Localization of toroidal motion and shear heating in 3‐D high Rayleigh number convection with temperature‐dependent viscosity

We have applied spectral‐transform methods to study three‐dimensional thermal convection with temperature‐dependent viscosity. The viscosity varies exponentially with the form exp(‐BT), where B controls the viscosity contrast and T is temperature. Solutions for high Rayleigh numbers, up to an effective Ra of 6.25×10⁶, have been obtained for an aspect‐ratio of 5×5×1 and a viscosity contrast of 25. Solutions show the localization of toroidal velocity fields with increasing vigor of convection to a coherent network of shear‐zones. Viscous dissipation increases with Rayleigh number and is particularly strong in regions of convergent flows and shear deformation. A time‐varying depth‐dependent mean‐flow is generated because of the correlation between laterally varying viscosity and velocity gradients.