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The interaction of long and short internal gravity waves: theory and experiment

Published online by Cambridge University Press:  20 April 2006

C. G. Koop  and
L. G. Redekopp
C. G. Koop
Affiliation:
Fluid Mechanics Department, TRW Systems, One Space Park, Redondo Beach, CA 90278
L. G. Redekopp
Affiliation:
Fluid Mechanics Department, TRW Systems, One Space Park, Redondo Beach, CA 90278 Permanent address: Department of Aerospace Engineering, University of Southern California, Los Angeles.
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Abstract

An analysis is presented which describes the slow-time evolution of an internal gravity wave in an arbitrarily specified stratification. The weakly nonlinear description of a single-wave mode, governed by the nonlinear Schrödinger equation, breaks down when certain resonant conditions are satisfied. One such condition occurs when the group velocity of the wavetrain is equal to the phase velocity of a higher-mode long wave of the system. The resonant interaction occurs on a faster time scale and is described by a coupled pair of nonlinear partial differential equations governing the evolution of both the short-wave and the long-wave modes. This long-wave/short-wave interaction is pursued further in an experimental investigation by measuring the modal interchange of energy between two internal waves of disparate length and time scales. The resulting data are compared with numerical solutions of the long-wave/short-wave resonant interaction equations. In general, the agreement between the theory and the experiment is reasonably good in the range of operating conditions for which the theory is valid.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 111 , October 1981 , pp. 367 - 409
Copyright
© 1981 Cambridge University Press

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References

Djordjevic, V. & Redekopp, L. 1977 On two dimensional packets of capillary—gravity waves. J. Fluid Mech. 79, 703.Google Scholar
Fornberg, B. 1977 On a Fourier method for the integration of hyperbolic equations. SIAM J. Numerical Analysis 12, 509.Google Scholar
Grimshaw, R. 1977 The modulation of an internal gravity wave packet, and the resonance with the mean motion. Studies Appl. Math. 56, 241.Google Scholar
Hasimoto, H. & Ono, H. 1972 Nonlinear modulation of gravity waves. J. Phys. Soc. Japan 33, 805.Google Scholar
Koop, C. G. 1981 Some observations of crosswave structure in an internal wave system. Phys. Fluids (submitted).
Koop, C. G. & Butler, G. 1981 An investigation of internal solitary waves in a two-fluid system. J. Fluid Mech. 112, 225.Google Scholar
Koop, C. G., Rungaldier, H. & Sherman, J. 1979 An infrared optical sensor for measuring internal interfacial waves. Rev. Sci. Instrum. 50, 20.Google Scholar
Lake, B. M., Yuen, H., Rungaldier, H. & Ferguson, W. 1977 Nonlinear deep water waves: theory and experiment. Part 2. Evolution of a continuous wavetrain. J. Fluid Mech. 83, 49.Google Scholar
Lewis, J., Lake, B. M. & Ko, D. 1974 On the interaction of internal waves and surface gravity waves. J. Fluid Mech. 63, 773.Google Scholar
Mcintyre, M. 1973 Mean motions and impulse of a guided internal gravity wave packet. J. Fluid Mech. 60, 801.Google Scholar
Ma, Y. C. & Redekopp, L. G. 1979 Some solutions pertaining to the resonant interaction of long and short waves. Phys. Fluids 22, 1872.Google Scholar
Pinkel, R. 1975 Upper ocean internal wave observation from FLIP. J. Geophys. Res. 80, 3892.Google Scholar
Yates, C. L. 1978 Internal wave generation by resonantly interacting surface waves. Ph.D. dissertation, The Johns Hopkins University.