Probability Distribution of Turbulent Kinetic Energy Dissipation Rate in Ocean: Observations and Approximations

The probability distribution of turbulent kinetic energy dissipation rate in stratified ocean usually deviates from the classic lognormal distribution that has been formulated for and often observed in unstratified homogeneous layers of atmospheric and oceanic turbulence. Our measurements of vertical profiles of micro-scale shear, collected in the East China Sea, northern Bay of Bengal, to the south and east of Sri Lanka, and in the Gulf Stream region, show that the probability distributions of the dissipation rate ɛ∼r in the pycnoclines (r ∼ 1.4 m is the averaging scale) can be successfully modeled by the Burr (type XII) probability distribution. In weakly stratified boundary layers, lognormal distribution of ɛ∼r is preferable, although the Burr is an acceptable alternative. The skewness Skɛ and the kurtosis Kɛ of the dissipation rate appear to be well correlated in a wide range of Skɛ and Kɛ variability.