Abstract
A low-order model of the unforced, inviscid barotropic model is examined as a dynamical system. Analytic solutions, consisting of linear and nonlinear oscillations (Rossby waves), are obtained in appropriate limiting initial conditions. These solutions are periodic. With less restrictive initial conditions the system shows quasi-periodic behaviour at low energies and chaotic behviour at high energies. This transition is accompanied by frequency-locking and period-doubling. Quasi-periodic and chaotic behaviour may coexist in phase space for the same values of the model invariants. The results are interpreted in terms of perturbed integrable Hamiltonian systems. Considerations of the low-frequency variability of the atmosphere are also made.
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