A Numerical Study of Baroclinic Instability at Large Supereriticality

Abstract

A series of numerical integrations of the two-layer quasi-geostrophic model were carried out to investigate the nonlinear dynamics of baroclinically unstable waves at supercriticalities of O(1). The results extend and are contrasted with the results of weakly nonlinear theory valid only for small supercriticality. Particular attention is paid to that sector of parameter space in which the transition from regular to aperiodic behavior is observed for weakly nonlinear waves. It is found that aperiodic, chaotic behavior extends to parameter domains of higher dissipation as a consequence of finite amplitude effects as the supercriticality increases. Sensitive dependence on parameters remains a hallmark of the system as intervals of chaotic, periodic and steady solutions are observed. For the supercriticality of O(1) a new stable periodic vacillation is observed. As the supercriticality is increased the system appears to ?stiffen? nonlinearly, e.g., wave amplitudes in the steady state are smaller than predicted by weakly nonlinear scaling arguments. This stiffening can be explained in terms of the dynamics of a truncated system. However, the truncated system appears always to overestimate the domain of chaotic behavior since it misrepresents a subtle effect of the higher harmonics on the process of wave-mean flow interaction. At much higher supercriticality (e.g., four times critical) where many waves are unstable, it is found that the linearly most unstable wave gives way to a longer, less unstable wave which conies to dominate the solution in qualitative agreement with the predictions of weakly nonlinear theory. In all cases, in order to separate truly nonlinear effects store the parametric variations already present in asymptotic weakly nonlinear theory calculations described here were done for increasing supercriticality at a fixed value of ?&equals (linear efolding time)/(spinup time) the numerator of which decreases with increasing supercriticality. Hence in our presentation at larger supercriticality the friction is also greater.