A review on the theory and application of Boussinesq-type equations for water waves

Sun Jiawen; Fang Kezhao; Liu Zhongbo; Fan Haoxu; Sun Zhaochen; Wang Ping

doi:10.3969/j.issn.0253-4193.2020.05.001

Volume 42 Issue 5

Nov. 2020

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Sun Jiawen，Fang Kezhao，Liu Zhongbo, et al. A review on the theory and application of Boussinesq-type equations for water waves[J]. Haiyang Xuebao，2020, 42(5)：1–11，doi:10.3969/j.issn.0253−4193.2019.05.001

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A review on the theory and application of Boussinesq-type equations for water waves

doi: 10.3969/j.issn.0253-4193.2020.05.001

Sun Jiawen^{1, 2, 3
,},
Fang Kezhao³,
Liu Zhongbo^{2
,
,},
Fan Haoxu³,
Sun Zhaochen³,
Wang Ping¹

1.
State Environmental Protection Key Laboratory of Marine Ecological Environment Restoration, National Marine Environmental Monitoring Center, Dalian 116023, China
2.
Transportation Engineering College, Dalian Maritime University, Dalian 116026, China
3.
State Key Laboratory of Coastal and Offshore Engineering/DUT-UWA Joint Research Center for Ocean Engineering, Dalian University of Technology, Dalian 116024, China

Received Date: 2019-04-17
Rev Recd Date: 2019-09-14

Available Online: 2020-11-18

Publish Date: 2020-05-25

Abstract

Abstract

Boussinesq-type equation is one of the important tools for simulating the propagation and evolution of water waves. The theoretical derivation and numerical application of the Boussinesq-type water wave equation dating back to 1967 are reviewed with the hope of promoting its deep development and application in the fields of coastal and ocean engineering. From the theoretical point of view, the derivation of such equations mainly starts from Euler equations or Laplace equations. Under the conditions of certain nonlinearity and gentle slope assumptions, a variety of Boussinesq-type water wave equations have been proposed worldwide. Through the comparisons with the related theories of Stokes waves, these equations are investigated with respect to phase velocity, group velocity, linear shoaling gradient, second-order nonlinearity, third-order nonlinearity, dispersion characteristics due to amplitude dispersion, velocity distribution along the vertical column, sub- and super harmonics etc. The majority of Boussinesq-type equations in literature for waves are reviewed and grouped into two categories, namely horizontal two-dimensional type and three-dimensional type. The usage of Boussinesq-type equations involved with permeable media and the presence of fluid stratification are also briefly described and commented. Finally, the application of these equations is summarized and analyzed.
- Boussinesq-type equations,
- dispersion,
- nonlinear property,
- linear shoaling property,
- numerical applications

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References(75)

References

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