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I am reading an Oceanography Textbook which explains that in the ocean, planetary vorticity tends to be much larger than relative vorticity therefore, the potential vorticity can be simplified to be f/H.

"This requires that the flow in an ocean of constant depth be zonal."

"...in general, currents tend to be east-west rather than north south. Wind makes small changes in relative vorticity, leading to a small meridional component to the flow."

If planetary vorticity is far larger than relative vorticity, how exactly do changes in f (planetary vorticity) cause ocean flow to be more zonal?

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    $\begingroup$ I try to reason it out, but other than hand-waving it to being different rotation speed -> different fluid movement rates... or thinking along the lines of meteorology, where the geostrophic wind equation of steady stead reduces to $u=-1/(f\rho) \cdot dP/dy$ (and $v=1/(f\rho) \cdot dP/dy$), and because the large-scale temperature is N/S, the greater pressure variation as a whole is N/S, leading to a heavily zonal wind overall. But not sure either of those cut it for your question... $\endgroup$
    – JeopardyTempest
    May 24, 2017 at 0:12
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    $\begingroup$ Perhaps you should post of preceding text, as often in textbook derivations they'll be quietly alluding back to some information in a recent discussion without explicitly explaining it. Or perhaps this meteorologist just isn't enough help in the water where things like salinity show their strange head! $\endgroup$
    – JeopardyTempest
    May 24, 2017 at 0:12
  • $\begingroup$ Most of the answer is wind curl. $\endgroup$
    – arkaia
    May 24, 2017 at 15:17

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It is more of a consistency argument: if a constant-depth ocean with much less relative vorticity than planetary vorticity is to stay that way, the flow must be zonal.

If there were significant meridional velocities, they would cause significant meridional displacements of water masses, which would then, by conservation of angular momentum, no longer have small relative vorticity. (Same angular momentum and same depth means same absolute vorticity. Different planetary vorticity then means different [in the opposite direction] relative vorticity. If planetary vorticity was zero before the displacement, it isn't anymore afterward.)

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    $\begingroup$ Welcome to SE. Nice answer. $\endgroup$
    – gansub
    Jan 18, 2018 at 9:22

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