jejjohnson / jejjohnson/spectraldiffx

Barotropic Vorticity Equation (on Plane or Sphere)

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Python
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Description

### Formulation
2D barotropic vorticity equation, pedagogical model for Rossby waves.

#### Governing Equation:
$$
\frac{\partial \zeta}{\partial t} + J(\psi, \zeta + f) = 0
$$
where $\zeta$ is relative vorticity, $\psi$ is streamfunction, $f$ is Coriolis parameter.

#### Forcing
- None (classic), or beta-plane ($f = f_0 + \beta y$)

#### Starter code
```python
# Grid setup
Nx, Ny = 128, 128
Lx, Ly = 2 * math.pi, 2 * math.pi
grid = FourierGrid2D.from_N_L(Nx=Nx, Ny=Ny, Lx=Lx, Ly=Ly)
psi = ...
zeta = laplacian(psi)

for t in timeline:
dzdt = -jacobian(psi, zeta + f)
```

#### Dependencies
- [nlocked by] PR: Spherical harmonics infrastructure (for sphere)

#### Reference: Salmon, Lectures on Geophysical Fluid Dynamics.

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