WANG Ben-long, LIU Hua. Higher Order Boussinesq-Type Equations for Water Waves on Uneven Bottom[J]. Applied Mathematics and Mechanics, 2005, 26(6): 714-722.
Citation: WANG Ben-long, LIU Hua. Higher Order Boussinesq-Type Equations for Water Waves on Uneven Bottom[J]. Applied Mathematics and Mechanics, 2005, 26(6): 714-722.

Higher Order Boussinesq-Type Equations for Water Waves on Uneven Bottom

  • Received Date: 2003-07-21
  • Rev Recd Date: 2004-12-03
  • Publish Date: 2005-06-15
  • Higher order Boussinesq-type equations for wave propagation over variable bathymetry were derived.The time dependent free surface boundary conditions were used to compute the change of the free surface in time domain.The free surface velocities and the bottom velocities were connected by the exact solution of the Laplace equation.Taking the velocities on half relative water depth as the fundamental unknowns,terms relating to the gradient of the water depth were retained in the inverse series expansion of the exact solution,with which the problem was closed.With enhancements of the finite order Taylor expansion for the velocity field,the application range of the present model was extended to the not so mild slope bottom.For linear properties,some validation computations of linear shoaling and Booij's tests were carried out.The problems of wave-current interactions were also studied numerically to test the performance of the enhanced Boussinesq equations associated with the effect of currents.All these computational results confirm perfectly to the theoretical solution as well as other numerical solutions of the full potential problem available.
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  • [1]
    Madsen P A,Schffer H A.Higher-order Boussinesq-type equations for surface gravity waves: derivation and analysis[J].Phil Trans Roy Soc,London A,1998,(356):3123—3184.
    Gobbi M F,Kirby J T,Wei G.A fully nonlinear Boussinesq model for surface wave—Ⅱ:Extension to O(kh)4[J].J Fluid Mech,2000,(405):181—210.
    HONG Guang-wen.Higher order model of nonlinear and dispersive wave in water of varying depth with arbitrary sloping bottom[J].China Ocean Engineering,1997,11(3):243—260.
    CHEN Qin,Madsen P A,Basco D R.Current effects on nonlinear interactions of shallow-water waves[J].Journal of Waterway, Port, Coastal, and Ocean Engineering,1999,125(4):176—186. doi: 10.1061/(ASCE)0733-950X(1999)125:4(176)
    Kristensen M K.Boussinesq equations and wave-current interaction[D].Master's thesis.International Research Center for Computed Hydrodynamics (ICCH) at Danish Hydraulic Institute,Denmark and ISVA,Technical University of Denmark,1995,130—142.
    Madsen P A,Bingham H B,Liu H.A new Boussinesq method for fully nonlinear waves from shallow to deep water[J].J Fluid Mech,2002,(462):1—30.
    Wu T Y.A unified theory for modeling water waves[A].In:Advances in Applied Mechanics[C].Boston:Academic Press,2000,37:1—88.
    Booij N.A note on the accuracy of the mild-slope equation[J].Coastal Engineering,1983,7(2):191—203. doi: 10.1016/0378-3839(83)90017-0
    Suh K D,Lee C,Park W S.Time-dependent equations for wave propagation on rapidly varying topography[J].Coastal Engineering,1997,32(2/3):91—117. doi: 10.1016/S0378-3839(97)81745-0
    Chen Q,Madsen P A.Schffer H A,et al.Wave-current interaction based on an enhanced Boussinesq approach[J].Coastal Engineering,1998,33(1):11—39. doi: 10.1016/S0378-3839(97)00034-3
    Agnon Y,Madsen P A,Schffer H A.A new approach to high order Boussinesq models[J].J Fluid Mech,1999,(399):319—333.
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    通讯作者: 陈斌,
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      沈阳化工大学材料科学与工程学院 沈阳 110142

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