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Bispectra of internal waves

Published online by Cambridge University Press:  19 April 2006

C. H. Mccomas
Affiliation:
Woods Hole Oceanographic Institution, Woods Hole, MA 02543
M. G. Briscoe
Affiliation:
Woods Hole Oceanographic Institution, Woods Hole, MA 02543

Abstract

This note summarizes a detailed numerical computation of bispectra arising from weak nonlinear resonant interactions of internal waves whose energies are represented by the Garrett & Munk (1975) model spectrum. Two spectra are computed – the bispectrum of power and the auto-bispectrum of vertical displacement. These are chosen because the first is the most informative and the second is easy to observe. The numerical computations indicate that the level of the bispectral signal is much too low to be detected by any reasonable observational programme. Even more disturbing, bispectra of Eulerian variables are subject to a kinematic contamination causing a significant bispectral level which can easily be misinterpreted as a nonlinear interaction.

Type
Research Article
Copyright
© 1980 Cambridge University Press

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References

Bendat, J. & Piersol, A. 1971 Random Data, pp. 156160. Wiley-Interscience.
Briscoe, M. G. & McComas, 1979 Calculations of bispectra of internal waves. In preparation.
Garrett, C. J. R. & Munk, W. H. 1975 Space—time scales of internal waves: A progress report. J. Geophys. Res. 80, 291297.Google Scholar
Hasselmann, K. 1966 Feynman diagrams and interaction rules of wave—wave scattering processes. Rev. Geophys. Space Phys. 4, 132.Google Scholar
Hasselmann, K., Munk, W. & MacDonald, G. 1963 Bispectrum of ocean waves. In Proc. Symp. on Time Series Analysis (ed. M. Rosenblatt), pp. 125139. Wiley.
Haubrich, R. A. 1965 Earth noise, 5 to 500 millicycles per second, 1. Spectral stationarity, normality, and nonlinearity. J. Geophys. Res. 20, 14151427.Google Scholar
Helland, K. N., Van Atta, C. W. & Steger, G. R. 1977 Spectral energy transfer in high Reynolds number turbulence. J. Fluid Mech. 79, 337359.Google Scholar
Lii, K. S., Rosenblatt, M. & Van Atta, C. 1976 Bispectral measurements in turbulence. J. Fluid Mech. 77, 4562.Google Scholar
McComas, C. H. 1977 Equilibrium mechanisms within the oceanic internal wave field. J. Phys. Oceanog. 7, 836845.Google Scholar
McComas, C. H. 1978 Bispectra of internal waves. Woods. Hole Oceanographic Inst. Tech. Rep. 7825.
McComas, C. H. & Bretherton, F. P. 1977 Resonant interactions of oceanic internal waves. J. Geophys. Res. 82, 13971412.Google Scholar
Neseyba, S. & Sobey, E. J. C. 1975 Vertical cross coherence and cross bispectra between internal waves measured in a multiple layered ocean. J. Geophys. Res. 80, 11521162.Google Scholar
Phillips, O. M. 1966 The Dynamics of the Upper Ocean. Cambridge University Press.