Hydraulic control and wave adjustment in a channel+plateau system: Deep Western Boundary Current passing through the Samoan Passage

Abstract:

Cold and dense waters originated in the polar areas form a deep western boundary current (DWBC), which flows meridionally towards lower latitudes and sometimes encounters such a topographic feature that multiple passages connect two ocean basins. In particular, for cases where there are two passages and the western passage is narrow and contains sills while the eastern passage is broad, it is possible that the flow in the western channel is hydraulically controlled and contains dissipative hydraulic jumps but the flow passing the eastern passage is not controlled. An imbalance in energy between the branches of the flow arises downstream of the passages if the flow is inviscid, as assumed by most hydraulic theories. Furthermore, a Kelvin wave may travel along the western boundary of the eastern passage and invade the western channel from downstream, which may cause the failure of hydraulic control. These put a question mark on whether the historical hydraulic formulations that are based on the assumption of two ocean basins connected by a single passage are valid. To gain insights into these mysteries, we first extend a formulation originally from Gill (1977) to estimate the transport partitioning of a single-layer western boundary current with uniform potential vorticity (PV) between a narrow western channel (rectangular or parabolic) and a broad eastern passage. The only upstream information needed is the total transport of the inflow. Its application to the Samoan Passage has shown results comparable to observations. We then employ a numerical model and tune the external friction. By introducing bottom friction in the eastern passage, where the uncontrolled flow features a western boundary current, a steady-state hydraulic control of the flow in the western channel is established. In this case, the frictional energy dissipation of the boundary flow in the eastern passage balances the implicit energy dissipation in the hydraulic jumps in the western channel, or to say, the Kelvin waves that tend to invade the western channel have been damped out.