Complexity of viscous dissipation in turbulent thermal convection

Abstract

Using direct numerical simulations of turbulent thermal convection for Rayleigh number ($\mathrm{Ra}$) between $10^6$ and $10^8$ and unit Prandtl number, we derive scaling relations for viscous dissipation in the bulk and in the boundary layers. We show that contrary to the general belief, the total viscous dissipation in the bulk is larger, albeit marginally, than that in the boundary layers. The bulk dissipation rate is similar to that in hydrodynamic turbulence with log-normal distribution, but it differs from $(U^3/d)$ by a factor of $\mathrm{Ra}^{-0.18}$. Viscous dissipation in the boundary layers are rarer but more intense with a stretched-exponential distribution.