Port sphere transport time-varying prescribed velocity fields

[cbegeman]

This PR ports time-varying prescribed velocity fields for the sphere transport cases:

• https://docs.e3sm.org/polaris/main/users_guide/ocean/tasks/correlated_tracers_2d.html
• https://docs.e3sm.org/polaris/main/users_guide/ocean/tasks/divergent_2d.html
• https://docs.e3sm.org/polaris/main/users_guide/ocean/tasks/nondivergent_2d.html

and provides an option for the constant prescribed velocity field in the sphere transport case:

• https://docs.e3sm.org/polaris/main/users_guide/ocean/tasks/rotation_2d.html

Checklist

• Documentation:
  • Design document has been generated and added to the docs
  • User's Guide has been updated
  • Developer's Guide has been updated
  • Documentation has been built locally and changes look as expected
• Linting
  • Pre-commit run locally
• Building
  • CMake build does not produce any new warnings from changes in this PR
• Testing
  • Add a comment to the PR titled Testing with the following:
    • Which machines CTest unit tests
      have been run on and indicate that are all passing.
    • The Polaris omega_pr test suite
      has passed, using the Polaris e3sm_submodules/Omega baseline
    • Document machine(s), compiler(s), and the build path(s) used for -p for both the baseline (Polaris e3sm_submodules/Omega) and the PR build
    • Indicate "All tests passed" or document failing tests
    • Document testing used to verify the changes including any tests that are added/modified/impacted.
    • Performance related PRs: Please include a relevant PACE experiment link documenting performance before and after.
  • New tests:
    • CTest unit tests for new features have been added per the approved design.
    • Polaris tests for new features have been added per the approved design (and included in a test suite)
• Stealth Features
  • If any stealth features are included in the PR, please confirm that they have been documented.

[overfelt]

@cbegeman
I see in MPAS-Ocean:
u = (1/twelve_days)*(10*(sin(lon_p)**2)*sin(2*lat)*cost + two_pi*coslat)
I think the factor of 10 was moved slightly. Might make a difference in time step stability if the change resulted in a larger velocity.

[cbegeman]

@overfelt Thanks for pointing that out! I'll fix and retest

[cbegeman]

@overfelt That fix seems to have resolved at least the stability issues with the divergent velocity case (top) but not the non-divergent case (bottom). I tried reducing the time step to 1s per km horizontal resolution. Only the rotation_2d has convergence with space and time refinement. Can I delegate the debugging to you?

[overfelt]

@cbegeman I'll take a look. Maybe I'll get lucky and find a difference with mpas-ocean. Maybe......

[cbegeman]

Thank you @overfelt!

[cbegeman]

After this fix and reducing the timestep, the velocity fields for MPAS-O and Omega match.

There is a significant increase in the error levels for Omega (convergence plots pending)

These are the results for the tracer fields with MPAS-O:

And these are the results with Omega:

[cbegeman]

I haven't been able to track down the reason for the discrepancy between MPAS-O's velocity field (top) and Omega's velocity field (bottom) for the divergent case. I need to pivot to other Omega work so @overfelt any time you have to look into this would be much appreciated!

It should be possible to reproduce these results using E3SM-Project/polaris#500. Let me know if you have any trouble