Convection in an ideal gas at high Rayleigh numbers

TL;DR

This paper investigates convection in an ideal gas at high Rayleigh numbers through numerical simulations, highlighting how density stratification affects key scaling laws and boundary layer relations.

Contribution

It introduces a density-adjusted data reduction method using an effective density, enabling power-law fits similar to Boussinesq fluids, and establishes boundary layer relations in stratified convection.

Findings

Density stratification influences Rayleigh, Peclet, and Nusselt number relations.

A new scaling law with an effective density fits the data well.

Boundary layer kinetic energy densities are equal at top and bottom.

Abstract

Numerical simulations of convection in a layer filled with ideal gas are presented. The control parameters are chosen such that there is a significant variation of density of the gas in going from the bottom to the top of the layer. The relations between the Rayleigh, Peclet and Nusselt numbers depend on the density stratification. It is proposed to use a data reduction which accounts for the variable density by introducing into the scaling laws an effective density. The relevant density is the geometric mean of the maximum and minimum densities in the layer. A good fit to the data is then obtained with power laws with the same exponent as for fluids in the Boussinesq limit. Two relations connect the top and bottom boundary layers: The kinetic energy densities computed from free fall velocities are equal at the top and bottom, and the products of free fall velocities and maximum horizontal velocities are equal for both boundaries.