross-spectrum of the contaminated signal obsi ,S , the ij is the cross-spectrum between

the jA and observed signals, the ij is the cross-spectrum of jA , and

***, lijljiijljilij BBB 11 (45)

Equation (44) is used to correct both the spectra ijφ and the time series. The time

series are corrected by convolving the accelerometer signals with the weighted function ijb

which is obtained from inverse Fourier transform of equation (45).

30

3.4.2. Despiking and Denoising

Spikes resulting from hits of plankton or other solid matter are inherent in every microstructure profile. Therefore, the first and most important step during the data processing, of e.g. shear probe data, is the spike removal. A typical procedure applied with profiler data is an iterative calculation of the signal variance over a certain record lengths and the removal of data that are larger than a specified value times the standard deviation.

Microstructure data are contaminated by all kinds of mentioned noise resources. Thus, cleaning the data is an important step that can be done by several techniques (Rodriguez 2005) such as

classical digital filters: Both low frequency motions of profiler and thermal drift of airfoil probe lead to low frequency noise of microstructure profiler. For cleaning these component of noises, classical filters such as Butterworth filter are used. Furthermore, high frequency electronic noises is removed by digital filters. Mechanical resources of noise can be removed by band path filters such as Lanczos filter.

wavelet denoising: Wavelets have an important application in signal denoising. After wavelet decomposition, the high frequency subbands contain most of the noise information and little signal information. In this level, soft thresholding is applied to the different subbands. The threshold is set to higher values for high frequency subbands and lower values for low frequency subbands.

4. Turbulence Numerical Modeling

There are various strategies for modeling turbulence, each of them resolving a different interval of the spectrum of the flow dynamics (Davies et al. 1995; Burchard et al. 2008a). In this section, a brief overview based upon simple eddy viscosity closure or the use of turbulence energy models is presented.

4.1. Direct Numerical Simulation

The large size of the ocean circulation requires decomposition of ocean flows into various scales. In direct numerical simulation (DNS), the Navier–Stokes equations are directly solved by means of discretization techniques for all scales of motion of a turbulent flow. The DNS requires very high spatial and temporary resolution that it is beyond simulation by the computer available at present time.

4.2. Large Eddy Simulation

In LES, the largest eddies are computed, and the effect of the smaller eddies on the flow is represented by using sub-grid scale (SGS) models. The main underlying concept is the striking feature of a turbulent flow field that, while large eddies migrate across the flow, they carry smaller-scale disturbances with them. Large eddies carry most of the Reynolds stress, and can be different in various types of flows, and thus must be computed. Smaller eddies, on the other hand, contribute much less to the Reynolds stress, and may possess a relatively more universal character. The fundamental idea is to compute the large eddies, which carry out most of the mixing and to model the smaller eddies, which dissipate the energy cascading from the larger scales. In this way, the resolution of the smallest dissipative scales is avoided, and this can potentially reduce the computational cost and/or be used to increase the Reynolds

31

number of the simulations (Ozgokmen et al. 2007). In oceanography, this method is usually applied for investigating near-surface mixed layers, mostly with horizontally homogeneous macroscopic conditions. Wave-driven Langmuir circulation, buoyancy-driven thermal convection and shear-driven Kelvin-Helmholtz billows are three dominant large eddies in the ocean surface mixed layer that can be solved successfully by LES (Li et al. 2005).

4.3. Statistical Turbulence Modeling

Reynolds averaging of the Navier Stokes equations lead to the unknown Reynolds stresses with different orders. For representation of vertical turbulence, these unknown stresses can be parameterized by means of turbulence closure techniques. These closure techniques can be divided into three major model classes (Burchard and Baumert 1995). 1- bulk models which use strict homogeneity of mixed layer; 2- one-equation closure which resolve TKE in the vertical, based on an algebraic or integral formulation for eddy length scale; and 3- two-equation closures which use an additional vertical equation for the length scale or a related quantity. The most popular closures of this group are Mellor-Yamada (Mellor and Yamada 1982) level 2.5 model and k model.

