Benjamin-feir wave instability on the opposite current

Igor V. Shugan, Hwung Hweng Hwung, Ray Yeng Yang

Research output: Chapter in Book/Report/Conference proceedingConference contribution


An analytical weakly nonlinear model of Benjamin-Feir instability of a Stokes wave on nonuniform unidirectional current is presented. The model describes evolution of a Stokes wave and its two main sidebands propagating on a slowlyvarying steady current. In contrast to the models based on versions of the cubic Schrodinger equation the current variations could be strong, which allows us to examine the blockage and consider substantial variations of the wave numbers and frequencies of interacting waves. Interaction with countercurrent accelerates the growth of sideband modes on a short spatial scale. An increase in initial wave steepness intensifies the wave energy exchange accompanied by wave breaking dissipation, results in asymmetry of sideband modes and a frequency downshift with an energy transfer jump to the lower sideband mode, and depresses the higher sideband and carrier wave. Nonlinear waves may even overpass the blocking barrier produced by strong adverse current. The frequency downshift of the energy peak is permanent and the system does not revert to its initial state. We find reasonable correspondence between the results of model simulations and available experimental results for wave interaction with blocking opposing current.

Original languageEnglish
Title of host publicationOcean Engineering
PublisherAmerican Society of Mechanical Engineers (ASME)
ISBN (Electronic)9780791849989
Publication statusPublished - 2016
EventASME 2016 35th International Conference on Ocean, Offshore and Arctic Engineering, OMAE 2016 - Busan, Korea, Republic of
Duration: 2016 Jun 192016 Jun 24

Publication series

NameProceedings of the International Conference on Offshore Mechanics and Arctic Engineering - OMAE


OtherASME 2016 35th International Conference on Ocean, Offshore and Arctic Engineering, OMAE 2016
Country/TerritoryKorea, Republic of

All Science Journal Classification (ASJC) codes

  • Ocean Engineering
  • Energy Engineering and Power Technology
  • Mechanical Engineering


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