The Effect of Beta on the Downstream Development of Unstable, Chaotic Baroclinic Waves

The weakly unstable, two-layer model of baroclinic instability is studied in a configuration in which the flow is perturbed at the inflow section of a channel by a slow and periodic perturbation. In a parameter regime where the governing equation would be the Lorenz equations for chaos if the development occurs only in time, the solution behavior becomes considerably more complex as a function of time and downstream coordinate. In the absence of the beta effect it has earlier been shown that the chaotic behavior along characteristics renders the solution nearly discontinuous in the slow downstream coordinate of the asymptotic model. The additional presence of the beta effect, although expunging the chaos for large enough values of the beta parameter, also provides an additional mechanism for abrupt spatial change.