Bifurcations in a convection problem with temperature-dependent viscosity

TL;DR

This paper investigates bifurcations in a convection system with temperature-dependent viscosity, providing theoretical proofs and numerical methods to analyze critical parameters relevant to mantle convection.

Contribution

It introduces a new numerical strategy for calculating bifurcation curves in systems with temperature-dependent viscosity and compares results with classical models.

Findings

Critical bifurcation thresholds decrease with increasing exponential rate of viscosity.

Numerical methods effectively determine unstable modes and bifurcation points.

Results have implications for understanding mantle convection dynamics.

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-B\'enard problem with constant viscosity indicate that the critical threshold decreases as the exponential rate parameter increases.