Flow states in two-dimensional Rayleigh-B\'enard convection as a function of aspect-ratio and Rayleigh number

TL;DR

This study investigates how flow states and heat transport in two-dimensional Rayleigh-Bénard convection depend on aspect ratio and Rayleigh number, revealing flow transitions, aspect ratio effects, and long-lived transient states.

Contribution

It provides new insights into flow transitions, aspect ratio influence, and transient behaviors in high Rayleigh number convection through extensive numerical simulations.

Findings

Sharp flow transition at high Ra in small aspect ratio cells.

Heat transport variations decrease with increasing aspect ratio.

Existence of long-lived transient flow states at high Ra.

Abstract

In this numerical study on two-dimensional Rayleigh-B\'enard convection we consider $10^7 \leq Ra \leq 10^{12}$ in aspect ratio $0.23 \leq \Gamma \leq 13$ samples. We focus on several cases. First we consider small aspect ratio cells, where at high Ra number we find a sharp transition from a low Ra number branch towards a high Ra number branch, due to changes in the flow structure. Subsequently, we show that the influence of the aspect ratio on the heat transport decreases with increasing aspect ratio, although even at very large aspect ratio of $\Gamma\approx10$ variations up to 2.5% in the heat transport as a function of \Gamma are observed. Finally, we observe long-lived transients up to at least $Ra=10^9$, as in certain aspect ratio cells we observe different flow states that are stable for thousands of turnover times.