Hydraulic control of flow in a multi-passage system connecting two basins

When a fluid stream in a conduit splits in order to pass around an obstruction, it is possible that one branch will be critically controlled while the other remains not so. This is apparently the situation in Pacific Ocean abyssal circulation, where most of the northward flow of Antarctic bottom water passes through the Samoan Passage, where it is hydraulically controlled, while the remainder is diverted around the Manihiki Plateau and is not controlled. These observations raise a number of questions concerning the dynamics necessary to support such a regime in the steady state, the nature of upstream influence and the usefulness of rotating hydraulic theory to predict the partitioning of volume transport between the two paths, which assumes the controlled branch is inviscid. Through the use of a theory for constant potential vorticity flow and accompanying numerical model, we show that a steady-state regime similar to what is observed is dynamically possible provided that sufficient bottom friction is present in the uncontrolled branch. In this case, the upstream influence that typically exists for rotating channel flow is transformed into influence into how the flow is partitioned. As a result, the partitioning of volume flux can still be reasonably well predicted with an inviscid theory that exploits the lack of upstream influence.

Automated summary

When a fluid stream splits to pass around an obstruction, one branch may be controlled while the other is not. This phenomenon is observed in the Pacific Ocean abyssal circulation, where most of the southward flow of Antarctic bottom water is controlled by the Samoan Passage, while the rest flows around the Manihiki Plateau without control. This raises questions about the dynamics involved in maintaining this regime, the influence of upstream factors, and the accuracy of hydraulic theory in predicting the distribution of flow. Through theoretical analysis and numerical modeling, it is shown that a steady-state regime similar to the observed circulation can be achieved if the uncontrolled branch experiences sufficient bottom friction.