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Nonlinear energy transfer and the energy balance of the internal wave field in the deep ocean

Published online by Cambridge University Press:  29 March 2006

Dirk J. Olbers
Affiliation:
Institut für Geophysik, Universität Hamburg, Germany

Abstract

The source function describing the energy transfer between the components of the internal wave spectrum due to nonlinear interactions is derived from the Lagrangian of the fluid motion and evaluated numerically for the spectral models of Garrett & Munk (1972a, 1975). The characteristic time scales of the transfer are found to be typically of the order of some days, so that nonlinear interactions will play an important role in the energy balance of the wave field. Thus implications of the nonlinear transfer within the spectrum for generation and dissipation processes are considered.

Type
Research Article
Copyright
© 1976 Cambridge University Press

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Footnotes

Contribution from the Sonderforschungsbereich 94 ‘Meeresforschung Hamburg’.

References

Ball, F. K. 1964 Energy transfer between external and internal gravity waves J. Fluid Mech. 19, 465478.Google Scholar
Bell, T. H. 1975 Topographically generated internal waves in the open ocean J. Geophys. Res. 80, 320327.Google Scholar
Bretherton, F. P. 1969 Waves and turbulence in stably stratified fluids Radio Sci. 4, 12791287.Google Scholar
Bretherton, F. P. 1971 The general linearized theory of wave propagation. In Mathematical Problems in the Geophysical Sciences, vol. 1 (ed. W. H. Reid), pp. 61102. Providence, R.I.: Am. Math. Soc.
Bretherton, F. P. & Garrett, C. J. R. 1968 Wave trains in inhomogeneous moving media. Proc. Roy. Soc A 302, 529554.Google Scholar
Briscoe, M. G. 1975a Internal waves in the ocean. Rev. Geophys. Space Phys. 13, 591810, 636810.Google Scholar
Briscoe, M. G. 1975b Preliminary results from the tri-moored internal wave experiment (IWEX) J. Geophys. Res. 80, 38723884.Google Scholar
Cairns, J. L. 1975 Internal wave measurements from a midwater float J. Geophys. Res. 80, 299360.Google Scholar
Desaubies, Y. J. F. 1975 A linear theory of internal wave spectra and coherences near the Väisälä frequency J. Geophys. Res. 80, 895899.Google Scholar
Dewar, R. L. 1970 Interaction between hydromagnetic waves and a time-dependent, inhomogeneous medium Phys. Fluids, 13, 27102720.Google Scholar
Dougherty, J. P. 1970 Lagrangian methods in plasma physics. Part 1 J. Plasma Phys. 4, 761785.Google Scholar
Fofonoff, N. P. & Webster, F. 1971 Current measurements in the western Atlantic. Phil. Trans A 270, 423436.Google Scholar
Frankignoul, C. J. 1974 Preliminary observations of internal wave energy flux in frequency, depth-space Deep-Sea Res. 21, 895899.Google Scholar
Garrett, C. J. R. & Munk, W. 1972a Space-time scales of internal waves Geophys. Fluid Dyn. 2, 225264.Google Scholar
Garrett, C. J. R. & Munk, W. 1972b Oceanic mixing by breaking of internal waves Deep-Sea Res. 19, 823832.Google Scholar
Garrett, C. J. R. & Munk, W. 1975 Space-time scales of internal waves: a progress report. J. Geophys. Res. 80, 291810.Google Scholar
Grant, H. L., Moilliet, A. & Vogel, W. M. 1968 Some observations of the occurrence of turbulence in and above the thermocline J. Fluid Mech. 34, 443448.Google Scholar
Grant, H. L., Stewart, R. W. & Moilliet, A. 1962 Turbulent spectra from a tidal channel J. Fluid Mech. 12, 241268.Google Scholar
Gregg, M. C. 1975 Oceanic fine and microstructure Rev. Geophys. Space Phys. 13, 586591.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. 1967 Nonlinear interactions treated by the methods of theoretical physics (with applications to the generation of waves by wind). Proc. Roy. Soc A 299, 77100.Google Scholar
Hasselmann, K. 1968 Weak interaction theory of ocean waves Basic Develop. Fluid Dyn. 2, 117182.Google Scholar
Hasselmann, K. et al. 1973 Measurements of wind-wave growth and swell decay during the Joint North Sea Wave Project (JONSWAP). Deutsche Hydrog. Z. Suppl. A(8°) no. 12.Google Scholar
Hayes, S. P., Joyce, T. M. & Millard, R. C. 1975 Measurements of vertical fine structure in the Sargasso Sea J. Geophys. Res. 80, 314319.Google Scholar
