Skip to main content Accessibility help
×
Home

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

  • C. G. Koop (a1) and L. G. Redekopp (a1) (a2)

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.

Copyright

References

Hide All
Djordjevic, V. & Redekopp, L. 1977 On two dimensional packets of capillary—gravity waves. J. Fluid Mech. 79, 703.
Fornberg, B. 1977 On a Fourier method for the integration of hyperbolic equations. SIAM J. Numerical Analysis 12, 509.
Grimshaw, R. 1977 The modulation of an internal gravity wave packet, and the resonance with the mean motion. Studies Appl. Math. 56, 241.
Hasimoto, H. & Ono, H. 1972 Nonlinear modulation of gravity waves. J. Phys. Soc. Japan 33, 805.
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.
Koop, C. G., Rungaldier, H. & Sherman, J. 1979 An infrared optical sensor for measuring internal interfacial waves. Rev. Sci. Instrum. 50, 20.
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.
Lewis, J., Lake, B. M. & Ko, D. 1974 On the interaction of internal waves and surface gravity waves. J. Fluid Mech. 63, 773.
Mcintyre, M. 1973 Mean motions and impulse of a guided internal gravity wave packet. J. Fluid Mech. 60, 801.
Ma, Y. C. & Redekopp, L. G. 1979 Some solutions pertaining to the resonant interaction of long and short waves. Phys. Fluids 22, 1872.
Pinkel, R. 1975 Upper ocean internal wave observation from FLIP. J. Geophys. Res. 80, 3892.
Yates, C. L. 1978 Internal wave generation by resonantly interacting surface waves. Ph.D. dissertation, The Johns Hopkins University.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

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

  • C. G. Koop (a1) and L. G. Redekopp (a1) (a2)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.