A Porous-Medium Theory for Barotropic Flow through Ridges and Archipelagos

Larry J. Pratt Woods Hole Oceanographic Institution, Woods Hole, Massachusetts

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Michael A. Spall Woods Hole Oceanographic Institution, Woods Hole, Massachusetts

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Abstract

A linear theory for the treatment of complex ridges and archipelagos as porous media is presented. The theory assumes a barotropic, wind-driven ocean with uniform depth. A porous ridge is formed by shrinking the meridional dimensions of the islands and straits (or gaps) composing a meridionally aligned island chain to infinitesimal values. The circulation integrals associated with a generalization of the “island rule” for each island then combine to form an ordinary differential equation. The solution determines the magnitude and structure of the zonal flow through the ridge. This solution could supply a boundary condition for numerical or inverse models that cannot resolve the topographic details of the ridge or archipelago. The physics of the throughflow is explored using a series of examples. It is shown that a concentrated zonal flow approaching the ridge from the east tends to spread meridionally before it passes through the ridge. If the spreading distance, which depends on the characteristics of the ridge, is small in comparison with the meridional scale of the zonal flow, the flow is unimpeded by the ridge. Otherwise the ridge may block or divert the flow. Paradoxically, ridges with high porosity are just as effective at blocking as are ridges with low porosity. The theoretical results are verified to a large extent by a barotropic numerical model.

Corresponding author address: Dr. Larry Pratt, Woods Hole Oceanographic Institution, Mail Stop 21, 360 Woods Hole Rd., Woods Hole, MA 02543. Email: lpratt@whoi.edu

Abstract

A linear theory for the treatment of complex ridges and archipelagos as porous media is presented. The theory assumes a barotropic, wind-driven ocean with uniform depth. A porous ridge is formed by shrinking the meridional dimensions of the islands and straits (or gaps) composing a meridionally aligned island chain to infinitesimal values. The circulation integrals associated with a generalization of the “island rule” for each island then combine to form an ordinary differential equation. The solution determines the magnitude and structure of the zonal flow through the ridge. This solution could supply a boundary condition for numerical or inverse models that cannot resolve the topographic details of the ridge or archipelago. The physics of the throughflow is explored using a series of examples. It is shown that a concentrated zonal flow approaching the ridge from the east tends to spread meridionally before it passes through the ridge. If the spreading distance, which depends on the characteristics of the ridge, is small in comparison with the meridional scale of the zonal flow, the flow is unimpeded by the ridge. Otherwise the ridge may block or divert the flow. Paradoxically, ridges with high porosity are just as effective at blocking as are ridges with low porosity. The theoretical results are verified to a large extent by a barotropic numerical model.

Corresponding author address: Dr. Larry Pratt, Woods Hole Oceanographic Institution, Mail Stop 21, 360 Woods Hole Rd., Woods Hole, MA 02543. Email: lpratt@whoi.edu

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