Rossby wave generation of poleward propagating Kelvin waves : the midlatitude quasigeostrophic approximation

The phenomenon of Rossby wave generation by poleward propagating baroclinic coastal Kelvin waves is discussed in the low-frequency quasigeostrophic (QG) limit. The response of the system is divided into three frequency regimes: a low-frequency regime (longer than annual periods) for which the previously studied long-wave models are quite accurate, a high-frequency regime (semiannual or shorter) for which the Kelvin waves are coastally trapped (and thus of negligible importance to the interior), and an intermediate regime for which dispersive effects are important to the scattering process. It is shown that the retention of the y dependence of the radius of deformation in a locally 1D, QG model is necessary and sufficient to describe the dominant energy flux out of the coastal waveguide for all three of these frequency regimes. This Rossby wave energy flux directly determines the interior Rossby wave amplitudes and modifies the evolution of the Kelvin wave amplitude along the coast. The result of the application of a QG midlatitude beta -plane model to this scattering process is contrasted with more accurate results from the locally 1D QG model and from a generalized QG model (which retains the linear variation of Coriolis force with latitude in all terms). A direct numerical simulation of the reduced-gravity shallow-water equations is used as a reference. It is shown that the traditional assumption of constant deformation radius in QG models causes O(1) errors in the Rossby wave response in the interior, and somewhat smaller errors in the prediction of the changes in the coastal Kelvin wave amplitude.