General description

As waves propagate into shallow water, the orbital wave velocities penetrate the water depth and the source terms due to wave-bottom interaction become important. Furthermore, the deep-water source terms are modified because of depth effects. A review of the different wave-bottom interaction processes is given by Shemdin et al. (1978), who consider dissipation due to friction in the turbulent boundary layer, percolation into a porous bottom, motion of a soft bottom and scattering on bottom irregularities. According to Shemdin et al. (1978) bottom friction is generally dominant when the sedi­ment is composed of fine sand, d50 = 0.1-0.4 mm or when sand ripples are present. In this case, the low permeability prohibits percolation and granular friction prevents viscous flow behaviour (Shemdin et al., 1978). In many prac­tical cases, the bed is composed of fine sand or wave-generated ripples are present (e.g. Dingler and Inman (1976) found this to be true on many conti­nental shelves).

For the fully spectral formulation the bottom dissipation source function is based on linear theory and can be generalised into Eq. (6.13) below, Weber (1991)

(6.13)   FemInputEditorSW_dialogs00058.jpg

where Cf  is a dissipation coefficient (= fwUbm), which depends on the hydro­dynamic and sediment conditions. Here fw is the wave friction factor and Ubm is the maximum near-bed particle velocity given by

(6.14)   FemInputEditorSW_dialogs00060.jpg

Further details are described in Johnson and Kofoed-Hansen (2000).