On the vertical structure of tidal currents in a homogeneous sea

Abstract

The vertical variation of tidal currents caused by friction at the sea-bed is investigated in both qualitative and quantitative ways with the Coriolis force being taken into account. The simple model with the assumption of constant eddy viscosity is employed to study the effects of friction on the vertical structure of tidal currents. The model explains these effects in vertical change of the maximum velocity, the ellipticity (the ratio of the minor to the major axis) of current ellipse, the time and the direction of the maximum velocity, and the ratio of diurnal current to semidiurnal current. To reach a quantitative agreement with the data observed by Bowden & Fairbairn in the Irish Sea, the mixing length theory is applied to numerical calculation of the vertical distribution of tidal currents with a finite difference scheme. A fair agreement with the observations is obtained in the calculation. The results show the following features: (1) the vertical profile of amplitude of the main component for the current is almost logarithmic throughout the depth; (2) the corresponding profde for the shearing stress is almost linear with depth; (3) the maximum stress lags the maximum velocity with the delay increasing with elevation; (4) the eddy viscosity coefficient has its maximum around the mid-depth; and (5) the vertically averaged viscosity lags the velocity magnitude. The dependence of the quadratic resistance coefficient and the coefficient k defined by Bowden's formulav̄=κhū(h— depth, v̄ and ū— depth-averaged eddy viscosity and velocity) on the roughness length is given for a steady flow in a non-rotating system. The numerical solution shows that these relations can be approximately applied to the tidal currents in shallow waters.