On the validity of the Millionshchikov quasi-normality hypothesis for open-ocean deep convection

Data from numerical simulations of free convection in the ocean with rotation are used to explore the validity of the Millionshchikov quasi-normality hypothesis. The parameterizations of fourth-order moments according to a universal model proposed by Gryanik et al. are found to be far more accurate than their corresponding Gaussian parameterizations, which are based on the Millionshchikov hypothesis. The universal model is marginally improved by fitting the model parameters to the data. The present results extend previous results that discuss shallow convection in the planetary boundary layer to rotationally controlled deep convection.