Reversals in infinite-Prandtl-number Rayleigh-B\'enard convection

TL;DR

This study uses direct numerical simulations to analyze the statistical properties of flow reversals in two-dimensional infinite-Prandtl-number Rayleigh-Bénard convection, revealing different behaviors near the sidewall and center.

Contribution

It provides new insights into the statistical characteristics and Fourier mode dynamics of reversals in infinite-Prandtl-number convection, highlighting differences between sidewall and center velocities.

Findings

Reversal waiting times follow a Poisson distribution on long time scales.

Velocity near the sidewall exhibits a bimodal distribution and $1/f^2$ power spectrum.

Fourier modes effectively capture the reversal dynamics.

Abstract

Using direct numerical simulations, we study the statistical properties of reversals in two-dimensional Rayleigh-B\'enard convection for infinite Prandtl number. We find that the large-scale circulation reverses irregularly, with the waiting time between two consecutive genuine reversals exhibiting a Poisson distribution on long time scales, while the interval between successive crossings on short time scales shows a power law distribution. We observe that the vertical velocities near the sidewall and at the center show different statistical properties. The velocity near the sidewall shows a longer autocorrelation and $1/f^2$ power spectrum for a wide range of frequencies, compared to shorter autocorrelation and a narrower scaling range for the velocity at the center. The probability distribution of the velocity near the sidewall is bimodal, indicating a reversing velocity field. We also find that the dominant Fourier modes capture the dynamics at the sidewall and at the center very well. Moreover, we show a signature of weak intermittency in the fluctuations of velocity near the sidewall by computing temporal structure functions.