Weak wave-tide interaction formulation and its application to Cadiz bay

Using a single-point, one-equation(k-l) model for an oscillatory turbulent bottom boundary layer (BBL) above a hydrodynamically rough bottom and varyi ng the external determining parameters over a wide range, we show that nonl inear wave/low-frequency current interaction effects are smaller, the great er are the ratio of near-bottom wave orbital velocity amplitude to friction -free, low-frequency current velocity amplitude and the ratio between frequ encies of wave and low-frequency components of motion. Specifically, in sha llow waters the bottom stress oscillations with wave and tidal frequencies are, with fair accuracy, weakly correlated, thereby suggesting that wave-ti de interaction is substantially weak interaction. A new weak wave-tide inte raction formulation is proposed. It involves a relationship for the drag co efficient in a wave-affected tidal flow and the surface Rossby number depen dences for the scaled wave and tidal friction velocity amplitudes inferred from the resistance law for an oscillatory turbulent BBL over a hydrodynami cally rough surface. This formulation is implemented within a 2D nonlinear, finite-difference, high-resolution, hydrodynamic model and the modified mo del is applied to quantify the wave-induced changes in the tidal dynamics a nd energetics of Cadiz Bay. The model results reveal one unexpected feature in the fields of maximum tidal velocity and mean tidal energy flux. Namely , wave-tide interaction responsible for enhancing the mean bottom stress th roughout the bay tends to increase the maximum tidal velocities and the mea n tidal energy fluxes at deeper depths and to reduce them at shallower dept hs. The reason for appearing this feature is an overall amplification of th e mean tidal energy transport into the bay from Gulf of Cadiz. Based on the sensitivity study to varying wave parameters, the wave-induced seasonal va riability in the M-2 tidal characteristics is found to be not pronounced in Cadiz Bay. This, however, does not rule out a clearly defined manifestatio n of such a variability in other shallow basins and/or in other tidal frequ ency bands. Special attention is given to identify the regions of potential suspended sediment transport and their wave-induced changes. (C) 2001 Else vier Science Ltd. All rights reserved.