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The Analytical Derivation of Rossby Waves

Consider the flow of fluid of constant depth on a latitudinal circle.
On the latitudinal circle the relative vorticity ζ is zero but if the
flow deviates from the latitudinal circle by an amount δy then
a nonzero relative vorticity will develop to conserve absolute vorticity η.
Along the path of the fluid flow η at time t_{1} is the
same as η at t_{0}. Since η=ζ+f it follows that
if ζ at t_{0} is zero then