The Scale of Turbulence and the Wind Profile in the Surface Boundary Layer

Abstract

The scale of turbulence in the surface boundary layer, l is investigated as a function of the thermal stability, ξ(ξ_z/L, L≡V*3/( kg/T0q/cpρ)). When the scale function, ψ is introduced as l(ξ)≡kzψ(ξ), the nondimensional wind shear, s(≡kz/V∂U/∂z) can be represented as follows: S4-γξS3-ψ-4=0 where γ' is constant. So-called Ellison-Yamamoto-Panofsky's equation is included as a special case (i.e., l=kz or ψ=1). And then the equation is solved exactly as a function of ξ and also ψ.
Now, the data obtained during "Project Prairie Grass" and also taken by Gurvich show that ψ is quite varied with ξ. A t present, there seems to be no way to estimate the formula of ψ except making use of the few available observational data. From the data taken during "Project Prairie Grass ", ψ is evaluated assuming that the vertical scale as a function of ξ is similar to the horizontal : ψ(ξ)=σ{ξ-(2+σ-2)1/2} where σ is constant. And then the concrete formulae of S are obtained in the various thermal conditions.