The gamma distribution as a model for temperature dissipation in intermittent turbulence

Abstract

Following a recent theory suggesting that the local average rate of energy dissipation εr follows statistics predicted by the gamma distribution rather than the lognormal distribution, the gamma distribution is further examined here as a model for the local temperature dissipation rate χr. Comparisons of measured moments 〈χmr〉 with those predicted by both the gamma and lognormal distributions clearly favor the gamma model for predicting the power-law exponents of r/L. Based on gamma models for both εr and χr, the bivariate gamma distribution is then examined as a possible model for the joint distribution of dissipation rates εr and χr. In particular, the bivariate gamma model and the bivariate lognormal model are both compared with the inertial-range behavior of measured temperature structure functions up to order 12. Some additional comparisons of these models are also made with data involving mixed moments of the velocity and temperature structure functions.