4.4. Empirical Turbulence Modeling

The models of this group are originated from the Reynolds-averaged Navier–Stokes equations similar to statistical turbulence models. Instead of approximation of turbulence fluxes by employing closure techniques, they use entirely empirical knowledge of fluxes. Thus, the accuracy of these techniques is directly related to accuracy of measurements (Burchard et al. 2008a). The non-local K-Profile Parameterization (KPP) is a widely used vertical empirical turbulence model.

5. Summary

Physical ocean properties and variables near the sea surface, particularly dynamical quantities such as currents, turbulence, and turbulent fluxes, are influenced significantly by ocean surface waves. In addition, movements of instruments and measurement platforms, which will be unavoidable on floating platforms which move with the waves, often bias the measurements, even if the instantaneous motions of the platform are corrected for. This complex nature of the near-surface layer of the ocean is covered in different sections of this report. Examples of measurement techniques and sensors are given with references to more detailed reviews. Finally, a short description of different numerical models was presented for simulation of turbulence in the upper ocean boundary layer.

32

6. References

Anis, A. and J. N. Moum, 1995: Surface Wave-Turbulence Interactions:Scaling e(z) Near the Sea Surface. American Meteorology Society, 25, 2025-2045.

Ardhuin, F. and A. D. Jenkins, 2006: On the Interaction of Surface Waves and Upper Ocean Turbulence. Journal of Physical Oceanography, 36, 551-557.

Ardhuin, F., L. Marie, N. Rascal, P. Forget, and A. Ronald, 2009: Observation and Estimation of Lagrangian, Stokes, and Eulerian Currents Induced by Wind and Waves at the Sea Surface. Journal of Physical Oceanography, 39, 2820-2838.

Brainerd, K. E. and M. C. Gregg, 1995: Surface mixed and mixing layer depths. Deep Sea Research Part I: Oceanographic Research Papers, 42, 1521-1543.

Burchard, H. and H. Baumert, 1995: On the Performance of a Mixed-Layer Model Based on the k-e Turbulence Closure. Journal of geophysical research, 100, 8523-8540.

Burchard, H., K. Bolding , T. P. Rippeth , A. Stips , J. H. Simpson , and J. Sundermann, 2002: Microstructure of Turbulence in the Northern North Sea: a Comparative Study of Observations and Model Simulations. Journal of Sea Research, 47, 223-238.

Burchard, H. and Coauthors, 2008a: Observational and Numerical Modeling Methods for Quantifying Coastal Ocean Turbulence and Mixing. Progress In Oceanography, 76, 399-442.

Burchard, H. and Coauthors, 2008b: Observational and numerical modeling methods for quantifying coastal ocean turbulence and mixing. Progress In Oceanography, 76, 399-442, doi: 10.1016/j.pocean.2007.09.005.

Craig, P. D., 1996: Velocity Profiles and Surface Roughness Under Breaking Waves. Journal of Geophysical Research 101, 1265-1277.

Craig, P. D. and M. L. Banner 1994: Modeling Wave-Enhanced Turbulence in the Ocean Surface Layer. Journal of Physical Oceanography, 24, 2546-2559

Davies, A. M., P. J. Luyte, and E. Deleersnijder, 1995: Turbulence Energy Models in Shallow Sea Oceanography. Quantitative Skill Assessment for Coastal Ocean Models, Coastal and Estuarine Studies, 47, 97-123.

Dillon, T. M., 1982: Vertical overturns: A comparison of Thorpe and Ozmidov length scales. Journal of Geophysical Research, 87, 9601-9613.

Dillon, T. M. and D. R. Caldwell, 1980: The Batchelor Spectrum and Dissipation in the Upper Ocean. Journal of geophysical research, 85, 1910-1916.

