Thermal Boundary Layer Equation for Turbulent Rayleigh-Benard Convection

TL;DR

This paper introduces a new thermal boundary layer equation for turbulent Rayleigh-Benard convection that incorporates turbulent fluctuations, leading to accurate analytical predictions of temperature profiles validated by numerical simulations.

Contribution

A novel thermal boundary layer equation for turbulent convection that accounts for turbulent fluctuations, improving upon existing steady-state laminar models.

Findings

Analytical temperature profiles match numerical simulations for Pr=4.38 and Pr=2547.9.

New equation captures effects of turbulence neglected in previous models.

Theoretical predictions are in excellent agreement with direct numerical simulations.

Abstract

We report a new thermal boundary layer equation for turbulent Rayleigh-Benard convection for Prandtl number Pr>1 that takes into account the effect of turbulent fluctuations. These fluctuations are neglected in existing equations, which are based on steady-state and laminar assumptions. Using this new equation, we derive analytically the mean temperature profiles in two limits: (a) Pr>1, Pr~1 and (b) Pr>>1. These two theoretical predictions are in excellent agreement with the results of our direct numerical simulations for Pr=4.38 (water) and Pr=2547.9 (glycerol) respectively.