High rayleigh number convection at infinite prandtl number with weakly temperature-dependent viscosity

Abstract

Abstract The effects of high Rayleigh number convection for temperature-dependent viscosity at infinite Prandtl number are studied with three-dimensional direct numerical simulations (using a fully spectral method) in a wide box with dimensions 5 × 5 × 1. The form of the temperature-dependent viscosity decreases exponentially with the temperature. Solutions for an volumetrically averaged Rayleigh numbers up to 6.25 × 106 have been obtained for a viscosity contrast of 25. Both models with and without viscous dissipation and adiabatic heatings have been considered. There is a distinct difference in the plume dynamics between models with a dissipation number D = 0 and D = 0.3. At zero dissipation number the hot plumes extend up to the top, while plumes at D = 0.3 are cooled due to adiabatic expansion and do not extend throughout the entire layer. The cold descending flows occur in sheets and they form longer wavelength networks and can reach the bottom, regardless of the value of D. A time-varying depth-depe...