The Circulation of the Depth-integrated Flow around an Island with Application to the Indonesian Throughflow

Roxana C. Wajsowicz The Institute of Low Temperature Science, Hokkaido University, Sapporo, Japan

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Abstract

Godfrey's Island Rule is rederived in terms of the barotrapic streamfunction for flow in a stratified ocean with a rigid lid. Modifications to include bottom topography and frictional effects along eastern boundaries are derived. The “Island Rule” has an important application in describing the net transport through the Indonesian seas, that is the Indonesian Throughflow. The original rule, derived from a Sverdrup model, yielded an annual mean throughflow of 16±4 Sv (Sv ≡ 106 m3) s−1). Observations of depth-integrated steric height differences indicate that frictional effects within the lndonesian seas will reduce this value by the order of 2 Sv. The reduction estimated from a frictional channel model depends on the parameterization and boundary conditions adopted, and ranges from 5%–20%. Topographic effects could give an increase in transport. For example, if the archipelago is represented as a simple sill, then warmer water on the Pacific slope than on the Indian slope would produce an increase in transport.

A diagnostic island rule for describing interannual variations is proposed. This rule expresses the throughflow as a line integral of the wind stress from the tip of Iria-Jaya along a line of latitude across the Pacific down the South American coast back along a line of latitude across the Pacific to the southern tip of Australia and up Australia's west coast, the original rule, plus a modulation due to the difference between the depth-integrated pressure on the Australian coast at the northern and southern entrances to the Indonesian seas in excess of that required to balance the alongshore wind stress. Frictional and hydraulic effects, which could produce an excess pressure difference are illustrated with a fine-resolution GCM.

Abstract

Godfrey's Island Rule is rederived in terms of the barotrapic streamfunction for flow in a stratified ocean with a rigid lid. Modifications to include bottom topography and frictional effects along eastern boundaries are derived. The “Island Rule” has an important application in describing the net transport through the Indonesian seas, that is the Indonesian Throughflow. The original rule, derived from a Sverdrup model, yielded an annual mean throughflow of 16±4 Sv (Sv ≡ 106 m3) s−1). Observations of depth-integrated steric height differences indicate that frictional effects within the lndonesian seas will reduce this value by the order of 2 Sv. The reduction estimated from a frictional channel model depends on the parameterization and boundary conditions adopted, and ranges from 5%–20%. Topographic effects could give an increase in transport. For example, if the archipelago is represented as a simple sill, then warmer water on the Pacific slope than on the Indian slope would produce an increase in transport.

A diagnostic island rule for describing interannual variations is proposed. This rule expresses the throughflow as a line integral of the wind stress from the tip of Iria-Jaya along a line of latitude across the Pacific down the South American coast back along a line of latitude across the Pacific to the southern tip of Australia and up Australia's west coast, the original rule, plus a modulation due to the difference between the depth-integrated pressure on the Australian coast at the northern and southern entrances to the Indonesian seas in excess of that required to balance the alongshore wind stress. Frictional and hydraulic effects, which could produce an excess pressure difference are illustrated with a fine-resolution GCM.

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