On the transport of mass by time-varying ocean currents

Abstract

In order to calculate the mean mass flux past a given recording station it is necessary to know more than the mean velocity in a fixed, vertical section. One must add an additional term—the ‘Stokes velocity’ which depends also on the time and distance scales of the fluctuating currents. In typical circumstances, where the fluctuations are larger than the mean current, the Stokes velocity may dominate the mass transport, and lead to the mass transport being opposite in direction to the mean current. Some general expressions are given for the Stokes velocity, and these are studied in detail for the particular case of waves propagated along a sloping sea bed (double Kelvin waves). Such waves are always propagated with the shallower water to their right in the northern hemisphere. It is shown that in regions of small bottom gradient the Stokes velocity is in the same direction as the phase velocity, but in the region of large bottom gradient the sign of the Stokes velocity is reversed. The mean Stokes velocity is in the direction of wave propagation. However, the total transport (integrated with respect to the depth and width) is in the opposite direction.