Scaling laws prediction from a solvable model of turbulent thermal convection

TL;DR

This paper introduces a solvable turbulent model to predict boundary layer structures and scaling laws in thermal convection, revealing various regimes and a new Nusselt-Rayleigh law with a specific exponent.

Contribution

It presents a novel solvable model that predicts diverse turbulent convection regimes and introduces a new scaling law for heat transfer.

Findings

Identification of classical 2/7 and 1/3 scaling laws.

Discovery of a new 4/13 Nusselt-Rayleigh law.

Model captures the influence of Prandtl and Reynolds numbers.

Abstract

A solvable turbulent model is used to predict both the structure of the boundary layer and the scaling laws in thermal convection. The transport of heat depends on the interplay between the thermal, viscous and integral scales of turbulence, and thus, on both the Prandtl number and the Reynolds numbers. Depending on their values, a wide variety of possible regimes is found, including the classical 2/7 and 1/3 law, and a new $4/13=0.308$ law for the Nusselt power law variation with the Rayleigh number.