Doron, P., L. Bertuccioli, and J. Katz, 2001: Turbulence Characteristics and Dissipation Estimates in the Coastal Ocean Bottom Boundary Layer from PIV Data. Journal of Physical Oceanography, 31, 2108-2134.

Edson, J. B., A. A. Hinton, K. E. Prada, J. E. Hare, and C. W. Fairall, 1998: Direct Covariance Flux Estimates from Mobile Platforms at Sea. Journal of Atmospheric and Oceanic Technology Science, 15, 547–562.

Fer, I. and A. Sundfjord, 2007: Observations of upper ocean boundary layer dynamics in the marginal ice zone. Journal of Geophysical Research, 112, doi: 10.1029/2005jc003428.

Fernandez, J. P., 2001: Signal Processing of Microstructure Profiles: Integrating Turbulent Spatial Scales in Aquatic Ecological Modeling, Oceanography, Universitat de Girona.

Gargett, A. E., 1997: “Theories” and Techniques for Observing Turbulence in the Ocean Euphotic Zone. Turbulence in the Ocean Euphotic Zone, Scientia Marina, 61, 25-45.

Garrett, C., 1996: Processes in the Surface Mixed Layer of the Ocean. Dynamics of Atmospheres and Oceans, 23, 19-34.

Garwood, R. W. J., 1976: A General Model of the Ocean Mixed Layer:Using a Two-Component Turbulent Kinetic Energy Budget with Mean Turbulent Field Closure.

33

Gemmrich, J., 2010: Strong Turbulence in the Wave Crest Region. American Meteorology Society, 40, 583–595.

Gemmrich, J. R. and D. M. Farmer, 2004: Near-Surface Turbulence in the Presence of Breaking Waves. Journal of Physical Oceanography, 34, 1067–1086.

Gill, A. E., 1982: Atmosphere-Ocean Dynamics. Vol. 30, Academic Press. Goodman, L., E. R. Levine, and R. G. Lueck, 2006: On Measuring the Terms of the Turbulent

Kinetic Energy Budget from an AUV. Journal of Atmospheric and Oceanic Technology, 23, 977-990.

Grant, A. L. and S. E. Belcher, 2009: Characteristics of Langmuir Turbulence in the Ocean Mixed Layer. Journal of Physical Oceanography, 39, 1871–1887.

Greenan, B. J. W. and N. S. Oakey, 1997: Measuring Ocean Turbulence with a Tethered Free-Fall Glider, 241-246 pp.

Gregg, M. C., 1999: Uncertainties and Limitations in Measuring e and xT. Journal of Atmospheric and Oceanic Technology, 16, 1483-1490.

Gregg, M. C., C. S. Cox, and P. W. Hacker, 1973: Vertical Microstructure Measurments in the Central North Pacific. Journal of Physical Oceanography, 3, 458-469.

Kanari, S.-i., 1991: Micro-Scale Profiler (MSP) for Measurment of Small-Scall Turbulence in the Ocean. Journal of the Oceanographical Society of Japan, 47, 17-25.

Levine, E. R. and R. G. Lueck, 1999: Turbulence Measurement from an Autonomous Underwater Vehicle. Journal of Atmospheric and Oceanic Technology, 16, 1533-1544.

Li, J. C., 1998: An overview of air-sea interface process studies. Indian Academy of Science, 23, 631-635.

Li, M., C. Garrett, and E. Skyllingstad, 2005: A regime diagram for classifying turbulent large eddies in the upper ocean. Deep Sea Research Part I: Oceanographic Research Papers, 52, 259-278.

Linklater, A., 2005: Design and Simulation of a Towed Underwater Vehicle, Aerospace Engineering, 170.

Lombardo, C. P. and M. C. Gregg, 1989: Similarity Scaling of Viscous and Thermal Dissipation in a Convecting Surface Boundary Layer. Geophysical Research 94, 6273-6284.

