INWAVE: THE INFRAGRAVITY WAVE DRIVER OF THE COAWST

SYSTEM

COAWST WORKSHOPWoods Hole, 23rd -27th July

Maitane Olabarrieta & John C. Warner

OUTLINE

1. INTRODUCTION AND MOTIVATION2. IG GENERATION AND DISSIPATION MECHANISMS3. IG MODELLING TECHNIQUES4. INWAVE

a. EQUATIONS AND NUMERICAL SCHEMEb. HOW IS IT LINKED TO THE VORTEX FORCE?c. APPLICATIONSd. FUTURE PLANS

OCEAN WAVES CLASIFICATION

Storms, tsunamis

WindSun, Moon

Frequency (Cycles per second)

24 h 12 h 5 min 30 s 1 s 0.1 s

Long Waves Short Waves

Coriolis

Gravity

Surface Tension

Restoring Force

Forcing

Tides Long Waves

Kind of Wave

Infra-gravity Waves

Gravity Waves Ultra-gravity Waves Capillarity Waves

Period

Ener

gy

IG WAVE CHARACTERISTICS

- They are generated by incoming wave groups.

- Account for 20-60% of the offshore energy.

- These long waves reflect from the shore to form cross-shore standing pattern (= minimal dissipation at

shoreline).

- They can propagate alongshore (edge waves),

sometimes forming standing pattern.

- Can significantly contribute to the surfzone circulation.

FIELD MEASUREMENTS OF IG WAVES

0

1

2

3

Hm

0 (m

)

0

2

4

6

8

Hm

0 (m

)

67 68 69 70 71 72 73 74 75 76 77 78 790

2

4

6

(m

)

Yearday

Ruessink, 2010sea-swell

infragravity

0 1 2 3 4 5 6 7 80

0.5

1

1.5

2

Hm0

offshore (m)

Hm

0,in

f bea

ch (

m) ≈ 15%

Herbers et al., 1995

SOME OF THE EFFECTS OF IG WAVES

RUNUP AND BEACH-DUNE EROSION

BEACH MORPHOLOGY ????

HARBOR RESONANCE

MOTIVATIONUnder storm conditions, in dissipative beaches, the

run up and swash zone dynamics are controlled mainly by the Infragravity Wave motion

(Raubenheimer and Guza, 1996)

We should include these processes if we want to solve the coastal

erosion, overwash and breaching

Hatteras Village, North Carolina

Frisco, North Carolina

IG GENERATION AND DISSIPATION MECHANISM

IG GENERATION MECHANISMS IN THE SURF ZONE

BOUND WAVE RELEASE (Munk, 1949; Tucker, 1950)

IG generation due to the breaking point movement (Symonds et al., 1984)

Pressure gradient

Radiation stress gradient

BOUND WAVE RELEASE (Munk, 1949; Tucker, 1950)

IG generation due to the breaking point movement (Symonds et al., 1982)

The dominance of each mechanism depends on the slope regime (Battjes, 2004)

With oblique wave incidence, free long waves can get trapped in the coast due to refraction as edge waves or be reflected offshore as leaky waves

Herbers et al., 1995

1 1 1, 1, 2 2 2, 2,sin( ) sin( )x y x ya t k dx k y a t k dx k y Incident waves

Su

rf z

one

Su

rf z

one

shoaling

Bound infragravity wave

0 0

,2 ,1 2 2 1 1( ) cos cosx x

x x x

x x

k x k k dx k k dx

arctan yb

x

k

k

5

2,ˆ ~l b h

1

4,ˆ ~l f h

released infragravity wave

(de)-shoaling

,

arctan yf

f x

k

k

2

2,f x yk k

gh

Trapping at:

0

,

arctan 90yf

f x

k

k

2

2turningy

hg k

Leaky if:

turning shelfh h

IG DISSIPATION MECHANISM

- Bottom friction.- IG wave breaking.- Energy transfer thru non-linear interactions to lower periods.

It is not clear which is the main dissipation mechanism and it might depend on the beach slope and on the frequency of the IG components.

