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  • Journal of Fluid Mechanics, Volume 399
  • November 1999, pp. 319-333

A new approach to high-order Boussinesq models

  • Y. AGNON (a1), P. A. MADSEN (a2) and H. A. SCHÄFFER (a3)
  • DOI:
  • Published online: 25 November 1999

An infinite-order, Boussinesq-type differential equation for wave shoaling over variable bathymetry is derived. Defining three scaling parameters – nonlinearity, the dispersion parameter, and the bottom slope – the system is truncated to a finite order. Using Padé approximants the order in the dispersion parameter is effectively doubled. A derivation is made systematic by separately solving the Laplace equation in the undisturbed fluid domain and then addressing the nonlinear free-surface conditions. We show that the nonlinear interactions are faithfully captured. The shoaling and dispersion components are time independent.

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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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