Spectrally-consistent regularization of turbulent Rayleigh-Bénard convection

Abstract

Direct numerical simulation (DNS) of turbulent Rayleigh-Bénard convection in an air filled (Pr = 0,7) rectangular cell of squared cross-section with periodic boundary conditions in the span-wise direction, has been carried out at Ra = 10^8. A fourth-order energy-conserving discretizations have been used that ensure non-physical dissipative effects introduced usually in other numerical schemes. The two sensitive fine-scales kinetic and thermal dissipation rates have been studied statistically to reveal high correlation within the thermal boundary layers and equilibrium zones of the two dissipations at strong thermal and kinetic interactions. It has been found that the foregoing zones could mark the plumes since these last reflect significant correlation regions of the kinetic and thermal fields. Afterwards, a novel class of symmetry-preserving regularization models that restrain the convective production of small scales of motion in unconditionally stable manner, have been applied on the studied problem. The obtained results are compared directly with the DNS ones to show a reasonable correspondence with and without model at this kind of moderate turbulence.