Lorke, A. and A. Wuest, 2005: Application of Coherent ADCP for Turbulence Measurements in the Bottom Boundary Layer. Journal of Atmospheric and Oceanic Technology, 22, 1822-1828.

Lu, Y. and R. Lueck, 1999: Using a Broadband ADCP in a Tidal Channel. Part II: Turbulence. Journal of Atmospheric and Oceanic Technology, 16, 1568-1579.

Lueck, R., 2005a: Converting Shear Probe and Thermistors Signals to Physical Units. Lueck, R., 2005b: Converting shear probe and thermistors signals to physical units. Lueck, R. and G. D. Huang, 1998: Dissipation Measurement with a Moored Instrument in a

Swift Tidal Channel. Journal of Atmospheric and Oceanic Technology, 16, 1500-1505.

Lueck, R., F. Wolk, and H. Yamazaki, 2002: Oceanic Velocity Microstructure Measurements in the 20th Century. Journal of Oceanography, 58, 153-174.

Lueck, R., G. D. Huang, D. Newman, and B. J., 1997: Turbulence Measurement with a Moored Instrument. Journal of Atmospheric and Oceanic Technology, 14, 143-161.

McWilliams, J. C., P. P. Sullivan, and C.-H. Moeng, 1997: Langmuir Turbulence in the Ocean. Journal of Fluid Mechanics, 334, 1-30.

Mellor, G. L. and T. Yamada, 1982: Development of a Turbulence Closure Model for Geophysical Fluid Problems. Reviews of Geophysics and Space Physics, 20, 851–875.

34

Miller, S. D., T. S. Hristov, J. B. Edson, and C. A. Friehe, 2008: Platform Motion Effects on Measurements of Turbulence and Air-Sea Exchange over the Open Ocean. American Meteorological Society, 25, 1683-1694.

Moum, A., 1996: Efficiency of Mixing in the Main Thermocline. Journal of Geophysical Research, 101, 12057-12069.

Moum, J. N., M. C. Gregg, R. C. Lien, and M. E. Carr, 1995: Comparison of Turbulence Kinetic Energy Dissipation Rate Estimates from Two Ocean Microstructure Profilers. Journal of Atmospheric and Oceanic Technology Science, 12, 346–366.

Nash , J. D. and J. N. Moum, 1999: Estimating Salinity Variance Dissipation Rate from Conductivity Microstructure Measurements. Journal of Atmospheric and Oceanic Technology 16, 263–274.

Nihoul, J. C. J., 1980: Marine Turbulence: Proceeding of the 11th International Liege Colloquium on Ocean Hydrodynamics. Elsivier Scientific Publishing Company.

Nikora, V. I. and D. G. Goring, 1998: ADV Measurements of Turbulence: Can We Improve Their Interpretation? Journal of Hydrolic Engineering, 124, 630-634.

Ninnis, R., 1984: The effects of Spatial Averaging on Airfoil Probe Measurements of Oceanic Velocity Microstructure, The Faculty of Graduate Studies, Oceanography, The University of British Columbia.

Noh , Y. and H. S. Min, 2004: Large Eddy Simulation of the Ocean Mixed Layer: The Effects of Wave Breaking and Langmuir Circulation. Journal of Physical Oceanography, 34, 720-735.

NortekUSA: Vector 3D Acoustic Velocitimeter Oakey, N. S., 1982: Determination of the Rate of Dissipation of Turbulent Energy from

Simultaneous Temperature and Velocity Shear Microstructure Measurements. Journal of Physical Oceanography, 12, 256-271.

Osborn, T. and C. S. Cox, 1972: Oceanic Fine Structure. Geophysics Fluid Dynamic, 3, 321-345.

Osborn, T. R., 1974: Vertical Profiling of Velocity Microstructure. Journal of Physical Oceanography, 4, 109-115.

Osborn, T. R., 1980: Estimates of the Local Rate of Vertical Diffusion from Dissipation Measurements. Journal of Physical Oceanography, 10, 83-89.

