A data-driven model for the prediction of local dissipation rates in stratified turbulent flows

We construct a probabilistic artificial neural network (ANN) model to calculate local values of the turbulent energy dissipation rate $\varepsilon$ in strongly stratified decaying turbulence using a limited number of inputs. In general, simplified models for turbulent dissipation are important from a practical perspective as calculating the true value requires that 9 velocity derivatives be resolved simultaneously. It is common to apply theoretical `surrogate models' for $\varepsilon$ that use one or two velocity derivatives as inputs based on assumptions of homogeneity and isotropy, though these models can often be inaccurate in a geophysical setting where the stabilising presence of a vertical stratification generates large-scale anisotropy in the flow. We argue that our ANN model has two main advantages over isotropic surrogates. Firstly, we find it to be robust over multiple stratified turbulent regimes, in particular outperforming surrogate models when the turbulence has decayed and the flow is in a characteristic `layered' state. Secondly, the probabilistic nature of the model - which comes from sampling output values from a learnt distribution - captures underlying turbulence intermittency and as a result can produce estimates of uncertainty along with predictions. We discuss the implications of our work for the determination of dissipation rates from oceanographic data.