Zonal flow reversals in two-dimensional Rayleigh-B\'enard convection

TL;DR

This paper investigates the nonlinear dynamics and flow reversals of large-scale zonal flows in two-dimensional Rayleigh-Bénard convection, revealing how flow states transition with increasing Rayleigh number and aspect ratio.

Contribution

It provides new insights into flow reversal mechanisms and the statistical behavior of large-scale modes in 2D Rayleigh-Bénard convection under different boundary conditions.

Findings

Flow reversals are characterized by bimodal and trimodal PDFs depending on aspect ratio.

Transitions from Gaussian to bimodal, trimodal, and unimodal PDFs occur as Rayleigh number increases.

Zonal flow reversals disappear at high Rayleigh numbers in certain geometries.

Abstract

We analyse the nonlinear dynamics of the large scale flow in Rayleigh-B\'enard convection in a two-dimensional, rectangular geometry of aspect ratio $\Gamma$. We impose periodic and free-slip boundary conditions in the streamwise and spanwise directions, respectively. As Rayleigh number Ra increases, a large scale zonal flow dominates the dynamics of a moderate Prandtl number fluid. At high Ra, in the turbulent regime, transitions are seen in the probability density function (PDF) of the largest scale mode. For $\Gamma = 2$, the PDF first transitions from a Gaussian to a trimodal behaviour, signifying the emergence of reversals of the zonal flow where the flow fluctuates between three distinct turbulent states: two states in which the zonal flow travels in opposite directions and one state with no zonal mean flow. Further increase in Ra leads to a transition from a trimodal to a unimodal PDF which demonstrates the disappearance of the zonal flow reversals. On the other hand, for $\Gamma = 1$ the zonal flow reversals are characterised by a bimodal PDF of the largest scale mode, where the flow fluctuates only between two distinct turbulent states with zonal flow travelling in opposite directions.