Finite-amplitude analysis of some Boussinesq-type equations

Recent progress in formulating Boussinesq-type equations includes improved features of linear dispersion and higher-order nonlinearity. Nonlinear char acteristics of these equations have been previously analysed on the assumpt ion of weak nonlinearity, being therefore limited to moderate wave height. The present work addresses this aspect for an important class of wave probl ems, namely, regular waves of permanent form on a constant depth. Using a n umerical procedure which is valid up to the maximum wave height, permanent- form waves admitted by three sets of advanced Boussinesq-type equations are analysed. Further, the characteristics of each set of the Boussinesq-type equations are discussed in the light of those from the potential theory sat isfying the exact free-surface conditions. Phase velocity, amplitude disper sion, harmonic amplitudes (namely, second and third) and skewness of surfac e profile are shown over a two-parameter space of frequency and wave height . (C) 1999 Elsevier Science B.V. All rights reserved.