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

Abstract

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 (epsilon) over barr in the pycnoclines ( r similar to 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 (epsilon) over barr is preferable, although the Burr is an acceptable alternative. The skewness SkE and the kurtosis KE of the dissipation rate appear to be well correlated in a wide range of SkE and KE variability. Plain Language Summary 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 homogeneous layers of atmospheric and oceanic turbulence. Our microstructure measurements, 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 in stably stratified layers can be successfully modeled by the Burr ( type XII) probability distribution. In weakly stratified boundary layers, lognormal distribution of the dissipation is preferable, although the Burr is an acceptable alternative.