Deep learning of mixing by two 'atoms' of stratified turbulence

Abstract

Current global ocean models rely on ad-hoc parameterizations of diapycnal mixing, in which the efficiency of mixing is globally assumed to be fixed at $20\%$, despite increasing evidence that this assumption is questionable. As an ansatz for small-scale ocean turbulence, we may focus on stratified shear flows susceptible to either Kelvin-Helmholtz (KHI) or Holmboe wave (HWI) instability. Recently, an unprecedented volume of data has been generated through direct numerical simulation (DNS) of these flows. In this paper, we describe the application of deep learning methods to the discovery of a generic parameterization of diapycnal mixing using the available DNS dataset. We furthermore demonstrate that the proposed model is far more universal compared to recently published parameterizations. We show that a neural network appropriately trained on KHI- and HWI-induced turbulence is capable of predicting mixing efficiency associated with unseen regions of the parameter space well beyond the range of the training data. Strikingly, the high-level patterns learned based on the KHI and weakly stratified HWI are `transferable' to predict HWI-induced mixing efficiency under much more strongly stratified conditions, suggesting that through the application of appropriate networks, significant universal abstractions of density stratified turbulent mixing have been recognized.