Note on wind drift in a channel in the presence of tidal currents

Abstract

In waters such as those surrounding the British Isles, wind currents appear as perturbations superimposed on the tidal currents. In treating this problem, it is assumed that the drift velocity is small compared with the amplitude of the tidal current. In this case, if the instantaneous value of the bottom friction is proportional to the square of the instantaneous velocity, the non-periodic component of friction, averaged over a tidal period, is linearly proportional to the drift velocity. It is assumed that the water is homogeneous and that, above a skin-friction layer close to the bottom, the eddy viscosity is constant with depth. In the steady state, the drift current due to a given wind stress is reduced in the presence of tidal currents. Steady-state solutions, involving the elevation of the surface as well as the currents, are given for a channel of uniform width and depth, a uniformly convergent channel and a non-uniform channel. Numerical calculations, based on the most probable estimates of wind stress, eddy viscosity and bottom friction available at present, are given for several particular cases. A discussion is given of their application to drift currents and surface gradients in the English Channel, a region in which it is proposed to carry out a programme of observations in the near future.