Numerical study of high Rayleigh number convection in a medium with depth-dependent viscosity

The equations of motion are solved numerically for a Boussinesq fluid with infinite Prandtl number in a square 2-D box where the viscosity increases with depth. Three heating modes are employed: bottom heating, internal heating, and half bottom and half internal heating. In all cases the boundaries are free slip. The range of Rayleigh numbers employed is 10-107. The viscosity increases as 10{3(IY), where y is distance measured from the bottom upwards and {3 is a free parameter. In the bottom heated cases, the convective velocities slow near the bottom and result in a large temperature drop between the bottom boundary and interior compared with the top boundary and the interior. This results in increased buoyancy in the ascending limb. In the internally heated case, the flow in the top half of the box resembles Rayleigh-Benard convection and in the bottom half it approaches a conductive thermal regime for {3 greater than about 2. In this case the top surface heat flux decays from ascending to descending limb and the ascending and descending limbs become more equal in their buoyancy. Increasing {3 decreases the efficiency of heat transport, but has little effect on the exponents of Nu-Ra and Pe-Ra relations. There is a larger decrease in heat transport efficiency for a given {3 in the bottom heated case compared to the internally heated case.