Turbulent fluxes. Vertical turbulent flux of pollutant mass. Turbulent stress. Vertical fluxes of momentum, heat, water vapor, and pollutant. Gradient-transport (K-theory).
Vertical turbulent flux of pollutant mass
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.
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
We can define a surface roughness parameter such that at , .
Therefore, we can obtain the well-known logarithmic velocity profile law, that is
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