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Exposure of internal waves on the sea surface

Published online by Cambridge University Press:  10 May 2009

HWUNG-HWENG HWUNG ,
RAY-YENG YANG  and
IGOR V. SHUGAN
HWUNG-HWENG HWUNG
Affiliation:
Tainan Hydraulics Laboratory, National Cheng Kung University, 5th floor, 500, Sec. 3, Anming Road, Tainan 709, Taiwan
RAY-YENG YANG
Affiliation:
Tainan Hydraulics Laboratory, National Cheng Kung University, 5th floor, 500, Sec. 3, Anming Road, Tainan 709, Taiwan
IGOR V. SHUGAN*
Affiliation:
Tainan Hydraulics Laboratory, National Cheng Kung University, 5th floor, 500, Sec. 3, Anming Road, Tainan 709, Taiwan
*
†Email address for correspondence: [email protected]
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Abstract

We theoretically analyse the impact of subsurface currents induced by internal waves on nonlinear Stokes surface waves. We present analytical and numerical solutions of the modulation equations under conditions that are close to group velocity resonance. Our results show that smoothing of the downcurrent surface waves is accompanied by a relatively high-frequency modulation, while the profile of the opposing current is reproduced by the surface wave's envelope. We confirm the possibility of generating an internal wave forerunner that is a modulated surface wave packet. Long surface waves can create such a wave modulation forerunner ahead of the internal wave, while other relatively short surface waves comprise the trace of the internal wave itself. Modulation of surface waves by a periodic internal wavetrain may exhibit a characteristic period that is less than the internal wave period. This period can be non-uniform while the wave crosses the current zone. Our results confirm that surface wave excitation by means of internal waves, as observed at their group resonance frequencies, is efficient only in the context of opposing currents.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 626 , 10 May 2009 , pp. 1 - 20
Copyright
Copyright © Cambridge University Press 2009

