Diagnostics for Eddy Viscosity Models of Turbulence Including Data-Driven/Neural Network Based Parameterizations

TL;DR

This paper develops a posteriori conditions to evaluate the necessity and failure of eddy viscosity models in turbulence, addressing issues of over-diffusion and model complexity, especially in data-driven neural network approaches.

Contribution

It introduces a posteriori criteria to determine when eddy viscosity models are needed or fail, improving understanding of model applicability and reliability.

Findings

Derived computable conditions for model necessity and failure

Addresses over-diffusion issues in eddy viscosity models

Provides tools for evaluating data-driven turbulence models

Abstract

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 a posteriori computable conditions that answer these two questions.