Skip to main content
×
Home
    • Aa
    • Aa
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 366
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Budiasih, L. K. and Wiryanto, L. H. 2016. Vol. 1707, Issue. , p. 050003.

    Cathala, Mathieu 2016. Asymptotic shallow water models with non smooth topographies. Monatshefte für Mathematik, Vol. 179, Issue. 3, p. 325.


    Donahue, Aaron S. Kennedy, Andrew B. Westerink, Joannes J. Zhang, Yao and Dawson, Clint 2016. Simulation of wave phenomena in the nearshore through application of O(μ2) and O(μ4) pressure-Poisson Boussinesq type models. Coastal Engineering, Vol. 114, p. 61.


    Duan, W. Y. Zheng, K. Zhao, B. B. Demirbilek, Z. Ertekin, R. C. and Webster, W. C. 2016. On wave–current interaction by the Green–Naghdi equations in shallow water. Natural Hazards,


    Fang, KeZhao Liu, ZhongBo and Zou, ZhiLi 2016. Fully Nonlinear Modeling Wave Transformation over Fringing Reefs Using Shock-Capturing Boussinesq Model. Journal of Coastal Research, Vol. 317, p. 164.


    Filippini, A.G. Kazolea, M. and Ricchiuto, M. 2016. A flexible genuinely nonlinear approach for nonlinear wave propagation, breaking and run-up. Journal of Computational Physics, Vol. 310, p. 381.


    Gallerano, F. Cannata, G. and Lasaponara, F. 2016. A new numerical model for simulations of wave transformation, breaking and long-shore currents in complex coastal regions. International Journal for Numerical Methods in Fluids, Vol. 80, Issue. 10, p. 571.


    GALLERANO, F. CANNATA, G. and LASAPONARA, F. 2016. Numerical simulation of wave transformation, breaking and runup by a contravariant fully non-linear Boussinesq equations model. Journal of Hydrodynamics, Ser. B, Vol. 28, Issue. 3, p. 379.


    Gao, Junliang Ji, Chunyan Gaidai, Oleg and Liu, Yingyi 2016. Numerical study of infragravity waves amplification during harbor resonance. Ocean Engineering, Vol. 116, p. 90.


    Ghadimi, Parviz Rahimzadeh, Amin Feizi Chekab, Mohammad A. Jabbari, Mohammad H. and Shademani, Roya 2016. Numerical modeling of solitary waves by 1-D Madsen and Sorensen extended Boussinesq equations. ISH Journal of Hydraulic Engineering, Vol. 22, Issue. 1, p. 30.


    Gomes, Esther R. Mulligan, Ryan P. Brodie, Katherine L. and McNinch, Jesse E. 2016. Bathymetric control on the spatial distribution of wave breaking in the surf zone of a natural beach. Coastal Engineering, Vol. 116, p. 180.


    Grilli, Stéphan T. Grilli, Annette R. David, Eric and Coulet, Christophe 2016. Tsunami hazard assessment along the north shore of Hispaniola from far- and near-field Atlantic sources. Natural Hazards, Vol. 82, Issue. 2, p. 777.


    Kalisch, Henrik Khorsand, Zahra and Mitsotakis, Dimitrios 2016. Mechanical balance laws for fully nonlinear and weakly dispersive water waves. Physica D: Nonlinear Phenomena, Vol. 333, p. 243.


    Lannes, David and Marche, Fabien 2016. Nonlinear Wave-Current Interactions in Shallow Water. Studies in Applied Mathematics, Vol. 136, Issue. 4, p. 382.


    Liu, Zhongbo and Fang, Kezhao 2016. A new two-layer Boussinesq model for coastal waves from deep to shallow water: Derivation and analysis. Wave Motion, Vol. 67, p. 1.


    Liu, Chi-Min 2016. Boussinesq equations for internal waves in a two-fluid system with a rigid lid. Ocean Systems Engineering, Vol. 6, Issue. 1, p. 117.


    Lynett, Patrick J. and Kaihatu, James M. 2016. Springer Handbook of Ocean Engineering.


    Maravelakis, N. Kalligeris, N. Lynett, P. and Synolakis, C. 2016. Ports 2016. p. 647.

    Memos, Constantine D. Klonaris, Georgios Th. and Chondros, Michalis K. 2016. On Higher-Order Boussinesq-Type Wave Models. Journal of Waterway, Port, Coastal, and Ocean Engineering, Vol. 142, Issue. 1, p. 04015011.


    Metallinos, Anastasios S. Repousis, Elpidoforos G. and Memos, Constantine D. 2016. Wave propagation over a submerged porous breakwater with steep slopes. Ocean Engineering, Vol. 111, p. 424.


    ×
  • Journal of Fluid Mechanics, Volume 294
  • July 1995, pp. 71-92

A fully nonlinear Boussinesq model for surface waves. Part 1. Highly nonlinear unsteady waves

  • Ge Wei (a1), James T. Kirby (a1), Stephan T. Grilli (a2) and Ravishankar Subramanya (a2)
  • DOI: http://dx.doi.org/10.1017/S0022112095002813
  • Published online: 01 April 2006
Abstract

Fully nonlinear extensions of Boussinesq equations are derived to simulate surface wave propagation in coastal regions. By using the velocity at a certain depth as a dependent variable (Nwogu 1993), the resulting equations have significantly improved linear dispersion properties in intermediate water depths when compared to standard Boussinesq approximations. Since no assumption of small nonlinearity is made, the equations can be applied to simulate strong wave interactions prior to wave breaking. A high-order numerical model based on the equations is developed and applied to the study of two canonical problems: solitary wave shoaling on slopes and undular bore propagation over a horizontal bed. Results of the Boussinesq model with and without strong nonlinearity are compared in detail to those of a boundary element solution of the fully nonlinear potential flow problem developed by Grilli et al. (1989). The fully nonlinear variant of the Boussinesq model is found to predict wave heights, phase speeds and particle kinematics more accurately than the standard approximation.

Copyright
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax