Standing and travelling waves in cylindrical Rayleigh-Benard convection

TL;DR

This paper investigates the transition from stationary to oscillatory azimuthal waves in cylindrical Rayleigh-Benard convection, revealing a Hopf bifurcation with standing and travelling wave solutions near a critical Rayleigh number.

Contribution

It provides a detailed analysis of wave transitions in cylindrical convection using simulations, stability analysis, and bifurcation theory, highlighting the role of O(2) symmetry.

Findings

At Ra ≈ 25,000, flow becomes unstable to azimuthal waves.

Standing waves are slightly unstable to travelling waves.

Transition characterized as a Hopf bifurcation with O(2) symmetry.

Abstract

The Boussinesq equations for Rayleigh-Benard convection are simulated for a cylindrical container with an aspect ratio near 1.5. The transition from an axisymmetric stationary flow to time-dependent flows is studied using nonlinear simulations, linear stability analysis and bifurcation theory. At a Rayleigh number near 25,000, the axisymmetric flow becomes unstable to standing or travelling azimuthal waves. The standing waves are slightly unstable to travelling waves. This scenario is identified as a Hopf bifurcation in a system with O(2) symmetry.