If one were to force a balance in the interior with only one mode (say
the barotropic) with allowance for even modest bathymetry
then the stretching term will completely
dominate over the planetary
term and the Sverdrup regime
is destroyed in favor of topographic control. However, a single
mode analysis is clearly not appropriate for a stratified
ocean.
In the folloiwng we take the next approximation by allowing for
M modes
(barotropic and (M-1) baroclinic
modes).