Abstract
A low-order model is used to study the behavior of large-scale planetary waves arising from the baroclinic instability of an east-west zonal wind that includes a weak modulation in time. The finite-amplitude equilibration model is equivalent to the modulated Lorenz equations, containing an externally forced time-periodic Rayleigh parameter. Without modulation the baroclinic instabilities equilibrate to steady waves for all values of the external parameters reasonably near the linear neutral curve. However, a small modulation with a period of the same order as the internal dynamical timescale can completely destabilize the non-linear system, leading to chaotic solutions even for small supercriticality. Low-frequency seasonal modulations give rise to tori in the solution phase space. As the amplitude of the periodic forcing increases to about 10% of the average zonal wind shear, the tori break up and chaotic orbits are again found. This latter behavior is interpreted by studying the effect of seasonal forcing on the adiabatic invariants of the system.
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