The Effect of β on the Chaotic Behavior of Unstable Baroclinic Waves

The role of β in the finite-amplitude dynamics of unstable baroclinic waves is studied with particular attention directed to its effect on the phenomenon of chaotic amplitude behavior. When the β effect is relatively small compared to the potential vorticity gradient of the basic shear flow analytical methods are easily able to yield the structure of the evolution dynamics of a slightly unstable baroclinic wave. The theory shows that even small planetary vorticity gradients lead to dramatic smoothing of the amplitude dynamics. As β increases (relatively) chaotic behavior gives way, through a sequence of period halvings, to regular steady waves.