On surface gravity waves crossing weak current jets

Variations in wave amplitude and steepness across current jets have been described for broad smooth-sided jets. Here, narrow jets are modelled by a top-hat pattern; an approximate solution is found for linear waves, based on conservation of wave action and vertical averaging. The results join remarkably well to those for a broad cosine-shaped jet (cf. McKee 1975). For jet widths less than about a third of a wavelength, there is little change in amplitude; the enhancement predicted by a WKB analysis is suppressed owing to interference with reflections from the far side of the jet. For directional spectra not too different from cos2 θ, some suppression occurs near the middle of jets of all scales, owing to exclusion of the glancing wave components by reflection from the near side; this suppression can be significant for jets more than a wavelength wide. For monochromatic waves, maximum amplitudes occur some distance outside the jet owing to interference; the net reflection appears to have a positive phase shift along the near caustic of about ¼ cycle.