Model Overview
QGYBJ+.jl simulates the interaction between mesoscale eddies and near-inertial waves.
The Two Components
| Component | Variable | Scale | Dynamics |
|---|---|---|---|
| Eddies | ψ (streamfunction) | 50-200 km, weeks | Advection of PV |
| Waves | B (wave envelope) | 10-50 km, hours | Advection + refraction |
Interactions: Eddies refract waves (focusing in anticyclones); waves feed energy back to eddies.
Governing Equations
QG Potential Vorticity
\[\frac{\partial q}{\partial t} + J(\psi, q) + J(\psi, q^w) = \text{dissipation}\]
where $q = \nabla^2\psi + \frac{f_0^2}{N^2}\frac{\partial^2\psi}{\partial z^2}$
YBJ+ Wave Envelope
\[\frac{\partial B}{\partial t} + J(\psi, B) = i\frac{k_h^2}{2 \cdot Bu \cdot Ro} A + \frac{1}{2}\zeta B + \text{dissipation}\]
where $B = L^+ A$ and A is recovered via elliptic inversion.
Physical Processes
| Process | Term | Effect |
|---|---|---|
| Advection | $J(\psi, B)$ | Waves carried by flow |
| Refraction | $\frac{1}{2}\zeta B$ | Waves focus in anticyclones |
| Dispersion | $i k_h^2 A$ | Horizontal spreading |
Effective frequency $f_{\text{eff}} = f_0 + \zeta/2$. In anticyclones (ζ < 0), waves slow and accumulate.
Variables
| Type | Variables |
|---|---|
| Prognostic | q (potential vorticity), B (wave envelope) |
| Diagnostic | ψ (from q), A (from B), u, v (from ψ) |
Boundary Conditions
- Horizontal: Doubly periodic
- Vertical: Rigid lid (w=0 at z=0, z=-Lz), no-flux (∂ψ/∂z=0)