On inertial instability of the equatorial undercurrent

Hughes (1979, Tellus 31, 447–455) has noted that given a particular distribution of potential vorticity with stream function, it may theoretically be possible to have two forms for the equatorial undercurrent. As the vertical thickness of the layer, through which the undercurrent is flowing, decreases the undercurrents approach each other in form until a critical thickness is reached at which the undercurrent forms coalesce. The present study considers the behaviour of a slowly moving, long wavelength, small amplitude symmetric wave disturbance in the presence of an undercurrent of near coalescent form. It is shown that the narrower of the undercurrents is inertially unstable and subcritical to a Kelvin-like disturbance. The wider of the undercurrents is inertially stable and supercritical to such a disturbance. High mode Rossby waves are only slightly affected by the equatorially confined undercurrent.