Repository logo
 

Bifurcation analysis of two-dimensional Rayleigh-Bénard convection using deflation.

Accepted version
Peer-reviewed

Type

Article

Change log

Authors

Boullé, N 
Dallas, V 
Farrell, PE 

Abstract

We perform a bifurcation analysis of the steady states of Rayleigh-Bénard convection with no-slip boundary conditions in two dimensions using a numerical method called deflated continuation. By combining this method with an initialization strategy based on the eigenmodes of the conducting state, we are able to discover multiple solutions to this nonlinear problem, including disconnected branches of the bifurcation diagram, without the need for any prior knowledge of the solutions. One of the disconnected branches we find contains an S-shaped curve with hysteresis, which is the origin of a flow pattern that may be related to the dynamics of flow reversals in the turbulent regime. Linear stability analysis is also performed to analyze the steady and unsteady regimes of the solutions in the parameter space and to characterise the type of instabilities.

Description

Keywords

4012 Fluid Mechanics and Thermal Engineering, 40 Engineering

Journal Title

Phys Rev E

Conference Name

Journal ISSN

2470-0045
2470-0053

Volume Title

105

Publisher

American Physical Society (APS)