Notes on “Waves and Circulation Driven by Oscillatory Winds in an Idealized Ocean Basin” by Haidvogel and Rhines (Geophys. Astrophys. Fluid Dynamics, 1983)¶

Model¶

The model resolves the nonlinear vorticity equation. This suggests that with high enough resolution, the vorticity equation should be respected.
Squared domain with 2000 km on a side.
Free-slip condition
Linear bottom friction + harmonic or biharmonic lateral friction
In the case of the open basin, the vorticity equation is decomposed into Fourier components in both x and y.
In the case of the closed basin, the vorticity equation is decomposed into Chebyshev functions in x and half-sine functions in y; in this case, biharmonic friction is not allowed.

“Whitehead (1975) showed experimentally, and Rhines (1977) showed analytically, how mean flow generation in a rotating fluid may be a general consequence of quasigeostrophic turbulent motion (eddies) on a beta-plane.” See Rhines (1977).
“Whitehead introduced oscillatory stirring at mid-depth and mid-radius in his rotating model, and observed not only transient Rossby waves, but an associated time-mean zonal flow, prograde at forced latitudes and retrograde at unforced latitudes.”