Hostname: page-component-7dd5485656-k8lnt Total loading time: 0 Render date: 2025-11-03T04:49:18.461Z Has data issue: false hasContentIssue false
  • English
  • Français

The spectral energy transfer from surface waves to internal waves

Published online by Cambridge University Press:  19 April 2006

Dirk J. Olbers  and
Klaus Herterich
Dirk J. Olbers
Affiliation:
Institut für Geophysik, Universität Hamburg, and Max-Planck-Institut für Meteorologie, Hamburg, Germany Present address: Institut für Meereskunde, Universität Kiel, Germany.
Klaus Herterich
Affiliation:
Max-Planck Institut für Meteorologie, Hamburg, Germany
Get access Rights & Permissions [Opens in a new window]

Abstract

The generation of internal waves by resonantly interacting surface waves is examined in the framework of spectral scattering theory in the random-phase approximation. Coupling coefficients are derived from Euler's equation of motion for arbitrary stratification. The spectral energy transfer is discussed for deep-water surface waves and a simple three-layer model of the stability frequency. Analytical and numerical evaluation of the transfer integral leads to a parametrization in terms of the basic model parameters. These are the depth, thickness and stability frequency of the thermocline and the scale parameters and bandwidth of the surface wave spectrum. Strong dependence on some of these parameters, in particular the surface wave energy and the ratio of surface and internal wave frequencies, indicates a large spatial and temporal variability of the transfer rate. The transfer to the internal wave field in the oceanic main thermocline is found to be negligible compared with the effect of other processes. High frequency waves in the seasonal thermocline may be generated very efficiently.

Information

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 92 , Issue 2 , 28 May 1979 , pp. 349 - 379
Copyright
© 1979 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Abramowitz, M. & Stegun, E. A. (ed.) 1972 Handbook of Mathematical Functions. Dover.
Apel, J. R., Byrne, H. M., Proni, J. R. & Charnell, R. L. 1975 Observations of oceanic internal and surface waves from the earth resources technology satellite. J. Geophys. Res. 80, 865–881.Google Scholar
Ball, F. K. 1964 Energy transfer between external and internal gravity waves. J. Fluid Mech. 19, 465.Google Scholar
Brekhovskikh, L. M., Goncharov, V. V., Kurtepov, V. M. & Naugol'nykh, K. A. 1972 Resonant excitation of internal waves by nonlinear interaction of surface waves. Izv. Atmos. Ocean. Phys. 8, 192–203.Google Scholar
Brekhovskikh, L. M., Konjaev, K. V., Sabinin, K. D. & Serikov, A. N. 1975 Short-period internal waves in the sea. J. Geophys. Res. 80, 856–864.Google Scholar
Davidson, R. C. 1967 The evolution of wave correlations in uniformly turbulent, weakly non-linear system. J. Plasma Phys. 1, 341–359.Google Scholar
Garrett, C. & Munk, W. 1975 Space-time scales of internal waves: a progress report. J. Geophys. Res. 80, 291–297.Google Scholar
Gradshteyn, I. S. & Ryzhik, I. M. 1965 Table of Integrals, Series and Products. Academic Press.
Hasselmann, K. 1966 Feynman diagrams and interaction rules of wave-wave scattering processes. Rev. Geophys. Space Phys. 4, 1–32.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, 77–100.Google Scholar
Hasselman, K. et al. 1973 Measurements of wind-wave growth and swell decay during the Joint North Sea Wave Project (JONSWAP). Dsche Hydr. Z. Suppl. A(8°) no. 12.Google Scholar
Hasselmann, K., Ross, D. B., Müller, P. & Sell, W. 1976 A parametric wave prediction model. J. Phys. Ocean. 6, 200–228.Google Scholar
Joyce, T. M. 1974 Nonlinear interactions among standing surface and internal gravity waves. J. Fluid Mech. 63, 801–825.Google Scholar
Käse, R. 1979 Calculations of the energy transfer by the wind to near-inertial internal waves. Deep-Sea Res. In press.Google Scholar
Käse, R. & Clarke, R. A. 1978 High frequency internal waves in the upper thermocline during GATE. Deep-Sea Res. 25, 815–825.Google Scholar
Kenyon, K. E. 1968 Wave-wave interactions of surface and internal waves. J. Mar. Res. 26, 208–231.Google Scholar
McComas, C. H. & Bretherton, F. P. 1977 Resonant interaction of oceanic internal waves. J. Geophys. Res. 82, 1397–1412.Google Scholar
Müller, P. & Olbers, D. J. 1975 On the dynamics of internal waves in the deep ocean. J. Geophys. Res. 80, 3848–3860.Google Scholar
Müller, P., Olbers, D. J. & Willebrand, J. 1977 The IWEX spectrum. J. Geophys. Res. 83, 479–500.Google Scholar
Nesterov, S. V. 1972 Resonant interactions of surface and internal waves. Izv. Atmos. Ocean. Phys. 8, 252–254.Google Scholar
Neu, H. J. A. 1976 Wave climate in the North Atlantic 1970. Bedford Inst. Oceanog., Rep. B1-R-76-10.Google Scholar
Olbers, D. J. 1976 Nonlinear energy transfer and the energy balance of the internal wave field in the deep ocean. J. Fluid Mech. 74, 375–399.Google Scholar
Phillips, O. M. 1977 The Dynamics of the Upper Ocean. Cambridge University Press.
Phillips, O. M. 1974 Wave interactions. In Nonlinear Waves (ed. S. Leibovich & A. R. Seebass). Cornell University Press.
Pierson, W. J. & Moskowitz, L. 1964 A proposed spectral form for fully developed wind seas based on the similarity theory of S. A. Kitaigorodskii. J. Geophys. Res. 69, 5181–5190.Google Scholar
Sabinin, K. D. 1973 Certain features of short-period internal waves in the ocean. Izv. Atmos. Ocean. Phys. 9, 66–74.Google Scholar
Thorpe, S. A. 1966 On wave interactions in a stratified fluid. J. Fluid Mech. 24, 737–751.Google Scholar
Watson, K. M., West, B. J. & Cohen, B. I. 1976 Coupling of surface and internal gravity waves: a mode coupling model. J. Fluid Mech. 77, 185–208.Google Scholar