Examining functional relationship between tau and u

[glugeorge]

I've added in a retreat scenario with Schoof's bed. We can see the retreat slow going up the sill, and then accelerate after moving past it. Weaker perturbations lead to a steady state on top of the sill. Regardless of the scenario, if I run it without coupling and the same initial steady state N (kept static), the uncoupled model halts retreat right away.

_Originally posted by @glugeorge in https://github.com/glugeorge/coupled_ice_hydrology/issues/3#issuecomment-1332789720_

Using the min/max of u and N, we plot different relationships between a non-dimensionalized tau and N. Based off this profile:

Here is the tau vs u plot:

[glugeorge]

Now looking at tau as a function of N, u, C, As.

It's quite interesting how both C and As play a role in changing the relationship. C has a big role in changing the order of magnitude of tau, but the general shape of how tau depends on N and u seem to rely on both As and C. These shapes also differ from the nondimensionalized "tau" that I had plotted earlier, so it might make more sense to stick to these dimensional tau plots to think about.