Onset of convection with temperature- and depth-dependent viscosity

Abstract

We derive a scaling law for the onset of convection in an incompressible fluid cooled from above with temperature- and depth-dependent viscosity, on the basis of 2-D numerical simulation. Rayleigh numbers up to 107 are considered. The activation energy is varied from 0 to 200 kJ mol-1, and a variation of up to 103 is considered in depth-dependent reference viscosity. Our scaling law is shown to be able to handle a variety of buoyancy distributions, including highly non-Gaussian and multimodal distributions, with a tightly constrained critical Rayleigh number.