Nonlinear Equilibration of Barotropic Waves in a Zonally Nonuniform Current

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Abstract
In this paper, nonlinear evolution and equilibration of the barotropic waves in a zonally inhomogeneous Bickley jet are investigated. The equilibrated state consists of a full spectrum of waves with a dominant frequency and its higher-frequency modes. The dominant wave scale in most equilibrated states is wavenumber 1 because of the changes in the local mean flow. Except for wave 1, the dominant wave scale varies with the governing parameters. The wavelength of the dominant wave increases for stronger and longer jets and for weaker dissipation. The equilibrations are highly dependent on the parametric settings. Steady wavy, limit cycle, and chaotic states are found as with other nonlinear equlibration studies. When the jet is weak but strong enough to produce waves, the equilibration behaves very smoothly. But when the jet becomes stronger, the equilibration process becomes much more complicated and the subregion in parameter space for each type of solution becomes very irregular. When the streamwise length scale of the jet is short, wave activity occurs only for a range of medium values of the jet strength. Multiple equilibrium steady wave states are not found in this study, because all wave components must be cooperative in their growth rather than competitive. The examination of the local energetics shows that the generation of the local kinetic energy by the barotropic instability process is nearly cancelled by redistribution by the pressure work both in linear and nonlinear cases. The energetics further confirm that the perturbation in the steady wave state with respect to the modified mean flow behaves as a linear wave.

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