On the theory of the boundary layer

Abstract

The problem of the diurnal wind variation inside the boundary layer is treated using the diffusion equation with a tensorial diffusion coefficient which is more adequate than the ordinary way of dealing with this question in terms of a ‘fictitious viscosity’ coefficient. The correlation tensor is expressed as a random function and using the equivalence between the diffusion and the wave equation some characteristics of the solution are given. In particular with the hypothesis of a fundamental periodicity of 24 hr. for the correlation function, the classical elliptical variation of the wind hodograph is obtained. An analogy is established between the general theory of relativity with its used of Riemann spaces and the non-euclidean frame necessary for the study of the movements in the lower layer due to the functional relation among space and time variations of diffused quantities. The study is restricted to the case of homogeneous turbulence and this excludes the application to the surface layer. The mathematical basis are the papers of Varadhan and Zauderer concerning the behaviour of the asymptotic solutions of the heat and wave equations.