On the Time-Dependent Meandering of a Thin Jet

Abstract A thin-jet model predicts the location of the axis of a strong current such as the Gulf Stream by using the vertical and cross-stream integrated vorticity balance, under the assumption that the meandering scales are large compared to the width of the jet. We demonstrate that such an integral provides a matching condition upon the barotropic component of the wave or eddy fields which, on either side of the jet, have north–south scales on the order of the meander wavelength. For steady meanders, these exterior fields do not influence the path and our model reproduces the dynamics of Robinson and Niiler, but for the transient case the determination of the jet axis motion and of the external field is a coupled problem. When the disturbances in the axis position are time-dependent but are very small, the exterior wave problem can be linearized and the matching conditions can be applied at the mean position of the jet. We can therefore derive a dispersion relation for the meandering motion, allowing us...