Contents

70 4 Long Waves in a ChannelIt can also be shown (Cushman-Roisin, 1994) that these waves are governed bythe well-known dispersion relation:c = λ T = √ gh (4.16)implying that the phase speed of a long surface gravity wave exclusively depends ontotal water depth. Consequently, it follows that the ratio between horizontal speedof a water parcel and phase speed is very small:u oc = η h >h). Accordingly,motions of water parcels in a shallow-water wave are largely horizontal. Anotherimportant feature inherent with long waves is that they reach the seafloo and arecapable of stirring up sediment from the seafloo , if energetic enough. Figure 4.4shows a snapshot of the analytical solution of a shallow-water wave.4.2.6 Animation ScriptA SciLab script, called “AnalWaveSol.sce”, can be found in the folder “Miscellaneous/Waves”on the CD-ROM accompanying this book. This script creates ananimation of the analytical wave solution.