Fun idea! I assume that your time scales are relatively short when you talk
about a stagnant lid? Or is your viscosity parameterization just not valid at
lower temperatures in the upper half of the mantle?
Best
W.
We are definitely thinking about short time scales, but the viscosity parameterization at low temperature is the main problem. In stagnant lid convection most of the temperature drop across the fluid layer occurs in the cold and strong layer at the top. This layer is stagnant because the viscosity is so high it does not participate in the convection. This leaves a relatively small temperature difference between the interior and the lower boundary. The resulting heat flow is too low to cool the core at the rate we need to power a magnetic field. Some workers add a yield stress to the viscosity parameterization of the near-surface. This allows the stagnant lid to be “broken” and entrained by the underlying convection. Once you can move the cold lid into the interior, you enhance the rate at which the interior cools and this increases the heat flow across the CMB. A yield stress is plausible but it is fairly ad hoc. We wanted to avoid these complications by focusing on the lower half of the domain. We’ve been able to reproduce the standard Nu - Ra relation in constant viscosity fluid, even though we only model the lower half. Extending the Nu-Ra relation to a temperature-dependent viscosity is usually done by defining the Rayleigh number using the average viscosity across the boundary layer. (Each boundary layer is usually handled separately in the theory although the top and bottom layers have identical temperature drops and thicknesses in the standard case of convection in a uniform plane layer). An average viscosity doesn’t work very well when Ra is modest but there is a hint (so far) that the approximation improves as Ra goes up. There are also speculations/folklore about small-scale convection developing in the boundary layer of fluid with strongly temperature dependent viscosity when Ra is sufficiently high. This idea is not so obvious to me, but we are now in a position to take a look.
Thanks again!
Bruce
Hi!
I am new in installation of ASPECT.
I am in trouble with installation of the Trilinos package for ASPECT. While running the candi.sh script, the terminal becomes unresponsive. My laptop has 15 GB free space and Ubuntu 14.04. Is there any way to fix this?
Thanks
Poulami