Large eddy simulations of turbulent thermal convection using renormalized viscosity and thermal diffusivity

We use renormalized viscosity and thermal diffusivity to construct a subgrid-scale model for large eddy simulations (LES) of turbulent thermal convection. This model is based on the observations [1, 2] that the behavior of turbulent thermal convection is similar to that of hydrodynamic turbulence. Therefore, for LES, we add renormalization viscosity, ν_ren ∼ Π^1/3(π/Δ)^-4/3, which is similar to that obtained for hydrodynamic turbulence, to the kinematic viscosity; here Π is the kinetic energy flux in the inertial range of wavenumbers and Δ is the grid spacing. The subgrid thermal diffusivity is assumed to be equal to subgrid viscosity; i.e. turbulent Prandtl number is assumed to be unity. We present a comparison between results - fluxes and spectra of temperature and velocity fields, time series of different quantities, temperature isosurfaces, scaling of Nusselt number with Rayleigh number - obtained using LES on a 128³ grid and DNS on a 512³ grid. A good agreement between LES and DNS results is obtained. [1] M.K. Verma, A. Kumar, and A. Pandey, New J. Physics 19, 025012 (2017). [2] A. Kumar, A.G. Chatterjee, and M.K. Verma, Phys. Rev. E 90, 023016 (2014)