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 20
  • 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.
    Das, S. Sahoo, T. and Meylan, M. H. 2018. Dynamics of flexural gravity waves: from sea ice to Hawking radiation and analogue gravity. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science, Vol. 474, Issue. 2209, p. 20170223.
    Euvé, L.-P. and Rousseaux, G. 2017. Classical analogue of an interstellar travel through a hydrodynamic wormhole. Physical Review D, Vol. 96, Issue. 6,
    Churilov, Semyon Ermakov, Andrei Rousseaux, Germain and Stepanyants, Yury 2017. Scattering of long water waves in a canal with rapidly varying cross-section in the presence of a current. Physical Review Fluids, Vol. 2, Issue. 9,
    Zippel, Seth and Thomson, Jim 2017. Surface wave breaking over sheared currents: Observations from the Mouth of the Columbia River. Journal of Geophysical Research: Oceans, Vol. 122, Issue. 4, p. 3311.
    DEBSARMA, SUMA and DAS, K. P. 2016. CURRENT-MODIFIED EVOLUTION EQUATION FOR A BROADER BANDWIDTH CAPILLARY–GRAVITY WAVE PACKET. The ANZIAM Journal, Vol. 58, Issue. 02, p. 143.
    Peloquin, Cédric Euvé, Léo-Paul Philbin, Thomas and Rousseaux, Germain 2016. Analog wormholes and black hole laser effects in hydrodynamics. Physical Review D, Vol. 93, Issue. 8,
    Suastika, Ketut 2012. Nonlinear-Dispersion Effects in Modeling of Blocking of Stokes Waves. Journal of Coastal Research, Vol. 283, Issue. , p. 829.
    Suastika, I. K. 2012. A Spectral Model for Blocking of Random Waves. Coastal Engineering Journal, Vol. 54, Issue. 2, p. 1250013-1.
    Rousseaux, Germain Maïssa, Philippe Mathis, Christian Coullet, Pierre Philbin, Thomas G and Leonhardt, Ulf 2010. Horizon effects with surface waves on moving water. New Journal of Physics, Vol. 12, Issue. 9, p. 095018.
    Suastika, I. K. and Battjes, J. A. 2009. A Model for Blocking of Periodic Waves. Coastal Engineering Journal, Vol. 51, Issue. 2, p. 81.
    Tian, Ye and Sato, Shinji 2008. A Numerical Model on the Interaction Between Nearshore Nonlinear Waves and Strong Currents. Coastal Engineering Journal, Vol. 50, Issue. 4, p. 369.
    Yao, Aifeng and Wu, Chin H. 2004. Energy Dissipation of Unsteady Wave Breaking on Currents. Journal of Physical Oceanography, Vol. 34, Issue. 10, p. 2288.
    Chawla, Arun 2002. Monochromatic and random wave breaking at blocking points. Journal of Geophysical Research, Vol. 107, Issue. C7,
    Bal, Guillaume and Chou, Tom 2002. Capillary–gravity wave transport over spatially random drift. Wave Motion, Vol. 35, Issue. 2, p. 107.
    Chawla, Arun and Kirby, James T. 1999. Experimental Study of Wave Breaking and Blocking on Opposing Currents. p. 759.
    Chen, Qin Madsen, Per A. Schäffer, Hemming A. and Basco, David R. 1998. Wave-current interaction based on an enhanced Boussinesq approach. Coastal Engineering, Vol. 33, Issue. 1, p. 11.
    Vogelzang, J. 1997. Mapping submarine sand waves with multiband imaging radar: 1. Model development and sensitivity analysis. Journal of Geophysical Research: Oceans, Vol. 102, Issue. C1, p. 1163.
    Ris, R.C. and Holthuijsen, L.H. 1997. Spectral Modelling of Current Induced Wave-Blocking. p. 1247.
    Longuet-Higgins, Michael S. 1996. Surface manifestations of turbulent flow. Journal of Fluid Mechanics, Vol. 308, Issue. -1, p. 15.
    Ramamonjiarisoa, A. 1995. On the kinematics of short waves in the presence of surface flows of larger scales. Journal of Fluid Mechanics, Vol. 298, Issue. -1, p. 249.
    ×
  • Get access
    Add to cart USD35.00
    Check if you have access via personal or institutional login
    Log in Register Recommend to librarian

