Add EquatorialLatitudeLongitudeGrid

[francispoulin]

Summary

This PR introduces an EquatorialLatitudeLongitudeGrid
for Oceananigans.

The coordinate singularities are relocated to the tropics
while preserving an orthogonal spherical coordinate system.

Current Status

Completed

• Grid construction
• Metric implementation
• Tracer initialization
• Uniform x-advection validation
• Uniform y-advection validation
• Combined x-y advection validation
• Resolution studies (64², 128², 256²)

Remaining Work

Physics

• Coriolis operator
• Momentum equations
• Pressure-gradient terms
• Geostrophic balance

Validation

• GPU validation
• Solid-body rotation
• Vortex transport tests

Validation Results

Grid	N	Peak
LLC	64	1.164
LLC	128	1.168
LLC	256	1.169
ELLC	64	0.997
ELLC	128	1.000
ELLC	256	1.000

Initial Profiles

Final Profiles

Reviewer Feedback Requested

• Any of your thoughts and/or suggestions are welcome.

[glwagner]

We don't need a new grid for this. Instead, you can use RotatedLatitudeLongitudeGrid, which builds OrthogonalSphericalShellGrid. Importantly, OrthogonalSphericalShellGrid is a fully general grid, so there is fundamentally no need for any more than this.

[navidcy]

You can get a grid with the singularities on the equator e.g. via

julia> using Oceananigans

julia> grid = RotatedLatitudeLongitudeGrid(; size = (24, 6, 5), latitude = (-90, 90), longitude=(0, 360), z=(-100, 0), north_pole = (0, 0))
24×6×5 OrthogonalSphericalShellGrid{Float64, Periodic, Bounded, Bounded} on CPU with 3×3×3 halo
├── centered at: North Pole, (λ, φ) = (116.565, 90.0)
├── longitude: Periodic  extent 360.0 degrees variably spaced with min(Δλ)=9.18485e-16, max(Δλ)=15.0
├── latitude:  Bounded  extent 180.0 degrees  variably spaced with min(Δφ)=30.0, max(Δφ)=30.0
└── z:         Bounded  z ∈ [-100.0, 0.0]     regularly spaced with Δz=20.0