Hysteresis of a periodic or leaking western boundary current flowing by a gap

A 1.5-layer quasi-geostrophic reduced gravity model is used to study the hysteresis of a periodic or leaking western boundary current(WBC) flowing by a gap. When the periods of the WBC variations are much longer than the Rossby adjustment time scales of the circulation in the vicinity of the gap, the Hopf bifurcations during the Reincrease and Re-decrease loops are delayed to produce a new domain of hysteresis of the Reynolds numbers, and the critical Reynolds numbers of the WBC regime transitions change significantly, with the domain of the hysteresis Reynolds number larger for shorter periodic forcing. When the periods of the WBC variations are comparable to those of the Rossby adjustment time scales of the circulation in the vicinity of the gap, the WBC path inside the gap becomes periodic without hysteresis. The intrusion of the WBC into the western basin generally gets smaller as the period decreases. In addition, the partial leakage of the WBC transport through the gap into the western basin is found to have significant impact on the hysteresis loop of the WBC path when the leaked transport is larger than 1/2 of the WBC. Both the intrusion extent and the critical Reynolds numbers of the WBC regime transition are changed, and the larger the throughflow transport, the larger the change.