Three-Dimensional Correlation and Spectral Functions for Turbulent Velocities inHomogeneous and Surface-Blocked Boundary Layers

摘要

A pair of three-dimensional (3D) models for correlation functions and spectra ofvelocity fluctuations in turbulent boundary layers is presented. First, the case of homogeneous turbulence is considered. Von Karman's energy spectrum is used to develop a complete set of 3D correlation and spectral equations. Second, it is shown how the homogeneous spectra can be modified to include the effect of eddy-blocking at the ground. Assuming that the disturbance to the turbulent flow resulting from the blocking is irrotational, an equation is developed that allows one to write the vertically inhomogeneous, 2D cross spectra as a function of the 2D cross spectra for a homogeneous flow. Although there are only two adjustable parameters in the inhomogeneous model, the variance and a length scale, the model is shown to agree quite well with a variety of previous results for the atmospheric convective boundary layer (CBL).