Solutions of the Steady-State Atmospheric Diffusion Equation

This latter result can be expressed in terms of the friction velocity m and the Monin-Obukhov length L as 

For a range of typical meteorological conditions this formulation results in diffusivities under unstable conditions of 0(50-100 m s ). In practical applications it is usually assumed that = A, . 

8 SOLUTIONS OF THE STEADY-STATE ATMOSPHERIC DIFFUSION EQUATION 

The Gaussian expressions are not expected to be valid descriptions of turbulent diffusion close to the surface because of spatial inhomogeneities in the mean wind and the turbulence. To deal with diffusion in layers near the surface, recourse is generally made to the atmospheric diffusion equation, in which, as we have noted, the key problem is proper specification of the spatial dependence of the mean velocity and eddy diffusivities. Under steady-state conditions, turbulent diffusion in the direction of the mean wind is usually neglected (the slender plume approximation), and if the wind direction coincides with the jc axis, then =0. Thus it is necessary to specify only the lateral, Ky, and vertical, A --, coefficients. It is generally assumed that horizontal homogeneity exists so that u and A are independent of y. Hence (18.52) becomes 

Section 18.7 has been devoted to expressions for w, K--, and Kyy based on atmospheric boundary layer theory. Because of the rather complicated dependence of u and K-- on r,( 18.65) must generally be solved numerically. However, if they can be found, analytical solutions are advantageous for studying the behavior of the predicted mean concentration. For solutions beyond those presented here we refer the reader to Lin and Hildemann (1996, 1997). 

---

D. Solutions of the Steady-State Atmospheric Diffusion Equation. 286... 

---