The Distribution of Shearing Stresses in a Tidal Current

Abstract

Summary Observations were made in a tidal current off Red Wharf Bay, Anglesey, North Wales. The frictional stress at the bottom, Fb, was determined from the velocity profile within the first zm above the bottom and found to be related to the velocity at I m by a quadratic law, Fb = kpUl2, where K has the value 3-5 x 10-3. The corresponding value of the roughness length xo is 0-16cm. Current meter measurements at a number of depths between surface and bottom were made at half-hourly intervals, enabling the acceleration terms in the equations of motion to be determined. From the bottom stress and the acceleration terms, the shearing stress in the water was computed as a function of depth and as a function of time during the tidal period. While at the times of maximum current the shearing stress increased approximately linearly from surface to bottom, as in the case of steady flow in a channel, at other times the acceleration terms caused the stress to deviate considerably from a linear variation. Estimates of the vertical eddy viscosity, N,, indicated that its value was somewhat higher at middepth than nearer the surface or bottom. N, varied during the tidal period, tending to reach maximum values when the current was at a maximum and to be larger during the flood than during the ebb. The numerical values of N, were of the order of 270cm2/s during the flood and 130cm2/s during the ebb, corresponding to depth-mean currents of 35 cm/s and 39cmls respectively. The depth of water averaged 22 m. The observed distributions of velocity and shearing stress are compared with those obtained from a theoretical model, in which the eddy viscosity is taken as constant above a friction layer near the bottom. x. Introduction In the steady flow of a liquid of uniform density along an open channel, with friction at the channel bed, it follows directly from dynamical considerations that the shearing stress in the liquid increases linearly from the surface to the bottom. This result is valid, whatever the state of turbulence within the fluid. If some assumption can be made about the structure of the turbulent flow, e.g. von Karman’s similarity law, the distribution of velocity with depth can be determined theoretically, as discussed by Hunt (1954). The well-known logarithmic law for the velocity distribution near the bed follows as a special case, in the 288