Atmospheric transport

Atmospheric TransportAtmospheric TransportRoy Wangintan

Teknik LingkunganInstitut Teknologi Bandung

Air motions play a key role Air motions play a key role Distributions of chemical species in the atmosphere

Three principal forces : Gravity, pressure-gradient, and Coriolis

The vertical distribution of mass : balance between gravity and the pressure-gradient force

In the horizontal direction: gravity does not operate,


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In the horizontal direction: gravity does not operate,

The equilibrium of forces usually involves a balance between the pressure-gradient force and the Coriolis force and the resulting steady flow is called the geostrophic flow

Below 1-km altitude, the horizontal flow is modified by friction with the surface.

GEOSTROPHIC FLOWGEOSTROPHIC FLOWCoriolis forceCoriolis force

Large-scale movement of air in the atmosphere is driven by horizontal pressure gradients originating from differential heating of the Earth’s surface


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Air moves from high to low pressure on the surfaceof the rotating Earth, it is deflected by the Coriolisforce

Spherical geometry of EarthSpherical geometry of Earth


t= 1 day

λ=420 (Boston)

vE= 1250 km h -1

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CoriolisCoriolis effect for rotating observereffect for rotating observerat North Poleat North Pole


The ball has been deflected to the right of the target. Such a deflection implies a force (the Coriolis force) exerted to the right of the direction of motion

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CoriolisCoriolis effect for effect for meridionalmeridional motionmotion


λ1 to λ2 conserve its angular momentum mvE (λ1)Rcosλ1, m is the mass of the ball

vE(λ1) is the translational velocity of the Earth at λ1

Rcosλ1 is the radius of rotation at λ1

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The The CoriolisCoriolis force applies similarly to force applies similarly to longitudinal motionslongitudinal motions


The ball experiences a centrifugal force perpendicular to the axis of rotation of the Earth

This force is balanced exactly by the acceleration of gravity and by the reaction from the surface

Since the ball is thrown in the direction of the Earth’s rotation, its angular velocity in the fixed frame of reference increases; it experiences an increased centrifugal force

the increase in the centrifugal force deflects the ball towards the Equator

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CoriolisCoriolis acceleration acceleration γγcc applied to applied to hhorizontalorizontal motionsmotions

γc = The Coriolis acceleration

ω = The angular velocity of the Earth

V = The speed of the moving object in the rotating frame of reference (not to be


V = The speed of the moving object in the rotating frame of reference (not to beconfused with vE, the translational speed of the Earth

The Coriolis force is zero at the equator

The displacement ∆Y incurred when throwing an object with speed v at a target at distance ∆X

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Geostrophic balanceGeostrophic balance


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The effect of frictionThe effect of friction


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VERTICAL TRANSPORTVERTICAL TRANSPORTBuoyancyBuoyancy

The difference between the pressure-gradient force and gravity, iscalled the buoyancybuoyancy


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Atmospheric stabilityAtmospheric stability

Buoyancy in the atmosphere is determined by the vertical gradient of temperature


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Adiabatic lapse rateAdiabatic lapse rate


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ProcessProcess(cycle an air parcel)(cycle an air parcel)

Process I (Adiabatic):

[T(z), P(z)] rises adiabatically from z to z+dz

Process II (isothermal):

H=E+PV H = Entalphi, E = Internal Energy


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H=E+PV H = Entalphi, E = Internal Energy

dH = dE + d (PV) = dW + dQ+ d (PV), dW=-PdV

dH= -PdV + dQ + PdV + VdP = dQ + VdP dQ= 0 (I)

dHI = VdP dE = 0, d(PV)= 0 ideal gas (II)

dHII 0

Process (Continue)Process (Continue)

Process III (isobaric):

dHIII = dQ = mCP(T(z)- T(z+dz)) = – mCPdT

CP= 1.0 X103j kg-1K-1

thermodynamic cycle


thermodynamic cycle

dHI + dHII + dHIII = 0

VdP = mCPdT

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Lapse rateLapse rate

Replacing equation dP/dz = - ρag and m =ρV into VdP = mCPdT yields the adiabatic


(dTATM/dz > 0); such a situation is called a temperature inversion

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Latent heat release from cloud formationLatent heat release from cloud formation

Cloudy conditions represent an exception to the constancy of Γ. Condensation of water vapor is anexothermicprocess, meaning thatit releases heat (in meteorological jargon this is called latent heat release)


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Formation of a subsidence inversionFormation of a subsidence inversion


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Atmospheric lapse rateAtmospheric lapse rate An atmosphere left to evolve adiabatically from an initial statewould eventually

achieve an equilibrium situation of neutral buoyancy where the temperatureprofile follows the adiabatic lapse. However, external sources and sinks of heat prevent thisequilibrium from being achieved.


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TURBULENCETURBULENCE

Two limiting regimes for fluid flow : laminar and turbulent.

Laminar flow is smooth and steady

Turbulent flow is irregular and fluctuating


U = The mean speed of the flow

L = A characteristic length defining the scale of the flow

ϑ = The kinematic viscosity of the fluid (ϑ= 1.5x10-5 m-2 s-1 for air)

Flows in the atmosphere are generally turbulent because the relevant values of U and L are large

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Turbulent flux (1)Turbulent flux (1)The number of molecules of X crossing an horizontal surface area dAcentered on M during time dt is equal to the number nXwdtdA of molecules in the volume element wdtdA, wherewis the vertical wind velocity measured at point M and nX is the number concentration of X


na = the number air density of air

CX = the mixing ratio of X

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Turbulent flux (2)Turbulent flux (2) the vertical flux Fof pollutant X at point M by continuous measurement of C and

w. Due to the turbulent nature of the flow, both C and w show large fluctuations with time.


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Parameterization of turbulenceParameterization of turbulence


Parallel to the Gaussian spreading in molecular diffusion, which is a consequence of the linear relationship between the diffusion flux and the gradient of the species mixing ratio (Fick’s Law)

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F = the molecular diffusion fluxD = themolecular diffusion coefficient.

Kz= turbulent diffusion cooffesien

Time scales for vertical transportTime scales for vertical transport


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Atmospheric transport

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