Does the Ulleung eddy owe its existence to β and nonlinearities?

Abstract

A nonlinear theory for the generation of the Ulleung Warm Eddy (UWE) is proposed. Using the nonlinear reduced gravity (shallow water) equations, it is shown analytically that the eddy is established in order to balance the northward momentum flux (i.e., the flow force) 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 imparted by the separating East Korean Warm Current (EKWC). It is found that, for a high Rossby number EKWC (i.e., highly nonlinear current), the eddy radius is roughly 2 R d / ε 1 / 6 (here ε ≡ β R d / f 0 , where R d is the Rossby radius), implying that the UWE has a scale larger than that of most eddies ( R d). This solution suggests that, 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. The solution also suggests that a weak WBC does not produce an eddy (due to the absence of nonlinearity). A reduced gravity numerical model is used to further analyze the relationship between β , nonlinearity and the eddy formation. First, we show that a high Rossby number WBC which is forced to separate from the wall on an f plane does not produce an eddy near the separation. To balance the northward momentum force imparted by the nonlinear boundary current, the f plane system moves constantly offshore, producing a southward Coriolis force. We then show that, as β is introduced to the problem, an anticyclonic eddy is formed. The numerical balance of forces shows that, as suggested by the analytical reasoning, the southward force produced by the eddy balances the northward flow force imparted by the boundary current. We also found that the observed eddy scale in the Japan/East Sea agrees with the analytical estimate for a nonlinear current.