The Boundary Layer and Related Phenomena - …twister.caps.ou.edu/MM2015/docs/chapter3/chapter3_presentation1.pdf · The Boundary Layer and Related Phenomena Jeremy A. Gibbs University

The Boundary Layer and Related Phenomena

Jeremy A. Gibbs

University of Oklahoma

[email protected]

February 10, 2015

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Overview

The Boundary Layer and Related PhenomenaIntroductionStructure and EvolutionThe Nature of Turbulent Fluxes

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What is the boundary layer?

Stull (1988):

Planetary boundary layer is the part of troposphere thatis directly influenced by the presence of the earth surfaceand responds to surface forcings with a timescale ofabout an hour or less.

Sorbjan (2012):

The lowest portion of the atmosphere, which extensivelyexchanges mass (water), momentum, and heat with theEarth’s surface.

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The boundary layer, also known as the atmospheric boundary layer(ABL) or planetary boundary layer (PBL), is a disturbance of thelower atmosphere induced by the underlying surface of the Earth.

In other words, the BL is an interfacial layer between thetroposphere and the ground.

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The forcings that originate at the surface include:

I frictional drag

I evaporation and transpiration

I heat transfer

I pollutant emissions

I terrain-induced flow modifications

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In the lowest few millimeters of the BL, conduction between the airand the ground is important.

This small layer is also known as the viscous sublayer.

Above this layer, the effects of molecular diffusion are ignored sincethey are negligible compared with the mixing effects of turbulenteddies.

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Molecular viscosity does not directly influence BL motions above afew centimeters.

However, the viscous sublayer is crucial in the formation of BLeddies.

In other words, the BL would not exist without an underlyingsurface.

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Specifically, as a result of molecular viscosity the flow vanishes atthe surface (no-slip boundary condition).

Consequently, large vertical wind shear is generated near theground (even with light winds).

This shear leads to the formation of small turbulent eddies that actto transfer momentum, heat, and moisture to the lower BL.

These turbulent motions have spatial and temporal variations atscales much smaller than those resolved by a meteorologicalobserving network.

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BL flow is dominated by these turbulent eddies, as well as by thosethat result from surface heating.

These eddies are most often ignored in the free atmosphere.

The transfer of momentum, heat, and moisture by these turbulenteddies must be accounted for in the dynamical equations in orderto accurately describe the BL evolution of θ and q and therelationship between the ∇p and u.

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In this part of the course, we:

I focus on a qualitative overview of the BL

I describe the inclusion of turbulence in the dynamical equations

I discuss several related phenomena

I consider applications of boundary layer theory.

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The importance of the boundary layer

Overheard across the years in SoM

I “My eyes are bleeding from all of these equations!”

I “This s#&! is a waste of time!”

I “Boundary layer? More like Boring Layer - amirite?!?”

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Found in the SoM bathroom stall

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The boundary layer is often perceived as a boring, esoteric topic tometeorology students.

This is likely due to the fact that much of the theory historicallystems from fluid mechanics and other engineering-focused areas ofresearch.

In other words, engineers have no souls :)

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Admittedly, boundary layer theory is laden with long equations andcomplex parameterizations.

It is understandable why so many students’ eyes glaze over whenthey are introduced to the boundary layer.

We will soon cover why these equations and parameterizations arenecessary to properly describe the evolution of mass, momentum,and moisture fields in the lowest portion of the atmosphere.

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First, let us put aside rigorous math exercises and considerreal-world examples that illustrate the importance of the boundarylayer.

Why should you care about the boundary layer? Let me count theways.

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We live there!!!!

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Some more reasons

I Forecasts of dew, frost, minimum and maximum temperatures(to name a few) are really boundary layer forecasts.

I Pollution is trapped and dispersed within the boundary layer.

I Fog occurs in the boundary layer

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Some more reasons

I The primary energy source for the atmosphere is solarradiation, which is generally absorbed by the surface.Boundary layer processes act to transmit this energy to therest of the atmosphere.

I ∼ 90% of the net radiation absorbed by oceans causesevaporation. The latent heat stored in water vapor accountsfor ∼ 80% of the fuel that drives atmospheric motions!

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Some more reasons

I Crops are grown in the boundary layer, where pollen isdistributed within.

I Cloud nuclei are sent into the air from the surface byboundary layer processes.

I Almost all water vapor that reaches the free atmosphere istransported through the boundary layer by turbulence andadvection.

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Some more reasons

I Thunderstorm/hurricane evolution is tied to the inflow ofmoist boundary layer air.

I Downward turbulent transport of momentum through theboundary layer to the surface is the single most importantatmospheric momentum sink.

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Some more reasons

I Turbulence and gustiness affect the design of structures.

I Wind turbines extract energy from boundary layer flows.

