Accounting for surface temperature variations in Rayleigh-B\'{e}nard convection

TL;DR

This paper introduces a modified Rayleigh-Bénard convection model that incorporates dynamic surface temperature variations, making it more applicable to geophysical systems like lakes.

Contribution

It presents a new parameter and a dynamical Rayleigh number to account for surface temperature variability in convection models.

Findings

Recovery of standard Rayleigh-Bénard results with the new model

Simplification of applying convection theory to geophysical systems

Enhanced modeling of surface temperature effects in convection simulations

Abstract

Turbulent Rayleigh-B\'{e}nard convection is often modelled with a constant surface temperature. However, the surface temperature of many geophysical systems, such as lakes, is coupled to the atmospheric forcing. In this paper, we account for this dynamic surface temperature through an additional parameter $\beta$. Using an appropriately defined dynamical Rayleigh number $\RaD$, we recover many of the results from the standard Rayleigh-B\'{e}nard model. We hope that this work will simplify the application of Rayleigh-B\'{e}nard theory in geophysical contexts, such as lakes.