On the Flow Through Broad Gaps with Application to the Windward Passage

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Abstract
The flow through broad passage connecting oceans and marginal seas is examined by a simplified two-layer analytical model. Attention is focused on the flow resulting from the difference between the upper layer depth in the two basis which imposes a pressure gradient along the passage. The land masses separating the ocean from the adjacent marginal sea are represented by two portions of an infinitely long wall extending from the free surface to the bottom of the ocean. The passage, whose width is larger than the deformation radius, is represented by a gap separating the two portions of the wall. The model is frictionless, hydrostatic and nondiffusive but the movements within the gap are not constrained to be quasi-geostrophic in the sense that the local Rossby number is not necessarily small and the interface displacements are of the same order as the upper layer depth. Steady solutions for the upstream and downstream fields are obtained analytically using the momentum equation in an integrated form, the Bernoulli integral and conservation of potential vorticity. It is found that, surprisingly, the transport through the gap is independent of the gap's width. Upstream the oceanic water approaches the gap only from one direction; upon reaching the gap, the approaching current splits into two branches. One continues to flow in the oceanic basin and never enters the gap whereas the other passes through the gap and penetrates into the marginal sea. Downstream, the pentrating flow forms a boundary current which is confined between the wall on the right (looking downstream) and a free bounding streamline on the left. A possible application of this theory to the flow from the Atlantic Ocean into the Caribbean Sea via the Windward Passage is discussed. The observed locations, positions and directions of both upstream and downstream flows agree with the model predictions. In addition, the predicted transport through the passage (∼12 × 106 m3 s−1) is approximately equal to the observed transport.

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