The Mindanao and Halmahera Eddies—Twin Eddies Induced by Nonlinearities
Journal of Physical Oceanography
Starting with the simple case of a nonlinear northward (southward) western boundary current (WBC) flowing along a concave solid boundary with a sharp corner on a -plane, it is shown analytically that an anticyclonic (cyclonic) eddy is established to balance the upstream momentum flux. (On an f-plane no eddy is established; similarly, no eddy is established in the linear limit.) The solution is derived by expanding the dependent variables in powers of ε 1/6 for the northward current
... urrent (anticyclonic eddy) and ε 1/2 for the southward current (cyclonic eddy). Here = R d /f 0 , where R d is the Rossby radius. It is found that, for a high Rossby number (i.e., highly nonlinear current), the length scales are R d / 1/6 and R d / 1/2 for the anticyclonic and cyclonic eddies (respectively) implying that these eddies are larger than most eddies in the ocean (which scale with R d ). The anticyclonic eddy scale is the same as that recently obtained for a WBC separating from the wall (Arruda et al. 2002) but the cyclonic eddy scale has not been obtained before. A reduced gravity numerical model is used to validate these analytical results. The balance of forces and the eddy size estimates (derived form the numerical simulations) agree with the analytical results. With the aid of the above analysis we then examine the collision of two opposing western boundary currents on a -plane. It is shown that this problem can be conceptually reduced to the above problem of two WBCs turning inside a solid corner on a -plane (where the streamline separating the two colliding currents acts like a zonal wall). We show that an eddy is established on each side of the dividing streamline. Based on the above collision problem, it is argued that the Halmahara and Mindanao eddies are required to balance the nonlinear momentum fluxes of their colliding parent currents, the southward flowing Mindanao Current (MC) and the northward flowing South Equatorial Current (SEC).