Some improvement in k theory for turbulent diffusion

Abstract—As an improvement of K theory, a modified turbulent diffusion equation is developed in this paper based on the classical Prandtl Mixing Length Theory. The initial numerical and theoretical analyses show that the improved K theory enable to describe countergradient transportation phenomenon and spatial inhomgenious contribution of conservative scalar properties in turbulence diffusion. For theoretical studies of first order turbulence closure, the turbulent flux or convariance of any physical quantity is to be properly parameterized in terms of following relation:

rather than widely used flux-gradient relation. For the improved K theory, the modified turbulent diffusion equation governing changes in the mean concentration of the property q

is suggested, with defined as SECOND ORDER EDDY DIFFUSIVITY for property .