The nonlinear behavior of varicose disturbances in a simple model of the Gulf Stream
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The behavior of varicose (width-altering) and mixed (sinuous-varicose) disturbances to an equivalent barotropic, f-plane jet is examined using analytical and numerical techniques. Specifically, we show that long waves are subject to nonlinear steepening, and we follow the evolution of such disturbances past the point of wave-breaking using the method of contour dynamics. Depending on the potential vorticity structure of the model, quantified by a parameter r, and on the amplitude of the initial wave, a variety of effects are produced including undular bores, ejected filaments, detaching eddies, and aneurisms. Most significantly, we show that r values in the range thought appropriate to the Gulf Stream produce detached eddies similar in appearance to “warm outbreaks”. Measurements of the propagation speed of Gulf Stream width values using satellite imagery support the prediction of wave steepening at long wavelengths.