Bound waves and triad interactions in shallow water

Boussinesq type equations with improved linear dispersion characteristics are derived and applied to study wave-wave interaction in shallow water. Weakly nonlinear solutions are formulated in terms of Fourier series with constant or spatially varying coefficients for two purposes: to derive higher order boundary conditions for regular and irregular wave trains and to derive evolution equations on constant or variable water depth. Wave transformation of monochromatic, bichromatic and irregular waves is studied and comparison with measurements and direct time domain solutions shows good agreement. The improvement relative to classical models from the literature is discussed.