World Library  

Add to Book Shelf
Flag as Inappropriate
Email this Book

Benjamin–feir Instability of Waves in the Presence of Current : Volume 1, Issue 2 (05/12/2014)

By Shugan, I. V.

Click here to view

Book Id: WPLBN0004020083
Format Type: PDF Article :
File Size: Pages 30
Reproduction Date: 2015

Title: Benjamin–feir Instability of Waves in the Presence of Current : Volume 1, Issue 2 (05/12/2014)  
Author: Shugan, I. V.
Volume: Vol. 1, Issue 2
Language: English
Subject: Science, Nonlinear, Processes
Collections: Periodicals: Journal and Magazine Collection (Contemporary), Copernicus GmbH
Publication Date:
Publisher: Copernicus Gmbh, Göttingen, Germany
Member Page: Copernicus Publications


APA MLA Chicago

Hwung, H. H., Yang, R. Y., & Shugan, I. V. (2014). Benjamin–feir Instability of Waves in the Presence of Current : Volume 1, Issue 2 (05/12/2014). Retrieved from

Description: International Wave Dynamics Research Center, National Cheng Kung University, Tainan, Taiwan. The development of Benjamin–Feir instability of Stokes waves in the presence of variable current is presented. We employ a model of a resonance system having three coexisting nonlinear waves and nonuniform current. The model is free from the narrow-band approximation for surface waves and relatively weak adverse current. The modulation instability of Stokes waves in nonuniform moving media has special properties. 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. Large transient or freak waves with amplitude and steepness several times those of normal waves may form during temporal nonlinear focusing of the resonant waves accompanied by energy income from sufficiently strong opposing current. We employ the resonance model for the estimation of the maximum amplification of wave amplitudes as a function of gradually increasing opposing current and compare the result obtained with recently published experimental results and modeling results obtained with the nonlinear Schrödinger equation.

Benjamin–Feir instability of waves in the presence of current

Chabchoub, A., Akhmediev, N., and Hoffmann, N.: Experimental study of spatiotemporally localized surface gravity water waves, Phys. Rev. E, 86, 016311, doi:10.1103/PhysRevE.86.016311, 2012.; Donato, A. N., Peregrine, D. H., and Stocker, J. R.: The focusing of surface. waves by internal Waves, J. Fluid Mech., 384, 27–58, 1999.; Dysthe, K. B.: Note on a modification to the nonlinear Schrodinger equation for application to deep water waves, P. R. Soc. A, 369, 105–114, 1979.; Gargett, A. E. and Hughes, B. A.: On the interaction of surface and internal waves, J. Fluid Mech., 52, 179–191, 1972.; Benjamin, T. B. and Feir, J. E.: Instability of periodic wavetrains in nonlinear dispersive systems, J. Fluid Mech., 27, 417–430, 1967.; Bridges, T. and Dias, F.: Enhancement of the Benjamin-Feir instability with dissipation, Phys. Fluids., 19, 104104, doi:10.1063/1.2780793, 2007.; Chavla, A. and Kirby, J.: Experimental study of breaking waves on a blocking current, Proc. 26th International Conference on Coastal Engineering, Copenhagen, 22–26 June, 759–772, 1998.; Chavla, A. and Kirby, J.: Monochromatic and random wave breaking at block points, J. Geophys. Res., 107, 4.1–4.19, 2002.; Dias, F. and Kharif, C.: Nonlinear gravity and capillary-gravity waves, Annu. Rev. Fluid Mech., 31, 301–346, 1999.; Gerber, M.: The Benjamin–Feir instability of a deep water Stokes wavepacket in the presence of a non-uniform medium, J. Fluid Mech., 176, 311–332, 1987.; Hjelmervik, K. B. and Trulsen, K.: Freak wave statistics on collinear currents, J. Fluid Mech., 637, 267–284, 2009.; Hwung, H., Chiang, W., and Hsiao, S.: Observations on the evolution of wave modulation, P. Roy. Soc. Lond. A. Mat., 463, 85–112, 2007.; Hwung, H., Yang, R., and Shugan, I.: Exposure of internal waves on the sea surface, J. Fluid Mech., 626, 1–20, 2009.; Hwung, H., Chiang, W., Yang, R., and Shugan, I.: Threshold Model on the Evolution of Stokes Wave Side-Band Instability, Eur. J. Mech. B-Fluid., 30, 147–155, 2011.; Janssen, P.: Nonlinear four-wave interactions and freak waves, J. Phys. Oceanogr., 33, 863–884, 2003.; Janssen, T. and Herbers, T.: Nonlinear Wave Statistics in a Focal Zone, J. Phys. Oceanogr., 39, 1948–1964, 2009.; Kharif, C. and Pelinovsky, E.: Freak waves phenomenon: physical mechanisms and modelling, in: Waves in Geophysical Fluids: CISM Courses and Lectures 489, edited by: Grue, J. and Trulsen, K., 107–172, New York, Springer Wein, 2006.; Lake, B. M. and Yuen, H. C.: A new model for nonlinear wind waves. Part 1. Physical model and experimental evidence, J. Fluid Mech., 88, 33–62, 1978.; Landrini, M., Oshri, O., Waseda, T., and Tulin, M. P.: Long time evolution of gravity wave systems, in: Proc. 13th Intl Workshop on Water Waves and Floating Bodies, edited by: Hermans,. A. J., Alphen aan den Rijn, 75–78, 1998.; Lavrenov, I. V.: The wave energy concentration at the Agulhas current off South Africa, Nat. Hazards, 17, 117–127, 1998.; Lewis, J. E., Lake, B. M., and Ko, D. R.: On the interaction of internal waves and surface gravity waves, J. Fluid Mech., 63, 773–800, 1974.; Lo, E. and Mei, C. C.: A numerical study of water-wave modulation base on a higher-order nonlinear Schrodinger equation, J. Fluid Mech., 150, 395–416, 1985.; Longuet-Higgins, M. and Stewart, R.: Radiation stresses in water waves: a physical discussion, with applications, Deep-Sea Res., 11, 529–562, 1964.; Ma, Y., Dong, G., Perlin, M., Ma, X., Wang, G., and Xu, J.: Laboratory observations of wave evolution, modulation and blocking due to spatially varying opposing currents, J. Fluid Mech., 661, 108–129, 2010.; Ma, Y., Ma, X., Perlin, M., and Dong, G.: Extreme waves generated by modulational instability on adverse currents, Phys. Fluids, 25, 114109, doi:10.1063/1.4832715, 2013.; Melville, W.: Wave modulation and break


Click To View

Additional Books

  • On Aspects of the Measurement of Non-lin... (by )
  • The Role of Subsidence in a Weakly Unsta... (by )
  • Manifestation of Nonlinear Elasticity in... (by )
  • Interactions Between Marine Biota and En... (by )
  • Total Ozone Time Series Analysis: a Neur... (by )
  • The Effect of Stochastic Perturbations o... (by )
  • A Deterministic Width Function Model : V... (by )
  • Statistical Optimization for Passive Sca... (by )
  • Fluctuation-response Relation and Modeli... (by )
  • Non-linear Analysis of Geomagnetic Time ... (by )
  • Evaluation of a Spectral Line Width for ... (by )
  • The Transformation of an Interfacial Sol... (by )
Scroll Left
Scroll Right


Copyright © World Library Foundation. All rights reserved. eBooks from Hawaii eBook Library are sponsored by the World Library Foundation,
a 501c(4) Member's Support Non-Profit Organization, and is NOT affiliated with any governmental agency or department.