Kenyon, K. 1968 Wave—wave interactions of surface and internal waves J. Mar. Res. 26, 208231.Google Scholar
Mcewan, A. D. 1971 Degeneration of resonantly-excited standing internal gravity waves J. Fluid Mech. 50, 431448.Google Scholar
Mcewan, A. D. 1973 Interactions between internal gravity waves and their traumatic effect on a continuous stratification Boundary-Layer Met. 5, 159175.Google Scholar
Mcewan, A. D., Mander, D. W. & Smith, R. K. 1972 Forced resonant second-order interaction between damped internal waves J. Fluid Mech. 55, 589608.Google Scholar
Martin, S., Simmons, W. F. & Wunsch, C. 1969 Resonant internal wave interactions Nature, 224, 10141016.Google Scholar
Martin, S., Simmons, W. F. & Wunsch, C. 1972 The excitation of resonant triads by single internal waves J. Fluid Mech. 53, 1744.Google Scholar
Monin, A. S. 1973 Turbulence and microstructure in the ocean Usp. Fiz. Nauk. (Adv. in Pys. Sci.) 109, 333354.Google Scholar
Mork, M. 1972 On oceanic responses to atmospheric forces Conseil International pour l'Exploration de la Mer, 162, 184190.Google Scholar
Müller, P. 1974 On the interaction between short internal waves and larger scale motion in the ocean. Hamburg. Geophys. Einzelschriften, 23.Google Scholar
Müller, P. & Olbers, D. J. 1975 On the dynamics of internal waves in the deep ocean J. Geophys. Res. 80, 38483860.Google Scholar
Munk, W. 1966 Abyssal recipes Deep-Sea Res. 13, 707730.Google Scholar
Mysak, L. A. & Howe, M. S. 1975 A kinetic theory for internal waves in a randomly stratified ocean. Geophys. Fluid Dyn. (in press).Google Scholar
Neshyba, 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
Okubo, A. 1970 Oceanic mixing. Johns Hopkins University, Tech. Rep. Ref. 70810.Google Scholar
Olbers, D. J. & Richter, A. 1973 Wave trains in the solar wind. I. General theory and its application to an ideal, isotropic one-fluid plasma Astrophys. Space Sci. 20, 373389.Google Scholar
Orlanski, I. & Ross, B. R. 1973 Numerical simulation of the generation and breaking of internal gravity waves J. Geophys. Res. 78, 88088826.Google Scholar
Pollard, R. T. 1970 On the generation by winds of inertial waves in the ocean Deep-Sea Res. 17, 795812.Google Scholar
Roether, W., Muennich, K. O. & ÖSTLUND, H. G. 1970 Tritium profile at the North Pacific (1969) Geosecs intercalibration station J. Geophys. Res. 75, 76727675.Google Scholar
Rooth, C. G. & ÖSTLUND, H. G. 1972 Penetration of tritium into the Atlantic thermocline Deep-Sea Res. 19, 481492.Google Scholar
Sanford, T. B. 1975 Observations of the vertical structure of internal waves J. Geophys. Res. 80, 38613871.Google Scholar
Siedler, G. 1971 Vertical coherence of short-periodic current variations Deep-Sea Res. 18, 179191.Google Scholar
Siedler, G. 1974 Observations of internal wave coherence in the deep ocean Deep-Sea Res. 21, 597610.Google Scholar
Stewart, R. W. & Grant, H. L. 1962 Determination of the rate of dissipation of turbulent energy near the sea surface in the presence of waves J. Geophys. Res. 67, 31773180.Google Scholar
Takenouti, Y., Nanniti, T. & Yasui, M. 1962 The deep-current in the sea east of Japan Oceanog. Mag. 13, 89101.Google Scholar
Thorpe, S. A. 1966 On wave interactions in a stratified fluid J. Fluid Mech. 24, 737751.Google Scholar
Thorpe, S. A. 1973 Turbulence in stable stratified fluids: a review of laboratory experiments. Boundary-Layer Met. 5, 95810.Google Scholar
Thorpe, S. A. 1975 The excitation, dissipation, and interaction of internal waves in the deep ocean J. Geophys. Res. 80, 328338.Google Scholar
Turner, J. S. 1973 Buoyancy Effects in Fluids. Cambridge University Press.
Webster, F. 1972 Estimates of the coherence of ocean currents over vertical distances Deep-Sea Res. 19, 3544.Google Scholar
Whitham, G. B. 1965 A general approach to linear and nonlinear dispersive waves using a Lagrangian J. Fluid Mech. 22, 273283.Google Scholar
Whitham, G. B. 1970 Two-timing, variational principles and waves J. Fluid Mech. 44, 373395.Google Scholar
Woods, J. D. 1968 Wave-induced shear instability in the summer thermocline J. Fluid Mech. 32, 791800.Google Scholar
Woods, J. D. & Wiley, R. L. 1972 Billow turbulence and ocean microstructure Deep-Sea Res. 19, 87121.Google Scholar
Wunsch, C. 1975 Deep ocean internal waves: what do we really know? J. Geophys. Res. 80, 339810.Google Scholar