Why Oceanic Dissipation Rates Are Not Lognormal

Abstract

In their derivation of the lognormal probability density function for volume-averaged dissipation rates, Gurvich and Yaglom assumed explicitly that these dissipation rates are statistically homogeneous and that the averaging scale is small compared to the domain scale of the turbulent flow and large compared to the Kolmogorov scale. Estimates of dissipation rates in the oceanic thermocline reported by various researchers do not, in general, distribute lognormally because these datasets are often not homogeneous, nor is the averaging scale small compared to the scale of the turbulent patches. The conventional method of computing dissipation rates, a spectral technique, is incompatible with the assumptions for a lognormal distribution. Dissipation rates do distribute lognormally when they are computed with an alternative method that is consistent with the assumptions made by Gurvich and Yaglom. The shortest averaging scale that produced a lognormal distribution is three Kolmogorov length scales.