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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.

Forcing

  • Isolated Gaussian 200-km wide oscillatory wind pattern.
  • No net vorticity input in the basin-averaged sense: Is this important?

Notes

  • “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.”

References to check

  • Rhines (1977)
  • Colin de Verdiere (1979)
  • McEwan et al. (1981)