#### Abstract

The classical question of how much water flows from one ocean to the other via connecting passages is addressed with a nonlinear analytical model. The focus is on gaps that are too broad to be influenced by the so-called “hydraulic control” and yet too narrow to allow free (“unchoked”) flow through them. We consider two rectangular oceanic basins, one containing a light upper layer overlying a slightly heavier deep layer and the other containing only one layer of fluid (whose density is identical to that of the lower fluid in the first basin). The basins are separated by a thin wall containing a gap which is initially blocked by a gate. All fluids are initially at rest and the pressure exerted on the gate corresponds to a sea-level difference (between the two basins) that is set up by the wind field. The conceptual gate is then removed and the resulting nonlinear flow from the inner basin to the outer basin is computed. The final steady state is taken to be analogous to the actual oceanic situation. The analytical calculations are based on an integrated momentum constraint which allows computation of the mass flow through the gap without solving for the rather complicated nonlinear flow within the gap itself and in its immediate vicinity. It is found that the sea-level difference between the oceans drives a nonlinear flow (i.e., high amplitude and large Rossby number flow) parallel to the separating wall. Surprisingly, only about 40% of the generated upstream flow enters the gap. The remaining transport stays in the inner basin. A simple “gap formula” which enables one to compute the nonlinear transport via the gap is derived. In terms of the sea-level difference, the transport is [g′H2/2f0](1 − 1/e)2, where H is the undisturbed upper layer depth in the inner basin and the remaining notation is conventional. For the special case of no wind stress curl above the inner basin and no significant western boundary current, it is possible to relate the transport directly to the wind field. One finds that, for this particular case, the transport is independent of the stratification and is given by 0.3996 ∫0L τs(x) dx/f, where L is the width of the inner basin, τ(x) s the zonal wind stress and ρ is the density of the water. Qualitative “kitchen-type” laboratory experiments on a rotating table demonstrate that, as the theory predicts, only a fraction of the generated flow enters the gap. Quantitative numerical experiments using the Bleck and Boudra reduced gravity isopycnic model provide an even stronger support for the theory. They show that the analytically calculated transports are within 10–15% of the numerical calculations. Possible application of this theory to a number of passages such as the Windward Passage and the Indonesian throughflow is discussed.

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