Limit Cycles and Unstable Baroclinic Waves

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Abstract
An analytical theory is presented for long-period pulsations of a finite-amplitude baroclinic wave. It is shown that for small dissipation a limit cycle is possible whether or not the steady wave regime is stable to infinitesimal disturbances. Moreover, the limit cycle is shown to be stable. A second limit cycle is shown to exist only when the steady wave regime is stable but in that case the second limit cycle is unstable. Abstract An analytical theory is presented for long-period pulsations of a finite-amplitude baroclinic wave. It is shown that for small dissipation a limit cycle is possible whether or not the steady wave regime is stable to infinitesimal disturbances. Moreover, the limit cycle is shown to be stable. A second limit cycle is shown to exist only when the steady wave regime is stable but in that case the second limit cycle is unstable.

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