The Distribution of Shearing Stresses in a Tidal Current

TLDR

The study compared observed velocity and shearing‑stress distributions with a theoretical model that assumes constant eddy viscosity above a bottom friction layer. Observations were made off Red Wharf Bay using half‑hourly current‑meter profiles to compute acceleration terms, bottom stress, and depth‑ and time‑dependent shearing stress, and these data were then compared with the theoretical model. The results showed that bottom frictional stress follows a quadratic law (k = 3.5 × 10⁻³) with a roughness length of 0.16 cm, that shearing stress is linear from surface to bottom at peak currents but deviates otherwise, and that vertical eddy viscosity peaks at mid‑depth, ranging from ~270 cm²/s during flood to ~130 cm²/s during ebb, corresponding to depth‑mean currents of 35–39 cm/s in a 22‑m deep channel.

Abstract

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 2 m above the bottom and found to be related to the velocity at 1 m by a quadratic law, Fb = kρU12, where k has the value 3.5 × 10−3. The corresponding value of the roughness length z0 is 0.16 cm. 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, Nz, indicated that its value was somewhat higher at mid-depth than nearer the surface or bottom. Nz 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 Nz were of the order of 270 cm2/s during the flood and 130 cm2/s during the ebb, corresponding to depth-mean currents of 35 cm/s and 39 cm/s 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.