Turbulent fluxes

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# Turbulent fluxes - PowerPoint PPT Presentation

Turbulent fluxes. Vertical turbulent flux of pollutant mass. Turbulent stress. Vertical fluxes of momentum, heat, water vapor, and pollutant. Gradient-transport (K-theory).

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## PowerPoint Slideshow about 'Turbulent fluxes' - martina-nichols

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Presentation Transcript
Turbulent fluxes

Vertical turbulent flux of pollutant mass

Turbulent stress

Vertical fluxes of momentum, heat, water vapor, and pollutant

Km, Kh, and Kz are called the eddy diffusivities or exchange coefficients of momentum, heat, and mss, respectively. (Km is also called eddy or turbulent viscosity).

The gradient-transport (K-theory) relations are not based on any rigorous theory, but only on an intuitive analogy between molecular and turbulent exchange processes.

Prandtl’s mixing length theory

From dimensional analysis, we recognizing that eddy diffusivity must be a product of appropriate length and velocity scales.

In the surface layer (constant flux layer)

k= 0.40 is thevon Karman constant

is the friction velocity that

is related to surface stress

Finally, we have

In the surface layer, under neutral condition, we have:

We can define a surface roughness parameter such that at , .

Therefore, we can obtain the well-known logarithmic velocity profile law, that is

FIRST-ORDER PARAMETERIZATION OF TURBULENT FLUX

Time-averaged

envelope

Near-Gaussian

profile

• Observed mean turbulent dispersion of pollutants is near-Gaussian eparameterize it by analogy with molecular diffusion:

z

Instantaneous

plume

Source

<C>

Turbulent diffusion

coefficient

• Typical values of Kz: 102 cm2s-1 (very stable) to 107 cm2 s-1 (very unstable); mean value for troposphere is ~ 105 cm2 s-1
• Same parameterization (with different Kx, Ky) is also applicable in horizontal direction but is less important (mean winds are stronger)

Mass conservation and diffusion equation

If U=0, the diffusion equation can be simplified to

For an instantaneous point source, the solution of the above equation is

Q is the total mass of pollutant in the puff

TYPICAL TIME SCALES FOR VERTICAL MIXING
• Estimate time Dt to travel Dz by turbulent diffusion:

tropopause

(10 km)

10 years

5 km

1 month

1 week

2 km

“planetary

boundary layer”

1 day

0 km