Probability law of turbulent kinetic energy in the atmospheric surface layer

The probability density function p(k) of the turbulent kinetic energy k is investigated for diabatic atmospheric surface layer (ASL) flows. When the velocity components are near-Gaussian and their squared amplitudes are nearly independent, the resulting p(k) is shown to be γ-distributed with exponents that vary from 0.8 to 1.8. A nonlinear Langevin equation that preserves a γ-distributed p(k), but allows linear relaxation of k to its mean state, is proposed and tested using multiple ASL data sets. The three parameters needed to describe the drift and nonlinear diffusion terms can be determined from the ground shear stress and the mean velocity at height z. Using these model parameters, the Langevin equation reproduces the measured p(k) with minimal Kullback-Leibler divergence.