Patterns and bifurcations in low-Prandtl number Rayleigh-Benard convection

TL;DR

This paper investigates the bifurcation structures and flow patterns in low-Prandtl number Rayleigh-Bénard convection near onset, revealing similarities to zero-Prandtl number convection and detailing how flow regimes change with parameters.

Contribution

It provides a detailed bifurcation analysis using simulations and a low-dimensional model for low-Prandtl number convection, highlighting differences from zero-Prandtl number behavior.

Findings

Low-Prandtl convection exhibits patterns similar to zero-Prandtl convection, including chaos.

Stationary 2D rolls are present at onset, unlike zero-Prandtl convection where chaos appears immediately.

The range of Rayleigh numbers supporting stationary rolls decreases rapidly as Prandtl number decreases.

Abstract

We present a detailed bifurcation structure and associated flow patterns for low-Prandtl number ($P=0.0002, 0.002, 0.005, 0.02$) Rayleigh-B\'{e}nard convection near its onset. We use both direct numerical simulations and a 30-mode low-dimensional model for this study. We observe that low-Prandtl number (low-P) convection exhibits similar patterns and chaos as zero-P convection \cite{pal:2009}, namely squares, asymmetric squares, oscillating asymmetric squares, relaxation oscillations, and chaos. At the onset of convection, low-P convective flows have stationary 2D rolls and associated stationary and oscillatory asymmetric squares in contrast to zero-P convection where chaos appears at the onset itself. The range of Rayleigh number for which stationary 2D rolls exist decreases rapidly with decreasing Prandtl number. Our results are in qualitative agreement with results reported earlier.