Skip to main content

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
Cancel
×
×
Home
  • Home
Article
  • Cited by 48
  • Cited by
    Crossref Citations
    Crossref logo
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.
    Wang, Jinghua Ma, Qingwei and Yan, Shiqiang 2018. A fully nonlinear numerical method for modeling wave–current interactions. Journal of Computational Physics, Vol. 369, Issue. , p. 173.
    Zhu, Ling and Chen, Qin 2017. Effects of Triad Interactions on Wave Attenuation by Vegetation. Journal of Engineering Mechanics, Vol. 143, Issue. 9, p. 04017100.
    Liu, Chi-Min 2017. Derivation and optimization of Boussinesq equations for internal waves with current effects in a two-fluid system. p. 1.
    Klonaris, Georgios Th. Memos, Constantine D. and Drønen, Nils K. 2016. High-Order Boussinesq-Type Model for Integrated Nearshore Dynamics. Journal of Waterway, Port, Coastal, and Ocean Engineering, Vol. 142, Issue. 6, p. 04016010.
    Duan, W. Y. Zheng, K. Zhao, B. B. Demirbilek, Z. Ertekin, R. C. and Webster, W. C. 2016. On wave–current interaction by the Green–Naghdi equations in shallow water. Natural Hazards, Vol. 84, Issue. S2, p. 567.
    Kirby, James T. 2016. Boussinesq Models and Their Application to Coastal Processes across a Wide Range of Scales. Journal of Waterway, Port, Coastal, and Ocean Engineering, Vol. 142, Issue. 6, p. 03116005.
    Ning, De-zhi Lin, Hong-xing Teng, Bin and Zou, Qing-ping 2014. Higher harmonics induced by waves propagating over a submerged obstacle in the presence of uniform current. China Ocean Engineering, Vol. 28, Issue. 6, p. 725.
    Chen, Xiaobo Li, Jing and Chen, JianYun 2014. Nonlinear wave and currents loads analysis of offshore wind turbines. KSCE Journal of Civil Engineering, Vol. 18, Issue. 6, p. 1877.
    Xiao, Hong Huang, Wenrui Tao, Jianhua and Liu, Changgen 2013. Numerical modeling of wave–current forces acting on horizontal cylinder of marine structures by VOF method. Ocean Engineering, Vol. 67, Issue. , p. 58.
    Sulisz, Wojciech and Paprota, Maciej 2013. Modeling of propagation and transformation of transient nonlinear waves on a current. China Ocean Engineering, Vol. 27, Issue. 5, p. 579.
    Huntley, D.A. 2013. Treatise on Geomorphology. p. 39.
    Zou, Z.L. Hu, P.C. Fang, K.Z. and Liu, Z.B. 2013. Boussinesq-type equations for wave–current interaction. Wave Motion, Vol. 50, Issue. 4, p. 655.
    Suastika, Ketut 2012. Nonlinear-Dispersion Effects in Modeling of Blocking of Stokes Waves. Journal of Coastal Research, Vol. 283, Issue. , p. 829.
    Tonelli, Mara and Petti, Marco 2012. Shock-capturing Boussinesq model for irregular wave propagation. Coastal Engineering, Vol. 61, Issue. , p. 8.
    Tonelli, Mara and Petti, Marco 2011. Simulation of wave breaking over complex bathymetries by a Boussinesq model. Journal of Hydraulic Research, Vol. 49, Issue. 4, p. 473.
    Belibassakis, K.A. Gerostathis, Th.P. and Athanassoulis, G.A. 2011. A coupled-mode model for water wave scattering by horizontal, non-homogeneous current in general bottom topography. Applied Ocean Research, Vol. 33, Issue. 4, p. 384.
    Kim, Dae-Hong and Lynett, Patrick J. 2011. Turbulent mixing and passive scalar transport in shallow flows. Physics of Fluids, Vol. 23, Issue. 1, p. 016603.
    ZHANG, Hong-sheng WANG, Wei-yuan FENG, Wen-jing WANG, Ya-ling and YANG, Jian-min 2010. Tests and Applications of A Boussinesq Model with Ambient Current. Journal of Hydrodynamics, Ser. B, Vol. 22, Issue. 4, p. 526.
    Park, Sang-Gil Kang, Sug-Jin Kim, Kang-Min Kim, Suk-Mun and Lee, Joong-Woo 2010. Field Application of the Slit Type Coastal Structures under Waves and Currents. Journal of Navigation and Port Research, Vol. 34, Issue. 9, p. 711.
    Dutykh, D. and Dias, F. 2009. Energy of tsunami waves generated by bottom motion. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 465, Issue. 2103, p. 725.
    Download full list
    ×
  • Get access
    Add to cart USD35.00
    Check if you have access via personal or institutional login
    Log in Register Recommend to librarian

