ABSTRACT
The Boussinesq-type equations have been applied for water surface wave modeling to increase the order of accuracy for wave frequency dispersion and consequentially for nonlinearity effects. The Boussinesqtype models have been derived using polynomial approximation in the vertical profile of the horizontal velocities. The classic Boussinesq equations rewritten in depth integrated form (Peregrine, 1967) assuming the second order variation of velocity in vertical direction ((0,2) Padé approximant). In these equations, the nonlinearity and frequency dispersion of wave is simulated in first and second order, respectively. As an improvement in (0,2) padé approximation of Boussinesq equations, some researchers rearranged the dispersive terms (Madsen and Schaffer 1998, Chen et al. 2000) or introduced a significant water depth, Zα, as a characteristic water depth in which, the horizontal velocity domain is defined. In this (2,2) Padé approximant, the value of Zα optimized using a least-square procedure aimed at minimizing errors in approximated waves phase speed (Beji & Nadaoka 1996). The extension of Boussinesq models to higher accuracy continued by Gobbi and his coworkers (Gobbi et al., 2000). They presented a (4,4) Padé approximant accurate to O(µ4) for retaining terms in dispersion, and to all consequential orders in nonlinearity. The work on extending the range of Boussinesq models to higher accuracy continued by Lynett and Liu multi-layer approach (Lynett & Liu 2002). The higher order Boussinesq type models with moving bottom
boundary is developed and applied to study the underwater landslide generated waves (Ataie-Ashtiani & Najafi-Jilani 2006). The main objective of this work is developing of a higher order Boussinesq-type wave equations to capture the frequency dispersion and nonlinearity effects of wave accurately. The higher order Boussinesq-type equation is derived in a depthintegrated form and is investigated in several cases.