I Wind stress on the ocean surface is the primary energy sourcefor ocean currents.

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The list is not exhaustive, but it shows several tangible examples inwhich the boundary layer directly impacts our lives, in addition toindirect effects through its influence on weather.

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Comparison of boundary layer and free atmospherecharacteristics

Another way to illustrate the importance of the boundary layer isto compare its characteristics with the overlying free atmosphere.

We will now describe these difference that highlight the role of theboundary layer and its importance to the entire atmosphere.

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Table: adapted from Stull (1988)

Property Boundary Layer Free Atmosphere

Turbulence Almost continuously tur-bulent over its wholedepth.

Turbulence in convectiveclouds and sporadic clearair turbulence in thinlayers of large horizontalextent.

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Friction Strong drag against theearth’s surface. Large en-ergy dissipation.

Small viscous dissipation.

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Dispersion Rapid turbulent mixing inthe vertical and horizon-tal

Small molecular diffusion.Often rapid horizontaltransport by the meanwind.

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Winds Near logarithmic windspeed profile in thesurface layer. Sub-geostrophic, cross-isobaricflow is common.

Winds nearly geostrophic.

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Vertical transport Turbulence domi-nates.

Mean wind andcumulus-scale dom-inate.

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Thickness Varies between ∼ 100 mto 3 km in time andspace. Diurnal oscilla-tions over land.

Less variable at 8-18 km.Slow time variations.

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Structure and evolution

The following figure illustrates the typical diurnal cycle of the BL.

This pronounced cycle is one of the defining features of the BLowing to its fast response time to surface forcings.

The diurnal evolution of the BL, as well as the associatedstructural changes, will be discussed in detail

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BL depth: dependencies

I morning atmospheric profile of temperatureI intensity of turbulent mixing, which itself depends on

I the amount of insolation and sensible heat flux(buoyancy-driven turbulence)

I mean vertical wind shear (mechanically-driven turbulence)

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BL depth: variationsI stable, nighttime conditions

I as shallow as a few tens of metersI intermittent turbulence can exist

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BL depth: variationsI unstable, daytime conditions

I as deep as several kilometersI layer is typically superadiabatic and dominated by convective

motions

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General BL Evolution

I After sunrise, the boundary layer is heated by the underlyingsurface through sensible heat flux.

I This heating drives the air in contact with the ground towardthe dry adiabatic lapse rate (∂θ/∂z = 0).

I Within a shallow layer in contact with the ground,superadiabatic conditions induce vertical mixing andturbulence.

I Mixing promotes homogeneity, which leads to moisture andwind speed profiles that are approximately constant withheight.

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General BL Evolution, continued

I Thermals rise and penetrate the stably-stratified atmosphere.

I This penetrative convection induces mixing through an evendeeper layer, leading to a deepening of the boundary layer.

I These overshooting thermals lead to cooling at the top of themixed layer within the penetrated stable region, which in turncreates a capping inversion.

I Continued surface heating generates more thermals, deepermixing, and a growing boundary layer.

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General BL Evolution

I The maximum boundary layer depth is attained near sunset.

I After sunset the surface sensible heat flux reverses sign.

I As a result of the negative surface sensible heat flux, coolingstarts and a stable region forms near the surface.

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Daytime BL Structure

I The layer of the daytimeboundary layer extendingfrom the surface to theentrainment zone (EZ;which tops the boundarylayer) is often referred to asthe mixed layer (ML) orconvective boundary layer(CBL).

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I Profiles of potentialtemperature (θ) areapproximately constant withheight, except within thelowest 10% of the CBL.This layer is called thesurface layer (SL).

I Transfer of momentum,mass, and moisture withinthis layer is able to overcomemixing effects (see Fig. ??).

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I Consequently, θ maydecrease by 1-2 K from theground to the top of the SL(i.e., super-adiabaticconditions). In addition,moisture (q) may alsodecrease with height withinthis layer, while wind speed(u) logarithmicallyapproaches zero from thetop of the layer to theground.

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I Turbulent fluxes generallyhave their largest magnitudeat the surface and decreasein magnitude with height,where they becomenegligible at the base of thefree atmosphere.

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I An exception to this is themoisture flux (w ′q′), whichcan have a maximummagnitude at a levelsignificantly above thesurface (it is still negligibleat the base of the freeatmosphere).

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I Since (u) generally increaseswith height, the momentumflux (w ′u′) tends to benegative.

I Thus, rising thermals areassociated with negativevelocity perturbations asthey carry lower momentumupward. Conversely, thedownward motions areassociated with positivevelocity perturbations asthey bring highermomentum downward.

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I w ′u′ tends to deceaselinearly with height from thesurface to the top of theCBL. The magnitudedecreases rapidly from thebase of the CBL to a valuenear zero at the top of theEZ.

