Stability of a western boundary current with curvature

Abstract The linear stability of an idealized western boundary current is studied with the emphasis on the effect of curvature. The barotropic quasigeostrophic vorticity equation is modified to incorporate the effect of small curvature. For eastward flow, the curvature increases the growth rate of the unstable mode that has the peak of the eigenfunction on the offshore side of the flow axis, while the growth rate of the unstable mode with its peak on the onshore side of the flow decreases. The curvature is found to shift the phase of the unstable waves, resulting in a change of the Reynolds stress, and a consequent change of the growth rate. The positive curvature enhances the dependence of the critical Reynolds number on the flow orientation. For the flow that has zero velocity on the coast, the cyclonic curvature is found to decrease the critical Reynolds number when the jet is northeastward.