Interactions of currents and weakly nonlinear water waves in shallow water

  • Sung B. Yoon (a1) (a2) and Philip L.-F. Liu (a1)
Abstract

Two-dimensional Boussinesq-type depth-averaged equations are derived for describing the interactions of weakly nonlinear shallow-water waves with slowly varying topography and currents. The current velocity varies appreciably within a characteristic wavelength. The effects of vorticity in the current field are considered. The wave field is decomposed into Fourier time harmonics. A set of evolution equations for the wave amplitude functions of different harmonics is derived by adopting the parabolic approximation. Numerical solutions are obtained for shallow-water waves propagating over rip currents on a plane beach and an isolated vortex ring. Numerical results show that the wave diffraction and nonlinearity are important in the examples considered.

Copyright
© 1989 Cambridge University Press
References
Hide All
Arthur, R. S. 1950 Refraction of shallow water waves: the combined effects of currents and underwater topography. EOS Trans. AGU 31, 549–552.
Boou, N. 1981 Gravity waves on water with nonuniform depth and current. Rep. 81-1. Dept. of Civil Engrg, Delft University of Technology, Delft.
Bretherton, F. P. & Garrett, C. J. R. 1969 Wave trains in inhomogeneous moving media. Proc. R. Soc. Lond. A 302, 529–554.
Kirby, J. T. 1984 A note on linear surface wave-current interaction over slowly varying topography. J. Geophys. Res. 89, 745–747.
Kirby, J. T. 1986 Higher-order approximations in the parabolic equation method for water waves. J. Geophys. Res. 91, 933–952.
Liu, P. L.-F. 1983 Wave-current interaction on a slowly varying topography. J. Geophys. Res. 88, 4421–4426.
Liu, P. L.-F. & Mei, C. C. 1975 Effects of a breakwater on nearshore currents due to breaking waves. Tech. Mem. 57. Coastal Engineering Research Center.
Liu, P. L.-F., Yoon, S. B. & Kirby, J. T. 1985 Nonlinear refraction-diffraction of waves in shallow water. J. Fluid Mech. 153, 184–201.
Longuet-Higgins, M. S. & Stewart, R. W. 1960 Changes in form of short gravity waves on long waves and tidal currents. J. Fluid Mech. 8, 565–583.
Longuet-Higgins, M. S. & Stewart, R. W. 1961 The changes in amplitude of short gravity waves on steady non-uniform currents. J. Fluid Mech. 10, 529–549.
McKee, W. D. 1974 Waves on a shearing current: a uniformly valid asymptotic solution. Proc. Camb. Phil. Soc. 75, 295–301.
Madsen, O. S. & Mei, C. C. 1969 Dispersion of long waves of finite amplitude over an uneven bottom. Rep. 117. Dept. of Civil Engrg, MIT.
Mapp, G. R., Welch, C. S. & Munday, J. C. 1985 Wave refraction by warm core rings. J. Geophys. Res. 90, 7153–7162.
Peregrine, D. H. 1967 Long waves on a beach. J. Fluid Mech. 27, 815–827.
Peregrine, D. H. 1976 Interaction of water waves and currents. Adv. Appl. Mech. 16, 10–117.
Peregrine, D. H. & Smith, R. 1975 Stationary gravity waves on non-uniform free streams. Math. Proc. Camb. Phil. Soc. 77, 415–438.
Phillips, O. M. 1966 The dynamics of the Upper Ocean. Cambridge University Press.
Smith, R. 1976 Giant waves. J. Fluid Mech. 77, 417–431.
Yoon, S. B. 1987 Propagation of shallow-water waves over slowly varying depth and currents. Ph.D. Thesis, Cornell University, Ithaca, NY.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *

CAPTCHA *

Skip to the audio challenge
×
MathJax

Metrics

Full text views

Total number of HTML views: 1
Total number of PDF views: 43 *
Loading metrics...

Abstract views

Total abstract views: 193 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 13th June 2018. This data will be updated every 24 hours.

Cancel
Confirm
×