Barotropic Circulation around Islands with Friction

Abstract

Godfrey?s Island Rule is generalized to include previously neglected dissipation on the north, south, and east boundaries of the island as well as the eastern basin boundary. The resulting extended island rule predicts the transport ?I between the island and the eastern basin boundary when strong frictional effects alter Godfrey?s original result. The new result is derived for a barotropic ocean with either Munk or Stommel friction and with no bottom topography. The Munk case is marked by the interesting feature that friction enhances the flow over a certain range of widths of the gap separating the island from the western (or eastern) basin boundary. Transport predictions for the Munk case are compared to results based on linear and moderately nonlinear numerical simulations. The original island rule overpredicts ?I by no more than 25% unless the island is within about 3 Munk layer thickness of the east or west boundary, in which case the errors are much larger. For such cases the extended island rule is able to predict ?I within 10%, at least for the cases explored. The numerical simulations also show the transport enhancement predicted by the extended island rule. Implications for possible frictional blocking of the Indonesian Throughflow are discussed. The authors argue that middle-of-the-road estimates for δM suggest lateral friction as a serious candidate for the overestimate of the Indonesian Throughflow transport by the original island rule. Implications for the English Channel, the Mozambique Channel, and the Denmark Strait are discussed.