Consequences of Symmetries on the Analysis and Construction of Turbulence Models

Since they represent fundamental physical properties in turbulence (conservation laws, wall laws, Kolmogorov energy spectrum, ...), symmetries are used to analyse common turbulence models. A class of symmetry preserving turbulence models is proposed. This class is refined such that the models respect the second law of thermodynamics. Finally, an example of model belonging to the class is numerically tested

Constructing Physically Consistent Subgrid-Scale Models for Large-Eddy Simulation of Incompressible Turbulent Flows

We studied the construction of subgrid-scale models for large-eddy simulationof incompressible turbulent flows, focusing on consistency with importantmathematical and physical properties. In particular, we considered the symmetriesof the Navier-Stokes equations, and the near-wall scaling and dissipation behaviorof the turbulent stresses. After showing that existing models do not all satisfy thedesired properties, we discussed a general class of subgrid-scale models based onthe local filtered velocity gradient. We provided examples of models from this classthat preserve several of the symmetries of the Navier-Stokes equations and exhibitthe same near-wall scaling behavior as the turbulent stresses. Furthermore, thesemodels are capable of describing nondissipative effects

A Framework for the Assessment and Creation of Subgrid-Scale Models for Large-Eddy Simulation

We focus on subgrid-scale modeling for large-eddy simulation of incompressible turbulent flows. In particular, we follow a systematic approach that is based on the idea that subgrid-scale models should preserve fundamental properties of the Navier–Stokes equations and turbulent stresses. To that end, we discuss the symmetries and conservation laws of the Navier–Stokes equations, as well as the near-wall scaling, realizability and dissipation behavior of the turbulent stresses. Regarding each of these properties as a model constraint, we obtain a framework that can be used to assess existing and create new subgrid-scale models. We show that several commonly used velocity-gradient-based subgrid-scale models do not exhibit all the desired properties. Although this can partly be explained by incompatibilities between model constraints, we believe there is room for improvement in the properties of subgrid-scale models. As an example, we provide a new eddy viscosity model, based on the vortex stretching magnitude, that is successfully tested in large-eddy simulations of turbulent plane-channel flow