Modeling the nonlinear effect of wind on rectilinear tidal flow

Abstract

Observations of near‐bed alongshore flow in 4–10 m depth at Terschelling, Netherlands, show that strong alongshore winds (≈15–20 m/s) in the flood direction reduce the tide current range and alter the tidal flow curve by bringing maximum flood flow forward in time and delaying maximum ebb flow. These nonlinear effects, which are more pronounced in shallower water, are reproduced well by a single‐point model in the vertical driven by large‐scale (O(km)) sea surface gradients and wind stress, using a quadratic bottom stress formulation and a time‐dependent eddy viscosity derived from a k‐ε turbulence closure model. Subsequent idealized model simulations using a (Terschelling based) M2 sea‐surface gradient and wind speeds between 0 and 20 m/s show that the wind‐induced modifications of the tidal flow are consistent with the interaction of the wind‐induced flow with the tidal flow through the quadratic bed stress. The wind‐driven flow enhances friction during the flood phase more than it reduces friction during the ebb flow, thereby increasing friction over a tidal cycle and, as a consequence, reducing the tide current range. The predicted increase in asymmetry of bed friction during flood and ebb flow with increasing wind speed also increases (decreases) the M4 (M6) amplitude, consistent with the observations. The M4/M2 amplitude ratio is predicted to be largest when the flow has just become unidirectional (that is, when the wind‐driven flow equals the tidal current).