The Interaction of an Eddy with an Unstable Jet
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Interactions between an unstable jet and eddy are explored using a jet with piecewise constant potential vorticity. A linear theory is developed for the case where the jet is nearly zonal and the eddy is far away in the sense that the eddy may be replaced by a point vortex that induces velocity perturbations in the jet small compared with the maximum jet velocity. The calculations are extended into the nonlinear domain by the method of contour dynamics. Specific examples of barotropic and equivalent barotropic jets are discussed, with particular attention to processes leading to eddy propagation. In the barotropic case, long-range eddy-jet interactions are dominated by the jet instability, which breaks the jet up into eddies downstream from the forcing eddy. For a forcing eddy south of an unperturbed eastward flowing jet, the initial eddy propagation tendency is southwestward (SW) for cyclones and northeastward (NE) for anticyclones. In the equivalent barotropic case, the fact that long waves in the jet are neutrally stable modifies the interaction considerably. The instability triggered by the eddy may be advected downstream rapidly enough that it does not affect the eddy. A long wavelength, steady lee wave may develop downstream from the forcing eddy, and this results in a propagation of the eddy in the opposite direction from the barotropic case (NE for cyclones, SW for anticyclones). Short-range interactions tend to be strongly nonlinear and can result in stripping of fluid from the edge of the jet. The detached fluid and eddy can then propagate as a vortex pair away from the jet, and the whole process therefore inhibits absorption of eddies by the jet. Some Gulf Stream warm outbreaks may result from such interactions.