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References

REFERENCES

Alpers, W. 1985 Theory of radar imaging of internal waves. Nature 314, 245–247.CrossRefGoogle Scholar
Andonovati, As., Karjanto, N. & Groesen van, E. 2007 Extreme wave phenomena in down-stream running modulated waves. Appl. Math. Model. 31, 1425–1443.CrossRefGoogle Scholar
Bakhanov, V. V., Belyakhov, D. L., Ryabinin, A. G., Titov, V. I. & Zuikova, E. M. 1994 Nonlocal effect of internal waves on the ocean surface. In Geoscience and Remote Sensing Symposium, IGARSS ‘94. Surface and Atmospheric Remote Sensing: Technologies, Data Analysis and Interpretation., International, 2, 760–762.Google Scholar
Bakhanov, V. V. & Ostrovski, L. A. 2002 Action of strong internal solitary waves on surface wave. J. Geophys. Res. 107 (C10), 3139.CrossRefGoogle Scholar
Basovich, A. Y., Bachanov, V. V., & Talanov, V. I. 1987 Transformation of wind-driven wave spectra by short internal wave trains. Izv., Acad. Sci., USSR, Atmos. Oceanic Phys 23 (7), 520–528.Google Scholar
Chereskin, T. & Mollo-Christensen, E. 1985 Modulational development of nonlinear gravity wave groups. J. Fluid Mech. 154, 337–365.Google Scholar
Donato, A. N., Peregrine, D. H. & Stocker, J. R. 1999 The focusing of surface. waves by internal waves. J. Fluid Mech. 384, 27–58.CrossRefGoogle Scholar
Gargett, A. E. & Hughes, B. A. 1972 On the interaction of surface and internal waves. J. Fluid Mech. 52, 179–191.CrossRefGoogle Scholar
Gasparovic, R. F., Apel, J. R. & Kasischke, E. S. 1988 An overview of the SAR internal wave experiment. J. Geophys. Res. 93, 12 304–12, 315.CrossRefGoogle Scholar
Hogan, G. G., Chapman, R. D., Watson, G. & Thompson, D. R. 1996 Observations of ship-generated internal waves in SAR images from Loch Linnhe, Scotland, and comparison with theory and in situ internal wave measurements. IEEE Trans. Geosci. Remote Sens. 34, 532–542.CrossRefGoogle Scholar
Holliday, D. 1973 Nonlinear gravity-capillary surface waves in a slowly varying current. J. Fluid Mech. 57, 797–802.CrossRefGoogle Scholar
Hughes, B. A. 1978 The effect of internal waves on surface wind waves. 2, Theoretical analysis. J. Geophys. Res. 83, 455–465.CrossRefGoogle Scholar
Hughes, B. A. & Grant, H. L. 1978 The effect of internal waves on surface wind waves. I: Experimental measurements. J. Geophys. Res. 83, 443–454.CrossRefGoogle Scholar
Karjanto, N. & Groesen, E. 2007 Note on wavefront dislocation in surface water waves. Phys. Lett. A 371, 173–179.CrossRefGoogle Scholar
Kropfli, R. A., Ostrovski, L. A., Stampton, T. P., Skirta, E. A., Keane, A. N. & Irisov, V. 1999 Relationships between strong internal waves in the coastal zone and their radar and radiometric signatures. J. Geophys. Res. 104 (C2), 3133–3148.CrossRefGoogle Scholar
Kuzmak, J. E. 1959 Asymptotic solutions of nonlinear second order differential equations with variable coefficients. Appl. Math Mech. 23, 730–744.CrossRefGoogle Scholar
Landau, L. & Lifshitz, E. 1977 Quantum Mechanics (non-relativistic theory): Course of Theoretical Physics, Vol. 3. Elsevier.Google Scholar
Lewis, J. E., Lake, B. M., & Ko, D. R. 1974 On the interaction of internal waves and surface gravity waves. J. Fluid Mech. 63, 773.CrossRefGoogle Scholar
Longuet-Higgins, M. S. & Stewart, R. W. 1964 Radiation stress in water waves, a physical discussion with application. Deep-Sea Res. 11, 529–562.Google Scholar
Luke, J. C. 1966 A perturbation method for nonlinear dispersive wave problems. Proc. R. Soc. Lond. Ser. A: Math. Phys. Sci. 292 (1430), 403–412.Google Scholar
Melville, W. 1983 Wave modulation and breakdown. J. Fluid Mech. 128, 489–506.CrossRefGoogle Scholar
Nayfeh, A. H. 1981 Introduction to Perturbation Techniques. John Wiley & Sons.Google Scholar
Osborne, A. R. & Burch, T. L. 1980 Internal solitons in the Andaman Sea. Science 208, 451–460.CrossRefGoogle ScholarPubMed
Phillips, O. M. 1974 Nonlinear dispersive waves. Annu. Rev. Fluid Mech. 6, 93–110.CrossRefGoogle Scholar
Phillips, O. M. 1977 Dynamics of the Upper Ocean Layer. John Wiley & Sons.Google Scholar
Shugan, I. & Voliak, K. 1998 On phase kinks, negative frequencies and other third order peculiarities of modulated surface waves. J. Fluid Mech. 368, 321–338.CrossRefGoogle Scholar
Smith, R. 1976 Giant waves. J. Fluid Mech. 77, 417–431.CrossRefGoogle Scholar
Stocker, J. R. & Peregrine, D. H. 1999 Three-dimensional surface. waves propagating over long internal waves. European J. Mech. B/Fluids 18, 545–559.CrossRefGoogle Scholar
Watson, G., Chapmen, R. D. & Apel, J. R. 1992 Measurements of the internal wave wake of a ship in a highly stratified sea Loch. J. Geophys. Res. 97 (C6), 9689–9703.CrossRefGoogle Scholar
Whitham, G. B. 1974 Linear and Nonlinear Waves. John Wiley & Sons.Google Scholar
Yuen, H. C. & Lake, B. M. 1982 Nonlinear dynamics of deep-water gravity waves. In Advances in Applied Mechanics 22, pp. 67–229. Academic Press.CrossRefGoogle Scholar