On Wind and Ocean-Velocity Correlations in a Coastal-Upwelling Systeml

This note studies the response of a simple linear baroclinic coastal-upwelling model to fluctuating longshore winds. Correlations between wind stress and velocities are computed explicitly. It is shown that these correlations depend primarily upon the wind-~ spectrum and that. for a realistic spectrum, the wind stress leads the longshore velocity by approximately one day. The computed correlations agree remarkably well with observations and dismiss the belief that time lags ought to be directly related to the local inertial period, i.e., some fraction of the local pendulum day. and 2) variability of the wind forcing which is external to the system. The inertial oscillations of a pendulum-day period or less, as those in response to a momentum impulse preceeding the formation of a steady, geostrophic adjustment (Cahn, 1945; Crepon, 1967), cannot account for tiI1)e lags greater than a quarter of a pendulum day. Explanation for greater lags, as observed, ought thus to be found in the alternate source of variability, viz.. in the variability of the surface wind stress. The aim of this note is to demonstrate with a maximum of simplicity and clarity that, indeed. the observed time lags are characteristic of the forcing variability. A wind-impulse model is thus inappropriate for such analysis. Before one can quantify on any correlation or time lag, one must investigate a realistic wind-stress spectrum and the corresponding ocean response. Here, a simple linear, baroclinic coastal-upwelling model is studied in response to an endless fluctuating surface stress. It is shown that correlations between wind stress and velocity components depend upon the shape of the wind-stress spectrum and that, for a realistic spectrum, time lags are unrelated to and substantially greater than the inertial period. Moreover, predicted values agree with those estimated from the data. These conclusions dis~ss the belief that time lags ought to be directly related to the local inertial period. i.e., some fraction of the local pendulum day.