Bifurcation phenomena in a convection problem with temperature dependent viscosity at low aspect ratio

In this paper we analyse convective solutions of a two dimensional fluid layer in which viscosity depends exponentially on temperature. This problem takes in features of mantle convection, since large viscosity variations are to be expected in the Earth’s interior. These solutions are compared with solutions obtained at constant viscosity. Special attention is paid to the influence of the aspect ratio in the solutions presented. The analysis is assisted by bifurcation techniques such as branch continuation, which has proven to be a useful, systematic method for gaining insight into the possible stationary solutions satisfied by the basic equations. One feature presented by the fluid with non constant viscosity is the presence of pitchfork and saddle-node subcritical bifurcations and the presence of convective solutions below the linear critical threshold. The analysis also provides limits of existence of stationary solutions and draws the boundaries for time dependent convection.