A Numerical Study of Baroclinic Instability at Large Supereriticality

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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... 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...

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