A three-dimensional correlation spectral model for turbulent velocities in a convective boundary layer

A three-dimensional model for correlation functions and spectra in the atmospheric, convective boundary layer (CBL) is presented. The model includes vertical inhomogeneities introduced by eddy-blocking at the ground. By assuming the disturbance to the turbulent flow resulting from the ground blocking is irrotational, an equation is developed which allows one to write the inhomogeneous, two-dimensional (2D) cross spectra for the blocked flow in terms of the 2D cross spectra for a homogeneous flow. Von Karman's energy spectrum then is used to determine the homogeneous, 2D cross spectra. Although there are only two adjustable parameters in the model, the variance and a length scale, the model is shown to agree quite well with a diversity of previous results for the CBL.