Invariant subgrid modelling in large-eddy simulation of heat convection turbulence

Symmetries have an important role in turbulence. To some extent, they contain the physics of the equations (conservation laws, etc.), and it is essential that turbulence models respect them. However, as observed by Oberlack (Annual Research Briefs. Stanford University, Stanford 1997) and next by Razafindralandy and Hamdouni (Direct and Large-Eddy Simulation 6: Proceedings of the 6th International ERCOFTAC Workshop on Direct and Large-Eddy Simulation. Springer, Heidelberg, 2006) in the case of an isothermal fluid, only few subgrid stress tensor models preserve the symmetries of the Navier–Stokes equations. In this communication, we present the symmetries of the equations of a non-isothermal fluid flow and analyze some common subgrid stress tensor and flux models under the point of view of these symmetries.