Circulation around islands and ridges
The circulation in an ocean basin containing an island is studied under nearly geostrophic, beta plane dynamics. The model is a fluid of uniform density driven by wind forcing or sources and sinks of mass at the upper boundary of the flow. The circulation is studied analytically, numerically, as well as in the laboratory through the device of the “sliced cylinder” model for the ocean circulation. Of particular interest is the estimate of the transport between the island and the oceanic basin's boundary. The model is conceived as relevant to both the wind-driven circulation as well as the circulation of abyssal waters around deep topographic features such as mid-ocean ridge segments.
Godfrey's Island Rule for the transport is re-derived in general form and the validity of the original approximation of Godfrey (1989) is examined in a variety of circumstances. In particular, the role of dissipative boundary layers and inertial effects such as vortex shedding are scrutinized to determine their role in determining the net transport around the island.
Linear theory in many cases predicts a recirculation on the eastern side of the island, provided the meridional extent of the island is large enough. The existence of the recirculation, containing trapped fluid, is confirmed in both laboratory and numerical experiments and the evolution of the structure of the recirculation is examined as a function of the boundary layer Reynolds number. In both the laboratory and numerical studies, the recirculation predicted by linear theory is joined and then superseded by an inertial recirculation springing from boundary layer separation as the Reynolds number increases past a critical value.
Even in the linear limit it is shown that the recirculation region, which is closed in quasi-geostrophic theory, is subject to a small leak due to planetary geostrophic effects, which prediction is confirmed in the laboratory.
The original island rule of Godfrey yields an estimate of the transport which is surprisingly robust and generally within 75% of the values measured in our numerical experiments. Agreement is moderately good when island western boundary layer transport is used as a basis for comparison. Several cases are discussed, however, in which the assumptions made by Godfrey are violated. One occurs when the frictional boundary layers of the island and the basin boundary overlap. We derive a threshold width for the gap for the case where the island is close to a northern or southern boundary of the basin and show how the transport is increasingly blocked as the gap is reduced. A second case occurs when the island is thin and zonally elongated so that the dissipative effects on the northern and southern boundaries of the island become important. Here the vorticity balance assumed in the simple Island Rule is fundamentally altered, and we extend the Island Rule to account for the new dissipation.
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The Journal of Marine Research publishes peer-reviewed research articles covering a broad array of topics in physical, biological and chemical oceanography. Articles that deal with processes, as well as those that report significant observations, are welcome. In the area of biology, studies involving coupling between ecological and physical processes are preferred over those that report systematics. Authors benefit from thorough reviews of their manuscripts, where an attempt is made to maximize clarity. The time between submission and publication is kept to a minimum; there is no page charge.
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