Hostname: page-component-7c8c6479df-27gpq Total loading time: 0 Render date: 2024-03-28T05:51:32.887Z Has data issue: false hasContentIssue false

Standing and travelling waves in cylindrical Rayleigh–Bénard convection

Published online by Cambridge University Press:  19 July 2006

KATARZYNA BOROŃSKA
Affiliation:
Laboratoire d'Informatique pour la Mécanique et les Sciences de l'Ingénieur (LIMSI–CNRS), BP 133, 91403 Orsay, Francekasia@limsi.fr; laurette@limsi.fr
LAURETTE S. TUCKERMAN
Affiliation:
Laboratoire d'Informatique pour la Mécanique et les Sciences de l'Ingénieur (LIMSI–CNRS), BP 133, 91403 Orsay, Francekasia@limsi.fr; laurette@limsi.fr

Abstract

The Boussinesq equations for Rayleigh–Bénard 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 25000, 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.

Type
Papers
Copyright
© 2006 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)