WVBetaPlanePVAdvection

Advection of QGPV from beta

---

Declaration

 WVBetaPlanePVAdvection < [WVForcing](/classes/wvforcing/)

Discussion

This applies \(\beta v_g\) to the PV (A0) flux of a simulation.

### Usage

Assuming there is a WVTransform instance wvt, to add this forcing,

  wvt.addForcing(WVBetaPlanePVAdvection(wvt));

### Notes

This may not be justified for a hydrostatic or Boussinesq flow, but it works.

A doubly-periodic domain with \(\beta\) has a different \(f\) at the northern and southern boundary. This is fine for quasigeostrophic dynamics, which only cares about the gradient of \(f\), but is not okay for internal waves. However, because the wave-vortex model evolves coupled QG-wave equations in the spectral domain, we can add this effect to only the PV part of the flow. I suspect this is actually justifiable with the correct asymptotics. – Jeffrey