Linear wave theory (coastal waters)

Abstract

Key concepts In this book, coastal waters are waters that are shallow enough to affect the waves, adjacent to a coast, possibly with (small) islands, headlands, tidal flats, reefs, estuaries, harbours or other features, with time-varying water levels and ambient currents (induced by tides, or river discharge). Horizontal variations in water depth cause shoaling and refraction. Horizontal variations in amplitude cause diffraction. Shoaling is the variation of waves in their direction of propagation due to depth-induced changes of the group velocity in that direction. These changes in group velocity generally increase the wave amplitude as the waves propagate into shallower water (the propagation of wave energy slows down, resulting in ‘energy bunching’). Refraction is the turning of waves towards shallower water due to depth- or current-induced changes of the phase speed in the lateral direction (i.e., along the wave crest). For harmonic, long-crested waves in situations with parallel depth contours, Snel's law can be used to compute the wave direction. If the depth contours are not parallel, the wave direction should be computed with wave rays. Diffraction is the turning of waves towards areas with lower amplitudes due to amplitude changes along the wave crest. Diffraction is particularly strong along the geometric shadow line of obstacles such as islands, headlands and breakwaters. For long-crested, harmonic waves, propagating over a horizontal bottom, Huygens' principle, or a generalisation thereof, can be used to compute the diffraction pattern. A long-crested, harmonic wave that reflects off an obstacle, with or without energy dissipation, creates a (partially) standing wave. The simultaneous occurrence of shoaling, refraction, diffraction and reflection of long-crested, harmonic waves can be computed with the mild-slope equation. […]