A determination of the frictional forces in a tidal current

Abstract

The frictional forces in a tidal current have been determined from simultaneous observations of the surface gradients and the currents at various depths. The observations were made a few miles from the coast, off Red Wharf Bay, Anglesey. The gradients were derived from measurements of the surface elevations obtained by a pair of open-sea tide-gauges of the Favé type, modified to give increased accuracy. The Doodson electrically recording current meter was used for the current measurements. Each set of observations extended over 24 h, and they were subjected to harmonic analysis for the semi-diurnal constituent. The data from these analyses were then used in the dynamical equations, giving the amplitudes and phases of the frictional force at the bottom, and of the internal shearing stress in the water at various depths. Five complete sets of records were obtained, three of which are considered to have given significant results. Expressing the amplitude of the frictional force at the bottom in the form F ═ kρU 2 , where U is the amplitude of the mean current from surface to bottom, and ρ is the density of the water, the results give the coefficient k an average value of 1⋅8 x 10 ─a . The internal frictional stress in the water was found to increase approximately linearly with depth from the surface to the bottom, and the corresponding values of the mean eddy viscosity have been derived.