Comparison of convection for Reynolds and Arrhenius temperature dependent viscosities

We present 2D simulations using the Lattice Boltzmann Method (LBM) of a fluid in a rectangular box being heated from below, and cooled from above, with a Rayleigh of 7We conduct numerical experiments for exponent b in the range 7 through 15.For both cases, we achieve stagnant-lid type convection.For the case of Reynolds temperature dependent viscosity, we obtain increasingly pulse-like plumes as b is increased where plume-head bubbles of hot upwelling material push upwards through pre-weakened pathways to the surface of the model.In contrast, the Arrhenius temperature dependent viscosity leads to long narrow plumes separated by long downwelling chutes that push through the entire model.These results demonstrate that the LBM can model different modes of convection for different temperature dependence of viscosity, and point to the need to accurately define the temperature dependence of viscosity in convection problems such as geodynamics.