Eddies along western boundaries

The Ulleung eddy owes its existence to β and nonlinearities . A nonlinear theory for the Ulleung Warm Eddy (UWE) in the Japan/East Sea is proposed. Using the nonlinear reduced gravity (shallow water) equations, it is shown analytically and numerically that the eddy is established in order to balance the northward momentum flux exerted by the separating western boundary current (WBC). In this scenario the presence of β produces a southward (eddy) force balancing the northward momentum flux of the separating East Korea Warm Current.; In contrast to the familiar idea attributing the formation of eddies to instabilities (i.e., the breakdown of a known steady solution), the UWE is an integral part of the steady stable solution.; On an f-plane no eddy is produced. To balance the northward momentum force imparted by the nonlinear WBC the f-plane system moves offshore producing a southward Coriolis force. We also found that the observed UWE scale agrees with the analytical and numerical estimates.; The Mindanao and Halmahera eddies are due to the bending of their parent currents, nonlinearities and β. Starting with the simple case of a northward (southward) WBC flowing along a concave solid boundary with a sharp corner on an β-plane, it is shown that an anticyclonic (cyclonic) eddy is established to balance the upstream momentum flux. (On an f-plane no eddy is established because a pressure force which balances the WBC momentum flux is generated.) With the aid of the above analysis we then examine the collision of two opposing WBCs on a β-plane. It is shown that this problem can be conceptually reduced to the above problem of two WBCs turning in a solid corner on a β-plane where the streamline separating the two colliding currents acts like a “zonal wall.” We show that an eddy is established (to balance the momentum flux of the respective WBC) on each side of the dividing streamline.; Based on the collision problem, an explanation for the Mindanao and Halmahera eddies in the equatorial western Pacific is proposed. It is argued that these eddies are required to balance the nonlinear momentum fluxes of their colliding parent currents, the southward flowing Mindanao Current and the northward flowing South Equatorial Current.