IG MODELING TECHNIQUES

WAVE RESOLVING TECHNIQUES:BOUSSINESQ , PARTICLE TRACKING OR RANS MODELS

WAVE AVERAGED OR PHASE AVERAGED TECHNIQUES:WAVE ACTION BALANCE EQUATION + NLSW

Reniers, 2012 (long wave and runup Workshop)

FREE SURFACE ELEVATION AND WAVE ENERGY ENVELOPE TIME VARIATION

Time varyingWave forcings

Infragravity wave generation

, , where , ,

, ,yxc A E x y tc A c AA D

A x y tt x y x y t

Boundary condition for the wave action

conservation equation

, , , , , , , , , , , , , , ,xx xy yx yyS x y z t S x y z t S x y z t S x y z t

Vortex Force terms varying in wave group scale

SWAN domain: Wave spectral time scale

InWave domain: Wave group time scale

DIRECTIONAL WAVE SPECTRUM

Boundary region

- Random phases- Double summation technique- Hilbert transform

SWAN DOMAIN

INWAVE DOMAIN

BOUNDARY

How do we model IG?

Offshore incident wave conditions (frequency-

directional spectra)

Bound in-coming infragravity waves (e.g.

Hasselmann, 1963)

Infragravity wave generation thru VF and propagation of the bounded IG wave

Wave group energy (Hilbert transform)

Leaky, bound and trapped infragravity waves

SWAN + INWAVE + ROMS COUPLING

Short wave (group) transformation

SWAN

INWAVE

ROMS

, ,( )

1

ˆ( , , ) *j x j y j j

Ni t k x k y

jj

x y t e

Random phase model

JONSWAP, D() ~ coss() 21( , , ) | ( , , ) |

2w lowE x y t g A x y t

Hilbert Transform and low-pass filter

Wave group energy (Hilbert transform)

Short wave (group) transformation: INWAVE equations

Wave action balance equation in curvilinear coordinate system

, , ,g g g wC A C A C AA

m nt

D

, cosg gC C U

, sing gC C V

, sin cos cos sin cos sin sin cossinh 2g

h h U U V VC m n m n m n

kh

2

0.5 1sinh 2g

khC C

kh

tanhgk kh

w k u

Wave dispersion relation + Doppler relation

tanh

sinh 2

gk khC

kh

Eikonal equation

ak wm

t

ak wn

t

2 2kk k

b bD D Q Total energy dissipationD

Energy dissipation in a breaking wavebD

Fraction of breaking wavesbQ

2b rep wD f E

Coefficient O(1)

Representative frequencyrepf

Wave energy integrated over directionswE min 1,1 expn

b

HQ

h

Breaking parameter

Coefficientn

Roelvink (1993)

H= γh Breaking parameter

water depthh

wave heightH

Battjes and Janssen (1978)

Short wave (group) transformation: INWAVE equations

Wave breaking

INWAVE MODEL: Incoming bound wave definition at ROMS boundaries

Van Dongeren et al. (2003) -> Hasselman (1963) & Herbers et al. (1994)

1. The energy of the secondary forced elevation E3 (Df) for one particular pair of interacting primary waves can be computed following Herbers et al. (1994)

Amplitude of the bound wave for each interacting pair

2. Bound wave out of phase with the envelope formed by each interacting pair

4. The time series of the surface elevation of the bound wave is

3. The direction of the bound wave is give by

5. This process is repeated for every pair of short-wave components. The summation of all components gives the total bound wave.

1D CASE APPLICATION:DUCK 85 TEST CASE (LIST 1991)

H5H4H3H2R1

H1R2 R3R4VS

Sea surface measurements in station H5

INWAVE MODEL: INPUTS

H5H4H3H2R1

H1R2 R3R4VS

INWAVE MODEL: RESULTS

2D CASE APPLICATION: OBLIQUE INCIDENT BICHROMATIC WAVES IN A UNIFORM BEACH

BATHYMETRY (m)

(m) (m)slope=0.0125

REAL APPLICATION: HURRICANE ISABEL

Time varying wave spectra

INWAVE MODEL: PRELIMINARY RESULTS

SEA SURFACE ELEVATION DUE TO IG WAVES(m)

FUTURE PLANS

- Validate Inwave with more test cases.- In the current configuration we need to define the wave enevelope with a netcdf file, but the idea is that the model will directly recontruct this signal from the paren t swan grid.- Inwave is not capable of including wave spectral variations along its boundaries and future efforts will be directed to include these capabilities.- Within a few months, before the end of the year Inwave will be distributed with COAWST and available for the public use.