Time-Dependent Island Rule and Its Application to the Time-Varying North Hawaiian Ridge Current*

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Abstract
Since November 1988, repeated shipboard ADCP transects have been made across the North Hawaiian Ridge Current (NHRC) north of Oahu. Prominent aspects of the NHRC transport time series include 1) a shift in late 1991 from a relatively strong and steady state to a weaker and more variable state and 2) the absence of an annual cycle, despite the annual cycle in the wind stress. A simple conceptual framework for understanding NHRC variability is provided by our extension of Godfrey’s island rule to upper-layer flow in the baroclinic time-dependent case. The interior ocean flow east of the islands is viewed as the sum of Ekman transport, geostrophic adjustment to Ekman pumping, and long Rossby waves. The net interior flow normal to the offshore edge of the NHRC is carried around the island barrier, with the split between northward and southward flow governed by a simple vorticity constraint involving only the inflow and outflow from the interior and the wind circulation around the island. The latter is of minor importance to the Hawaiian Islands. The time-dependent island rule calculation does not reproduce the observed time series, but it approximates the observed magnitude and character of variability. The result is sensitive to the choice of wind product. To improve the simulation and to investigate the importance of processes missing from the island rule, a numerical 2½-layer reduced-gravity model of the Pacific Ocean is driven by the FSU winds. Although the modeled NHRC does not match the ADCP observations in every detail, the mean transport and some aspects of the variability are similar: the model shows the 1991 transition and lacks an annual cycle. Experiments with and without temporal wind variability near the equator show that the NHRC is governed primarily by winds east of the Hawaiian Islands; equatorial winds have little effect. Nonlinearity is shown to be important.

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