Diagnostics for eddy viscosity models of turbulence including data-driven/neural network based parameterizations

Classical eddy viscosity models add a viscosity term with turbulent viscosity coefficient whose specification varies from model to model. Turbulent viscosity coefficient approximations of unknown accuracy are typically constructed by solving associated systems of nonlinear evolution equations or by data driven approaches such as deep neural networks. Often eddy viscosity models over-diffuse, so additional fixes are added. This process increases model complexity and decreases model comprehensibility, leading to the following two questions: Is an eddy viscosity model needed? Does the eddy viscosity model fail? This report derives diagnostic quantities of interest that answer these two questions. A notable quality of the derived quantities of interest for the eddy viscosity model is that they are a posteriori computable and require no a priori knowledge of the parameterization. For neural network based parameterizations these diagnostic quantities provide an indication of when the eddy viscosity model fails due to over diffusion of the flow.