A statistical theory for the distribution of energy dissipation in intermittent turbulence

Abstract

A new statistical theory involving the gamma distribution is presented for the local average rate of dissipation εr. The gamma distribution for εr leads to results for the high-order moments of the velocity structure function that lie between those predicted by the lognormal model and β model and closely follow those of the multifractal model. Comparisons of results predicted by the gamma distribution are made with previously published experimental data, showing excellent agreement. Based on the gamma distribution for εr, the one-dimensional K distribution is developed as a plausible model for the distribution of energy dissipation ε. Some laboratory measurements of velocity fluctuations and certain derived quantities from a modified airjet are also discussed. A good agreement is found by making comparisons of the measured cumulative probability distribution of the squared time derivative of the streamwise velocity component with that predicted by this new model.