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arXiv · 0810.3799

Bifurcations in a convection problem with temperature-dependent viscosity

Francisco Pla·Henar Herrero·Olivier Lafitte
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Abstract

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-Bénard problem with constant viscosity indicate that the critical threshold decreases as the exponential rate parameter increases.

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Francisco Pla, Henar Herrero, Olivier Lafitte. 2008-10-21. Bifurcations in a convection problem with temperature-dependent viscosity. https://doi.org/10.1016/j.physd.2008.12.015

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