(4.22–4.25) assume that there are no energy losses due to bed friction, white-capping or other wave energy dissipation processes. This decrease in wave height, followed by increasing wave height, has been observed in laboratory studies ( Iversen, 1952).Įqs. This occurs because EC g must remain constant, therefore a localised increase in C g must result in a localised decrease in energy density E and thus in wave height. This increase in wave group velocity results in a local decrease in wave height. One interesting aspect of wave shoaling is that there is a slight increase in group velocity for the range 0.058 < h/ L o < 1 prior to group velocity decreasing (red line in Fig 4.4B). Hence, wave group velocity changes with an overall decrease relative to the deep-water wave speed. Similarly, n transitions from ½ to 1 as waves move from deep to shallow water. decreasing h/ L o or from left to right in the figure), wavelength and phase velocity systematically decrease with decreasing depth. This clearly shows that as waves progress into shallower water (i.e. The variability of n, C/C o, H/H o and L/L o are shown against h/ L o in Fig. 4.4B. (4.25) shows how local wave height is a function of H o, n and C/C o. Wave period, all the while, remains constant during wave shoaling.Įq. Wave shoaling can happen in any wave where its behaviour is controlled by the seabed, both linear and non-linear. This transformation of wave characteristics, termed wave shoaling, involves a progressive decrease in wave phase velocity and wavelength, while wave height increases. This process continues until the wave becomes unstable and breaks (see Chapter 6 for a discussion of wave breaking in shallow water). As waves progress into shallower water, the waveform transitions such that the wave crests become more peaked and the troughs flatten and widen due to the influence of changing depths on wave behaviour ( Fig. 4.3A). In deep water, the waveform approximates a sinusoid and wave behaviour is unaffected by water depth. This results in decreases in wave speed and wavelength while wave height increases. Wave shoaling is the change in shape and behaviour as waves propagate into water of decreasing depth. Power, in Sandy Beach Morphodynamics, 2020 4.3.1 Wave shoaling
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