Thus, velocity is basically unchanged if the initial width of the jet is much smaller than the radius of deformation.
b) If b/X » 1 the approximate solution is in the following forms u (0) = Uoe-b/X « 0
Thus, if the initial velocity jet is much wider than the deformation radius, the velocity field is totally destroyed. As will be shown later, the final state after geostrophic adjustment depends on the horizontal scale of the initial perturbations.
This approach has been extended to multi-layer models, such as the geostrophic adjustment associated with density fronts and currents. In such cases, there are the barotropic mode and the baroclinic modes; each mode has its own phase speed and plays different roles in the geostrophic adjustment.
Application to a finite step in free surface Another interesting application of this technique is the case with an initial step in the sea surface elevation and an ocean at rest (Fig. 4.92). Since the initial velocity is zero, Eqn. (4.461) is reduced to d2 Yn Yn dy2
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