Bifurcations in a convection problem with temperature-dependent viscosity

Details Bifurcations in a convection problem with temperature-dependent viscosity Bifurcations in a convection problem with temperature-dependent viscosity

2008-10-21

arxiv.org/abs/0810.3799v1

Nonlinear Sciences

Pattern Formation and Solitons

16 pages, 5 figures

Scientific paper

10.1016/j.physd.2008.12.015

A convection problem with temperature-dependent viscosity in an infinite layer is presented. As described, this problem has important applications in mantle convection. The existence of a stationary bifurcation is proved together with a condition to obtain the critical parameters at which the bifurcation takes place. For a general dependence of viscosity with temperature a numerical strategy for the calculation of the critical bifurcation curves and the most unstable modes has been developed. For a exponential dependence of viscosity on temperature the numerical calculations have been done. Comparisons with the classical Rayleigh-B\'enard problem with constant viscosity indicate that the critical threshold decreases as the exponential rate parameter increases.

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