Double reflection of capillary/gravity waves by a non-uniform current: a boundary-layer theory

  • Karsten Trulsen (a1) and Chiang C. Mei (a1)
Abstract

When a train of gravity waves encounters an opposing current, the wavelength is shortened and the waves may be reflected. If capillarity is included, the shortened waves may be reflected for a second time and experience further shortening. By this process the initially long gravity waves can be damped by viscosity quickly without breaking. In this paper a boundary-layer approximation is obtained close to the reflection points, and is matched to the ray approximations outside. This is then applied to the propagation of a wavepacket. Damping is accounted for in the ray solution and the result is compared to the undamped solution. The case where the two reflection points coalesce is also considered. It is found that as the separation between the reflection points decreases, the wavepacket appears to remain longer in the region of reflections relative to the width of this region.

Copyright
© 1993 Cambridge University Press
References
Hide All
Badulin, S. I., Pokazeyev, K. V. & Rozenberg, A. D. 1983 A laboratory study of the transformation of regular gravity-capillary waves in inhomogeneous flows. Izv. Atmos. Ocean. Phys. 19 (10), 782–787.
Basovich, A. Y. & Talanov, V. I. 1977 Transformation of short surface waves on inhomogeneous currents. Izv. Atmos. Ocean. Phys. 13 (7), 514–519.
Bretherton, F. P. & Garrett, C. J. R. 1968 Wavetrains in inhomogeneous moving media. Proc. R. Soc. Lond. A 302, 529–554.
Henyey, F. S., Creamer, D. B., Dysthe, K. B. Schult, R. L. & Wright, J. A. 1988 The energy and action of small waves riding on large waves. J. Fluid Mech. 189, 443–462.
Lai, R. J., Long, S. R. & Huang, N. E. 1989 Laboratory studies of wave—current interaction: kinematics of the strong interaction. J. Geophys. Res. 94 (C11), 16201–16214.
Longuet-Higgins, M. S. & Stewart, R. W. 1960 Changes in the 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.
Paris, R. B. 1991 The asymptotic behaviour of Pearcey's integral for complex variables. Proc. R. Soc. Lond. A 432, 391–426.
Pearcey, T. 1946 The structure of an electromagnetic field in the neighbourhood of a cusp of a caustic. Phil. Mag. 37, 311–317.
Peregrine, D. H. & Smith, R. 1979 Nonlinear effects upon waves near caustics. Phil. Trans. R. Soc. Lond. A 292, 341–370.
Phillips, O. M. 1981 The dispersion of short wavelets in the presence of a dominant long wave. J. Fluid Mech. 107, 465–485.
Pokazeyev, K. V. & Rozenberg, A. D. 1983 Laboratory studies of regular gravity-capillary waves in currents. Okeanologiya 23 (4), 429–435.
Shyu, J.-H. & Phillips, O. M. 1990 The blockage of gravity and capillary waves by longer waves and currents. J. Fluid Mech. 217, 115–141.
Smith, R. 1975 The reflection of short gravity waves on a non-uniform current. Math. Proc. Camb. Phil. Soc. 78, 517–525.
Stamnes, J. J. 1986 Waves in Focal Regions. Adam Hilger.
Stiassnie, M. & Dagan, G. 1979 Partial reflexion of water waves by non-uniform adverse currents. J. Fluid Mech. 92, 119–129.
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: 0
Total number of PDF views: 20 *
Loading metrics...

Abstract views

Total abstract views: 100 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 12th June 2018. This data will be updated every 24 hours.

Cancel
Confirm
×