Alternative forms of the higher-order Boussinesq equations: Derivations and validations |
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| Authors: | ZL Zou KZ Fang |
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| Institution: | State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian 116024, PR China |
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| Abstract: | An alternative form of the Boussinesq equations is developed, creating a model which is fully nonlinear up to O(μ4) (μ is the ratio of water depth to wavelength) and has dispersion accurate to the Padé 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 σ-transformation. Two reduced forms of the model are also presented, which simplify O(μ4) terms using the assumption ε = O(μ2/3) (ε is the ratio of wave height to water depth). These can be seen as extensions of Serre's equations, with dispersions given by the Padé 2,2] and Padé 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. |
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| Keywords: | Boussinesq equations Wave propagation Nonlinear waves |
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