Osborn, T. R. and L. E. Bilodeau, 1979: Temperature Microstructure in the Equatorial Atlantic. Journal of Physical Oceanography, 10, 66-82.

Ozgokmen, T. M., T. Iliescu, P. F. Fischer, A. Srinivasan, and J. Duan, 2007: Large Eddy Simulation of Stratified Mixing in Two-Dimensional Dam-Break Problem in a Rectangular Enclosed Domain. Ocean Modelling, 16, 106-140.

Payne, R. E., 1972: Albedo of the Sea Surface. Journal of Atmospheric Science, 29, 959-970. Peters, H., C. M. Lee, M. Orlic, and C. E. Dorman, 2007: Turbulence in the Wintertime

Northern Adriatic Sea under Strong Atmospheric Forcing. Journal of geophysical research, 112, 1-21.

Piera, J., E. Roget, and J. Catalan, 2002: Turbulent Patch Identification in Microstructure Profiles: A Method Based on Wavelet Denoising and Thorpe Displacement Analysis. Journal of Atmospheric and Oceanic Technology, 19, 1390-1402

Piirto, M., P. Saarenrinne, H. Eloranta, and R. Karvinen, 2003: MeasuringTurbulence Energy with PIV in a Backward-Facing Step Flow. Experiments in Fluids, 35, 219-236.

Pio, R. L., 1966: Euler Angle Transformations. IEEE Transactions on Automatic Control, 11, 707-715.

Polton, J. A., J. A. Smith, J. A. MacKinnon, and A. E. Tejada-Martınez, 2008: Rapid Generation of High-Frequency Internal Waves Beneath a Wind and Wave Forced Oceanic Surface Mixed-Layer. Geophysical Research Letters, 35, 1-5.

35

Pond, S. and G. L. Pickard, 1983: Introductory Dynamical Oceanography. Elsevier Science and Technology

Prandke, H. and A. Stips, 1998: Test Measurements with an Operational Microstructure-Turbulence Profiler: Detection Limit of Dissipation Rates Acquatic Sciences, 60, 191-209.

Qun, S., G. Changlong, and S. Jinbao, 2007: Wave Breaking on Turbulent Energy Budget in the Ocean Surface Mixed Layer. Chinese Journal of Oceanology and Limnology, 26, 9-13.

Rehmann, C. R. and J. H. Hwang, 2005: Small-Scale Structure of Strongly Stratified Turbulence. Journal of Physical Oceanography, 35, 151–164.

Rodriguez, J. M. F., 2005: Dynamics and Mixing in the Upper Ocean Layer, Oceanography Department, University de Girona.

Schudlich, R. and S. Emerson, 1996: Gas Supersaturation in the Surface Ocean: The Roles of Heat Flux, Gas Exchange, and Bubbles. Deep-Sea Research, 43, 569-589.

Smith, S. D., C. W. Fairall, G. L. Geernaert, and L. Hasse, 1995: Air-Sea Fluxes: 25 Years of Progress. Boundary-Layer Meteorology, 78, 247-290.

Soloviev, A. and R. Lukas, 2003a: Observation of Wave-Enhanced Turbulence in the Near-Surface Layer of the Ocean during TOGA COARE. Deep Sea Research Part I: Oceanographic Research Papers, 50, 371-395, doi: 10.1016/s0967-0637(03)00004-9.

Soloviev, A. and R. Lukas, 2003b: Observation of wave-enhanced turbulence in the near-surface layer of the ocean during TOGA COARE. Deep Sea Research Part I: Oceanographic Research Papers, 50, 371-395, doi: 10.1016/s0967-0637(03)00004-9.

Soloviev, A. and R. Lukas, 2006: The Near-Surface Layer of the Ocean: Structure, Dynamics and Applications. Vol. 31, Springer.

