## Abstract

The theory of quasigeostrophic motion developed in previous chapters required several conditions for its validity. Foremost, of course, was the condition that the time scale of the motion is large compared to *f* ^{ - } ^{1}. This is not always sufficient, as the discussion of the Kelvin wave in Section 3.9 indicated. When the wavelength of the Kelvin wave is long compared to the deformation radius, the frequency is small compared to *f*. Yet the equation of motion in the direction along the boundary does not reduce to geostrophic balance. A longshore* pressure gradient exists and is balanced by the acceleration of the longshore velocity, and the onshore flow is identically zero. This result is not inconsistent with the quasigeostrophic theory developed previously, for in the quasigeostrophic dynamics so far considered, we have assumed that there existed only a single horizontal scale for the motion, i.e., that the scaling of the motion is isotropic horizontally. The low-frequency Kelvin wave is not horizontally isotropic, since its offshore scale is the deformation radius, which for low frequencies is small compared with the wavelength. In this chapter we consider some of the refinements to quasigeostrophic theory that are required when the motion is strongly anisotropic.

### Keywords

Vortex Ozone Stratification Vorticity Advection## Preview

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