Limit Cycles and Unstable Baroclinic Waves

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.