B. Ataie-Ashtiani - Associate Professor of Civil Engineering, Sharif University of Technology, Tehran, Iran
A. Najafi Jilani - Ph.D. Candidate of Civil Engineering, Sharif University of Technology, Tehran, Iran

Extended Boussinesq-type water wave equations are derived in two horizontal dimensions to capture the nonlinearity effects and frequency dispersion of wave in a high accuracy order. A multi-parameter perturbation analysis is applied in several steps to extend the previous second order Boussinesq-type equations in to 6th order for frequency dispersion and consequential order for nonlinearity terms. The presented high-order Boussinesq-type equation is applied in a numerical model to simulate the wave field transformation due to physical processes such as shoaling, refraction and diffraction. The models results are compared with available experimental data which obtained in a laboratory wave flume with varying bottom in Delft Hydraulic Institute and an excellent agreement is obtained.

Boussinesq equations, Perturbation analysis, Varying bathymetry