Stochastic bifurcation analysis of Rayleigh-Bénard convection

Document Type

Article

Publication Date

5-10-2010

Abstract

Stochastic bifurcations and stability of natural convection within two-dimensional square enclosures are investigated by different stochastic modelling approaches. Deterministic stability analysis is carried out first to obtain steady-state solutions and primary bifurcations. It is found that multiple stable steady states coexist, in agreement with recent results, within specific ranges of Rayleigh number. Stochastic simulations are then conducted around bifurcation points and transitional regimes. The influence of random initial flow states on the development of supercritical convection patterns is also investigated. It is found that a multi-element polynomial chaos method captures accurately the onset of convective instability as well as multiple convection patterns corresponding to random initial flow states. Copyright © Cambridge University Press 2010.

Publication Source (Journal or Book title)

Journal of Fluid Mechanics

First Page

391

Last Page

413

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