Notes:
The last lecture we saw how conservation of potential vorticity governs the evolution of flows in the ocean. What can we learn from vorticity about the steady, large-scale circulation using vorticity?
Sverdrup combined geostrophy with Ekman dynamics to find a powerful relation for the size and pattern of ocean's circulation in response to the winds. We are going to derive Sverdrup's balance by first considering the geostrophic interior and the frictional surface boundary layer (Ekman layer) separately, in order to highlight how these two regimes couple to form an ocean gyre.
Initially, we cross differentiate the u and v momentum equations as we did in last class, but this time we assume a steady state:
Cross-differentiating:
Again we cross-differentiate these equations:
We can combine the Ekman and geostrophic layers very simply by looking at the two vorticity equations we have.
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