Coastal-trapped waves with finite bottom friction

Abstract

Coastal-trapped waves with finite-amplitude bottom friction are explored. “Finite-amplitude” in this context means that the bottom stresses are large enough to change the wave modal structure. The importance of bottom friction is measured by the nondimensional number r/(ωh), where r is a bottom resistance coefficient, ω is the wave frequency and h is the water depth. Increasing bottom drag causes free wave modes to adjust by having their amplitude maxima for alongshore current translate offshore to the point that, with relatively large bottom stress, the alongshore current variance is trapped entirely on the slope, even though pressure variations remain substantial right up to the coast. In conjunction with these adjustments, wave frequency, hence propagation speed, varies and the wave damping is usually less than would be expected based on a weak-friction perturbation calculation. Stronger density stratification increases wave damping, all else being the same. A mean alongshore flow can strongly affect modal structure and wave damping, although general trends are difficult to discern. Results suggest that bottom friction may cause an observed tendency for lower frequency alongshore current fluctuations to become relatively more important with distance offshore.