We study a hysteresis western boundary current (WBC) flowing across a gap impinged by a mesoscale eddy, with an island of variable meridional size in the gap, using a 1.5-layer ocean model. The hysteresis curves suggest the island with a larger size facilitates the WBC intrusion by shedding the eddy more easily. Both anticyclonic and cyclonic eddies are able to induce the critical WBC transition from penetration regime to leap regime, and vice versa. The vorticity balance analysis indicates increased (decreased) meridional advection that induces the critical WBC shifting from the eddy shedding (leaping) regime to the leaping (eddy shedding) regime. The meridional size of the island significantly affects the critical WBC transition in terms of the critical strength of the mesoscale eddy. The regime shift from penetration to leap is most sensitive to the eddy upstream of the WBC for small islands and most sensitive to the southern anticyclonic eddy and northern cyclonic eddy for moderate and large islands. It is least sensitive to the central cyclonic eddy for small islands and to the cyclonic eddy upstream of the WBC for moderate and large islands and to the northern anticyclonic eddy regardless of island size. The regime shift from leap to penetration is most sensitive to the cyclonic eddy upstream of the WBC and to the northern anticyclonic eddy. It is least sensitive to the anticyclonic eddy from the south, and the least sensitive location of the cyclonic eddy shifts northward from the gap center as the island size increases.
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