98-361 Duan, J. , Holm, D. D. and Li, K.

Variational Methods and Nonlinear Quasigeostrophic Waves (943K, PostScript File) May 25, 98

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Abstract. In this paper, the authors discuss the zonally periodic steady quasigeostrophic waves in a $\beta-$plane channel, by using variational methods. A class of steady quasigeostrophic waves are determined by the potential vorticity field profile, $g(\cdot)$, which is a function of the stream function. They show that zonally periodic steady quasigeostrophic waves exist when the bottom topography and the potential vorticity field are bounded. They also show that these waves are unique if, in addition, the potential vorticity field profile is increasing and passes through the origin. Finally, they show that the zonal periodic wave in the case with $g(\psi)=\arctan(\psi)$ is nonlinearly stable in the sense of Liapunov, under a boundedness condition for the potential vorticity field for this zonal periodic wave, or equivalently, under suitable conditions on the bottom topography, $\beta$ parameter, and zonal period $T$.

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