Axially-homogeneous Rayleigh-Benard convection in a cylindrical cell

TL;DR

This study investigates how confinement in a cylindrical cell affects the approach to the ultimate regime of thermal convection in Rayleigh-Benard systems, revealing that key scaling laws persist despite boundary layers and confinement.

Contribution

It demonstrates that the ultimate regime scaling laws hold in confined cylindrical geometries and explores the influence of modes and aspect ratio on system stability and heat transfer.

Findings

Nu and Re scale as Ra^{1/2} despite confinement

Exact solutions with exponentially growing modes exist and influence dynamics at low Ra

Increasing aspect ratio stabilizes the system and reduces fluctuations

Abstract

Previous numerical studies have shown that the "ultimate regime of thermal convection" can be attained in a Rayleigh-Benard cell when the kinetic and thermal boundary layers are eliminated by replacing the walls with periodic boundary conditions (homogeneous Rayleigh-Benard convection). Then, the heat transfer scales like Nu ~ Ra^{1/2} and turbulence intensity as Re ~ Ra^{1/2}, where the Rayleigh number Ra indicates the strength of the driving force. However, experiments never operate in unbounded domains and it is important to understand how confinement might alter the approach to this ultimate regime. Here we consider homogeneous Rayleigh-Benard convection in a laterally confined geometry - a small aspect-ratio vertical cylindrical cell - and show evidence of the ultimate regime as Ra is increased: In spite of the confinement and the resulting kinetic boundary layers, we still find Nu ~ Re ~ Ra^{1/2}. The system supports exact solutions composed of modes of exponentially growing vertical velocity and temperature fields, with Ra as the critical parameter determining the properties of these modes. Counterintuitively, in the low Ra regime, or for very narrow cylinders, the numerical simulations are susceptible to these solutions which can dominate the dynamics and lead to very high and unsteady heat transfer. As Ra is increased, interaction between modes stabilizes the system, evidenced by the increasing homogeneity and reduced fluctuations in the r.m.s. velocity and temperature fields. We also test that physical results become independent of the periodicity length of the cylinder, a purely numerical parameter, as the aspect ratio is increased.