A unified formulation of the instability of a mean zonal flow with uniform shear is proposed, which includes both the coupled density front and the coastal current. The unified formulation shows that the previously found instability of the coupled density front on the f-plane has natural extension to coastal currents, where the instability exists provided that the net transport of the current is sufficiently small. This extension of the coupled front instability to coastal currents implies that the instability originates from the interaction between Inertia-Gravity waves and a vorticity edge wave and not from the interaction of the two edge waves that exist at the two free streamlines due to the Potential Vorticity jump there. The present study also extends these instabilities to the β-plane and shows that β slightly destabilizes the currents by adding instabilities in wavelength ranges that are stable on the f-plane but has little effect on the growthrates in wavelength ranges that are unstable on the f-plane. An application of the β-plane instability theory to the generation of rings in the retroflection region of the Agulhas Current yields a very fast perturbation growth of the scale of 1 day and this fast growth rate is consistent with the observation that at any given time, as many as 10 Agulhas rings can exist in this region.
Paldor, Nathan, Yona Dvorkin, and Doron Nof. 2011. "Linear instability of uniform shear zonal currents on the β-plane." Journal of Marine Research 69, (4). https://elischolar.library.yale.edu/journal_of_marine_research/323