…nanigans.jl into ncc-glw/cubed-sphere-dynamics

(a) Fixed a bug in the filling of south-west corner halos of odd panels;

(b) Filled south-east corner halos of odd panels and north-west corner halos of
    even panels.

Filled the north-west corner halos of odd panels and the south-east corner halos
of even panels.

Integrated the modification of the script src/Operators/vorticity_operators.jl
from commit 55355d9 on branch sb-ncc/cubed-sphere-corner-vorticity.

…nanigans.jl into cubed-sphere-dynamics

…nanigans.jl into ncc-glw/cubed-sphere-dynamics

(a) Overwrote vorticity computation in the validation script
    validation/multi_region/cubed_sphere_vorticity.jl
    using only interior points.

(b) The vorticity field looks fine now.

Compare vorticity values against those generated by MITgcm.

Plot the initial zonal and meridional velocities for Oceananigans and the
difference w.r.t. their MITgcm counterparts.

Added lines of code to understand how the cubed sphere grid from the solid body
test case of MITgcm is related to the cubed sphere grid used in Oceananigans.
After all, it only makes sense to compare the output from two different models
on the same grid.

Executed the MITgcm solid body rotation test case on the grid configuration used
by Oceananigans, followed by an equivalent test run in Oceananigans for direct
output comparison. Observed differences in model outputs are now significantly
reduced, aligning with expectations. Notably, the greatest discrepancies are
located at the corners of certain cubed sphere panels.

…nanigans.jl into cubed-sphere-dynamics

…nanigans.jl into ncc-glw/cubed-sphere-dynamics

(a) Adjusted initial surface elevation to ensure unit consistency;

(b) Expanded visualization options.

Imported changes from commit 99940c8 of origin/ss-sb/implicit-free-surface.

Resolved color range specification bug and renamed functions for clarity in the
visualization script validation/multi_region/cubed_sphere_visualization.jl.

Filled velocity halos in non-existent corner regions of the cubed sphere panels
for the implicit free surface solver in the script
src/Models/HydrostaticFreeSurfaceModels/implicit_free_surface.jl.

Plotted the initial velocity fields with and without halos, alongside the
initial vorticity field with halos. The observed discrepancies along the domain
boundaries in the vorticity field suggest potential issues with the current
implementation of velocity halo filling.

Commented out debug-specific lines of code in
src/Operators/vorticity_operators.jl.
These lines, originally introduced for debugging, were inadvertently overriding
the computed vorticity values, potentially leading to incorrect outcomes.

This commit introduces the initial setup for the Rossby-Haurwitz test case.
Currently, the simulation has not been executed; this commit only defines the
initial conditions. This setup is intended for comparison with the earlier
working version 0.82.0 to verify accurate halo filling and to ensure the initial
vorticity field values are correct.

This update involves streamlining the code by commenting out unnecessary lines
and employing more straightforward u and v velocity assignments. Moreover, a
smaller interior horizontal mesh, consisting of 5x5 cells, is used. The zonal
velocity (u) is assigned a unique value in each panel using lexicographic
ordering of the cells. Correspondingly, the meridional velocity (v) at indices
(i, j) is set to be the negative of u at these indices, i.e. v[i, j] = -u[i, j].
These changes are primarily implemented to facilitate more effective debugging.