Alternative forms of the higher-order Boussinesq equations: Derivations and validations

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Indexed by:期刊论文

Date of Publication:2008-06-01

Journal:COASTAL ENGINEERING

Included Journals:SCIE、EI

Document Type:J

Volume:55

Issue:6

Page Number:506-521

ISSN No.:0378-3839

Key Words:Boussinesq equations; wave propagation; nonlinear waves

Abstract:An alternative form of the Boussinesq equations is developed, creating a model which is fully nonlinear up to O(mu U-4) (mu is the ratio of water depth to wavelength) and has dispersion accurate to the Pade [4,4] approximation. No limitation is imposed on the bottom slope; the variable distance between free surface and sea bottom is accounted for by a sigma-transformation. Two reduced forms of the model are also presented, which Simplify O(mu(4)) terms using the assumption epsilon = O(mu(2/3)) (epsilon is the ratio of wave height to water depth). These can be seen as extensions of Serre's equations, with dispersions given by the Pade [2,2] and Pade [4,4] approximations. The third-order nonlinear characteristics of these three models are discussed using Fourier analysis, and compared to other high-order formulations of the Boussinesq equations. The models are validated against experimental measurements of wave propagation over a submerged breakwater. Finally, the nonlinear evolution of wave groups along a horizontal flume is simulated and compared to experimental data in order to investigate the effects of the amplitude dispersion and the four-wave resonant interaction. (C) 2008 Elsevier B.V. All rights reserved.