Soloviev, A., R. Lukas, P. Hacker, H. Schoeberlein, M. Baker, and A. Arjannikov, 1999: A Near-Surface Microstructure Sensor System Used during TOGA COARE. Part II: Turbulence Measurements. Journal of Atmospheric and Oceanic Technology Science, 16, 1598–1618.

Souza, A. J., 2007: The Use of ADCPS to Measure Turbulence and SPM in Shelf Seas. 2nd International Conference & Exhibition on "Underwater Acoustic Measurements: Technologies & Results", 1-8.

Stacey, M. W., 1999: Simulation of the Wind-Forced Near-Surface Circulation in Knight Inlet: A Parameterization of the Roughness Length. Journal of Physical Oceanography, 29, 1363-1367.

Stull, R. B., 1988: An Introduction to Boundary Layer Meteorology. Kluwer Academic Publishers.

Sverdrup, H. U., 1953: On Conditions for the Vernal Blooming of Phytoplankton. J. Cons. Perm. Int. Explor. Mer, 18, 287-295.

Taylor, P. A., 1972: Wind Profile Development above Locally Adjusted Sea Surface. Boundary-Layer Meteorology, 2, 381-389.

Teixeira, M. A. C. and S. E. Belcher, 2010: On the Structure of Langmuir Turbulence. Ocean Modelling, 31, 105-119.

Tennekes, H. and J. L. Lumley, 1972: A first course in turbulence. MIT Press, 300 pp. Thorpe, S. A., 1977: Turbulence and Mixing in a Scottish Loch. Philosophical Transactions

of the Royal Society of London, 286, 125-181. Thorpe, S. A., 2004: Recent Development in the Study of Ocean Turbulence. Annual Review

of Earth and Planetary Science, 32, 91–109. Thorpe, S. A., 2007: An Introduction to Ocean Turbulence. Cambrige University Press.

36

Thwaites, F. T., 1995: Development of Acoustic Vorticity Meter to Measure Shear in Ocean-Boundary Layers, Applied Ocean Science and Engineering, Massachussetts Institute of Technology.

Toba, Y. and H. Kunish, 1970: Breaking of Wind Waves and the Sea Surface Wind Stress. Oceanographical Society of Japan, 26, 71-80.

Veron, F., W. K. Melville, and L. Lenain, 2009: Measurements of Ocean Surface Turbulence and Wave–Turbulence Interactions. Journal of Physical Oceanography, 39, 2310-2323.

Ward, B., R. Wanninkhof, P. J. Minnett, and M. Head, 2004: SkinDeEP: A Profiling Instrument for Upper-Decameter Sea Surface Measurements. Journal of Atmospheric and Oceanic Technology, 21, 207-222.

Weller, R. A., F. Bradley, and R. Lukas, 2004: The Interface or Air–Sea Flux Component of the TOGA Coupled Ocean–Atmosphere Response Experiment and Its Impact on Subsequent Air–Sea Interaction Studies. Journal of Atmospheric and Oceanic Technology, 21, 223-257.

WOM: Guide to Wave Analysis and Forecasting. [Available online from http://www.wmo.int/pages/prog/amp/mmop/documents/WMO%20No%20702/.]

Wu, J., 1975: Sea-Surface Drift Currents. Offshore Technology Conference, North Centeral Expressway.

Wu, J., 1983: Viscous Sublayer below a Wind-Disturbed Water Surface. Physical Oceanography, 14, 138-144.

Yamazaki, H. and T. Osborn, 1993: Direct estimation of heat-flux in a seasonal thermocline. Journal of Physical Oceanography, 23, 503-516.

Zappa, C. J., W. E. Asher, and A. T. Jessup, 2001: Microscale Wave Breaking and Air-Water Gas Transfer. Journal of geophysical research, 106, 9385-9391.

Zhang, H. and E.-S. Chan, 2003: Modeling of the Turbulence in the Water Column under Breaking Wind Waves. Journal of Oceanography, 59, 331-341.