Gonzalo Simarro, Alvaro Galan, Alejandro Orfila


A fully nonlinear Boussinessq-type model with 7 Nwogu’s α-like coefficients is considered. The model is one-layer and low-order to simplify the numerical solvability. The coefficients of the model are here considered functions of the local water depth so as to allow an improvement of the dispersive properties for narrow banded trains in very deep waters. The proposed model is fully nonlinear in weakly dispersive conditions, so that nonlinear wave decomposition in shallower waters is well reproduced.


Boussinesq-type equations; deep water propagation


Y. Chen and P. L.-F. Liu. Modified boussinesq equations and associated parabolic models for waterwave propagation. Journal of Fluid Mechanics, 288:351–381, 1995.

R. G. Dean and R. A. Dalrymple. Water wave mechanics for engineers and scientists. Prentice-Hall, Inc., Englewoods Clis, New Jersey 07632, 1984.

M. W. Dingemans. Water wave propagation over uneven bottoms. World Scientific, Singapore, 1997.

A. Galan, G. Simarro, A. Orfila, J. P. Simarro, and P. L.-F. Liu. A fully nonlinear model for water wave propagation from deep to shallow waters. Journal of Waterway, Port, Coast and Ocean Engineering, page in press, 2012.

M. F. Gobbi, J. T. Kirby, and G. Wei. A fully nonlinear boussinesq model for surface waves: part ii. extension to o (kh)4. Journal of Fluid Mechanics, 405:182–210, 2000.

A. E. Green and P. M. Naghdi. A derivation of equations for wave propagation in water of variable depth. Journal of Fluid Mechanics, 78:237–246, 1976.

C. Lee, Y.-S. Cho, and S. B. Yoon. A note on linear dispersion and shoaling properties in extended boussinesq equations. Ocean Engineering, 30:1849–1867, 2003.

P. Lynett and P. L.-F. Liu. A two layer approach to wave modeling. The Royal Society London, A, 460: 2637–2669, 2004.

P. A. Madsen and H. A. Schaer. Higher-order boussinesq-type equations for surface gravity waves: derivation and analysis. Phil. Trans. Royal Society of London A, 356:3123–3184, 1998.

O. Nwogu. Alternative form of boussinesq equations for nearshore wave propagation. Journal of Waterway, Port, Coastal and Ocean Engineering, 119(6):618–638, 1993.

D. H. Peregrine. Long waves on a beach. Journal of Fluid Mechanics, 27:815–827, 1967.

G. Wei, J. T. Kirby, S. T. Grilli, and R. Subramnya. A fully nonlinear boussinesq model for surface waves 1. highly nonlinear unsteady waves. Journal of Fluid Mechanics, 294:71–92, 1995.

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