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I Since w ′u′ is negative at thesurface and the magnitudedecreases with height,∂(w ′u′)/∂z > 0. Thisimplies a net drag on themean winds within theboundary layer for u > 0.

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I The kinematic heat flux(w ′θ′) is generally positivein the CBL as a result ofrising air being positivelybuoyant.

I (w ′θ′) generally decreaseslinearly with height from thesurface to the top of theCBL.

I Within the EZ, w ′θ′ isgenerally negative and∼ 10-20% of its surfacemagnitude.

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I Under these conditions,∂(w ′θ′)/∂z < 0 in the CBL,which implies meanwarming.

I Conversely, ∂(w ′θ′)/∂z > 0in the EZ, which points tomean cooling. Penetratingthermals are responsible forcooling this layer.

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I w ′q′ also changes linearlywith height, though thechange can either benegative or positivedepending on whether thereis drying or moistening ofthe CBL.

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I The sign of ∂(w ′q′)/∂zlargely depends on thesurface moisturecharacteristics.

I ∂(w ′q′)/∂z < 0 in the EZ,which implies net moisteningin the layer.

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Nighttime BL Structure

I A shallow inversion layerforms near the surface atnight due to heat loss by theground.

I This layer is called thestable boundary layer (SBL)or nocturnal boundary layer(NBL).

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I The SBL becomes decoupledfrom the ML because theinversion inhibits mixing.

I The decoupled “leftover”ML from the daytime CBL iscalled the residual layer(RL).

I The RL is characterized bynearly constant θ and q.

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I The daytime’s EZ is referredto as the capping inversionat night since there is notmuch exchange between thefree atmosphere and theresidual layer.

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I Turbulent fluxes aregenerally negative in theSBL.

I The maximum magnitude ofeach turbulent flux islocated at the surface, whileeach flux becomes negligibleat the top of the layer.

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I Put another way,∂(w ′u′)/∂z , ∂(w ′θ′)/∂z ,

and ∂(w ′q′)/∂z are all > 0.

I Thus, the SBL ischaracterized at night bycooling and drying, whileacting as an effective dragon the mean wind.

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I The shallow inversion layergrows in steps, which areoften interrupted byintermittent turbulentevents. These events are theresult of small,mechanically-generatededdies.

I These intermittentturbulence events act todeepen the SBL and reduceits stability.

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I Relative humidity increasesin the SBL, forming dew,which may act to reduce qthrough condensation.

I Radiational cooling isstrongest on nights withweak winds and infrequentturbulence events. On thesenights, the inversion israther strong and shallow,leading to especially lownear-surface air temperature.

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I The depth of the RLcompared to the depth ofthe SBL is largely a functionof mean wind shear.

I The SBL can be as shallowas ∼ 10 m on clear nightswith minimal winds.

I Conversely, the SBL depthmay be of the same order asthe daytime CBL on cloudynights with strong winds.

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I q at the surface can eitherincrease or decrease aftersunset depending on thedegree of dew formationversus the degree to whichmoisture was reduced in thedaytime SL due to mixing.

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I Winds at the top of the SBLand within the RL accelerateat night as surface drag iseffectively eliminated.

I As a result, a nocturnallow-level wind maximumforms. This is often calledthe low-level jet. We willdiscuss the dynamics of thelow-level jet in an upcomingsection.

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I At the surface, negativelybuoyant air tends to sinktoward lower elevations.This results in so-calleddrainage winds, which arecold-air-runoff winds thatare produced when air incontact with terrain surfacesis cooled and flowsdownslope (katabatic)and/or downvalley.

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I Drainage winds also refer togravity winds that drain coldair into frost hollows, rivervalleys, and otherlower-lying terrain.

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The nature of turbulent fluxes

Before considering specific boundary layer phenomena, we need todevelop a set of equations that properly account for turbulentmotions.

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Reynolds averaging

Consider the time series plot of the wind speed shown here. Thetrace contains many high-frequency (fast) fluctuations. Suchfluctuations are due to small turbulent eddies, which do notreliably represent the mean flow.

Figure: Trace of wind speed observed in early afternoon. [From Stull1988]

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Reynolds averaging

To obtain a wind speed measurement representative of thelarge-scale flow, one must obtain take an average over a timeperiod long enough to smooth over the fluctuations but still shortenough for keep the trend.

Such averaging was first proposed by Reynolds, and is thereforenamed after him.

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The End∗

∗ After a math break!

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Documents

The Boundary Layer and Related Phenomena - …twister.caps.ou.edu/MM2015/docs/chapter3/chapter3_presentation1.pdf · The Boundary Layer and Related Phenomena Jeremy A. Gibbs University