Appendix B.3. Solitary wave theory
The solitary wave type consists only of one water surface elevation and no wave trough such that the wave length L is theoretically infinite (Fig. 11(d)). Russell (1837) investigated solitary waves in a hydraulic model and derived some basic features. The theory of the solitary wave was independently derived by Boussinesq (1871) and Rayleigh (1876) by assuming non-hydrostatic pressure distribution and rotational flow. The solitary wave is translative involving a considerable fluid mass transport (Le Me´haute´, 1976). For this wave type the nonlinearity, tending to steepen the wave front, balances dispersion, which tends to spread the wave front. Therefore, its profile is constant without damping along the travel distance in a horizontal channel of constant width b, if boundary layer friction is neglected. According to Laitone (1960), the solitary wave celerity c is