Dissipation Layers in Rayleigh-B\'{e}nard Convection: A Unifying View

TL;DR

This paper introduces dissipation layers in Rayleigh-Bénard convection as a unifying concept that captures near-wall structures across different boundary conditions, extending the applicability of scaling theories to natural systems.

Contribution

It demonstrates that dissipation layers share key features with classical boundary layers and can be used to unify the treatment of boundary effects in convection.

Findings

Dissipation layers are similar to classical boundary layers but applicable to arbitrary boundary conditions.

Differences in scaling behavior for no-slip and stress-free boundaries are explained.

The approach extends scaling theories from laboratory to natural convection systems.

Abstract

Boundary layers play an important role in controlling convective heat transfer. Their nature varies considerably between different application areas characterized by different boundary conditions, which hampers a uniform treatment. Here, we argue that, independent from boundary conditions, systematic dissipation measurements in Rayleigh-B\'enard convection capture the relevant near-wall structures. By means of direct numerical simulations with varying Prandtl numbers, we demonstrate that such dissipation layers share central characteristics with classical boundary layers, but, in contrast to the latter, can be extended naturally to arbitrary boundary conditions. We validate our approach by explaining differences in scaling behavior observed for no-slip and stress-free boundaries, thus paving the way to an extension of scaling theories developed for laboratory convection to a broad class of natural systems.