Complexity of viscous dissipation in turbulent thermal convection

TL;DR

This study uses direct numerical simulations to analyze viscous dissipation in turbulent thermal convection, revealing that bulk dissipation slightly exceeds boundary layer dissipation and exhibits a log-normal distribution similar to hydrodynamic turbulence.

Contribution

It provides new scaling relations for viscous dissipation in both bulk and boundary layers, challenging the belief that boundary layer dissipation dominates.

Findings

Bulk viscous dissipation is marginally larger than boundary layer dissipation.

Bulk dissipation follows a log-normal distribution similar to hydrodynamic turbulence.

Dissipation in boundary layers is rarer but more intense with a stretched-exponential distribution.

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.