The vertical structure of tidal currents and other oscillatory flows

Abstract

Assuming a linearized equation of motion in the absence of stratification, the vertical structure of tidal currents is shown to be a function of two dimensionless parameters. The first of these, Y = (ω/E)1/2D, is analogous to an Ekman height with ω the tidal frequency, D the depth, and E the (constant) vertical eddy viscosity. The second parameter, J = (ωE)1/2[(8/3π)kŪ], introduces the effect of a quadratic bed stress through the bed-stress coefficient k and the depth-averaged velocityÜ. From these it is possible to illustrate the full range of possible vertical structure and to understand the basic scaling laws involved. By assuming E =aU¯D good agreement between theory and observation was found. With this assumption vertical structure reduces to a function of just one parameter, namely kS, where S =Ū2π/Dω is the Strouhal number. By resolving tidal current ellipses into clockwise and anticlockwise rotating components the original theory developed for recti-linear flow can be applied to fully three-dimensional flow. In this way, many of the observed characteristics of current structure in shallow seas may be explained.