Weak wind-wave/tide interaction over fixed and moveable bottoms: a formulation and some preliminary results

The formulation of weak wind-wave/low-frequency current interaction is discussed comprehensively as applied to fixed- and moveable-bottom cases. It involves (1) a dependence of the drag coefficient on the ratio between wave and current bottom friction velocity amplitudes, (2) the resistance law for the oscillatory, rough, turbulent bottom boundary layer (BBL) which accounts for the usually neglected effects of rotation and the phase difference between the bottom stress and the friction-free current velocity, (3) the expression for the BBL depth in terms of the bottom Rossby number and (4) the bottom roughness predictor of Grant and Madsen (J. Geophys. Res., 87 (1982) 469) in the version of Tolman (J. Phys. Oceanogr., 24 (1994) 994). The formulation is implemented in the UCA (University of Cadiz) 2D nonlinear, high-resolution, hydrodynamic model and used to study the influence of wind-wave/tide interaction, bottom mobility and the improved flow-resistance description on the M2 tidal dynamics of Cadiz Bay. The inclusion of either of the first two factors can cause the drag coefficient to increase significantly over its reference value. If the third factor is included, changes in the drag coefficient are quite moderate. This is because the effect of rotation is opposite in sign to the effect of phase difference, so that these effects taken together very nearly balance. The reason why bottom mobility has such an important influence on shallow-water tidal dynamics as wind-wave/tide interaction has, is the occurrence of the large irregular variations in the drag coefficient that accompany sediment motion.