Fig. 4.64 An inertial solution in a model basin for two values of f.
The dynamical effects due to the nonlinear advection term can be explored through a model based on the shallow-water equation (Veronis, 1966). In his study, the model is formulated for a single-layer ocean under wind stress forcing and a linear bottom friction. The complete momentum equation also includes the time-dependent term and the nonlinear advection term d -> -> Vhp _ T
where H = const is the layer thickness. The next crucial assumption implicitly made in this model is that layer thickness perturbations remain much smaller than the undisturbed layer thickness. As a result, the continuity equation is
and we can introduce a streamfunction
The corresponding vorticity equation is
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