Chaotic traveling rolls in Rayleigh-B\'enard convection

TL;DR

This study uses direct numerical simulation to explore chaotic traveling rolls in 2D Rayleigh-Bénard convection, revealing flow reversal phenomena driven by mode interactions under various boundary conditions.

Contribution

It demonstrates the existence of chaotic traveling rolls and flow reversals in 2D Rayleigh-Bénard convection, highlighting the role of mode interactions and boundary conditions.

Findings

Chaotic traveling rolls occur in a specific Rayleigh number range.

Flow reversal can result from lateral shifts of the rolls.

Traveling rolls are observed under different boundary conditions.

Abstract

In this paper we investigate two-dimensional (2D) Rayleigh-B\'enard convection using direct numerical simulation in Boussinesq fluids of Prandtl number $P = 6.8$ confined between thermally conducting plates. We show through the simulation that in a small range of reduced Rayleigh number $r$ ($770 < r < 890$) the 2D rolls move chaotically in a direction normal to the roll axis. The lateral shift of the rolls may lead to global flow reversal of the convective motion. The chaotic traveling rolls are observed in simulation with {\it free-slip} as well as {\it no-slip} boundary conditions on the velocity field. We show that the traveling rolls and the flow reversal are due to an interplay between the real and imaginary parts of the critical modes.