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The reflection of water waves by shear currents

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Abstract

The refraction and reflection of linear water waves entering a following jet-type current is considered. A short-wave asymptotic solution is presented and the reflection coefficient found. This varies continuously from zero when the waves are normal to the current to unity when they are very oblique to it. The trapping of waves by an opposing current is also considered.

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References

  • Buchwald, V. T. (1968),Long waves on oceanic ridges, Proc. Roy. Soc.308, 343–354.

    Google Scholar 

  • Chao, Y.-Y. (1971),An asymptotic evaluation of the wave field near a smooth caustic, J. Geophys. Res.76, 7401–7408.

    Google Scholar 

  • Chao, Y.-Y. andPierson, W. J. (1972),Experimental studies of the refraction of uniform wave trains and transient wave groups near a straight caustic, J. Geophys. Res.77, 4545–4554.

    Google Scholar 

  • Hughes, B. A. andStewart, R. W. (1961),Interaction between gravity waves and a shear flow, J. Fluid Mech.10, 385–400.

    Google Scholar 

  • Keller, J. B. (1958),Surface waves on water of non-uniform depth, J. Fluid Mech.4, 607–614.

    Google Scholar 

  • Keller, J. B. andMow, V. C. (1969),Internal wave propagation in an inhomogeneous fluid of non-uniform depth, J. Fluid Mech.38, 365–374.

    Google Scholar 

  • Kenyon, K. E. (1971),Wave refraction in ocean currents, Deep-Sea Res.18, 1023–1034.

    Google Scholar 

  • McKee, W. D. (1974),Waves on a shearing current: a uniformly valid asymptotic solution, Proc. Camb. Phil. Soc.75, 295–301.

    Google Scholar 

  • McKee, W. D. (1975),A two turning-point problem in fluid mechanics, Math. Proc. Camb. Phil. Soc.77, 581–590.

    Google Scholar 

  • Peregrine, D. H. (1976),Interaction of water waves and currents, Advan. Appl. Mech.16, 9–129.

    Google Scholar 

  • Peregrine, D. H. andSmith, R. (1975),Stationary gravity waves on non-uniform free streams: jet-like flows, Math. Proc. Camb. Phil. Soc.77, 415–438.

    Google Scholar 

  • Smith, R. (1970),Asymptotic solutions for high-frequency trapped wave propagation, Phil. Trans. Roy. Soc.268, 289–324.

    Google Scholar 

  • Smith, R. (1975),Second-order turning point problems in oceanography, Deep-Sea Res.22, 837–852.

    Google Scholar 

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McKee, W.D. The reflection of water waves by shear currents. PAGEOPH 115, 937–949 (1977). https://doi.org/10.1007/BF00881217

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  • DOI: https://doi.org/10.1007/BF00881217

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