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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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