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Self-consistent effective-medium parameters for oceanic internal waves

Published online by Cambridge University Press:  20 April 2006

R. J. Dewitt  and
Jon Wright
R. J. Dewitt
Affiliation:
Physics Department, Southern Arkansas University, Magnolia, Arkansas 71753
Jon Wright
Affiliation:
Center for Studies of Nonlinear Dynamics, La Jolla Institute, 8950 Villa La Jolla Drive, Suite 2150, La Jolla, CA 92037
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Abstract

In this paper we apply a formalism introduced in a previous paper to write down a self-consistent set of equations for the functions that describe the near-equilibrium time behaviour of random oceanic internal waves. These equations are based on the direct-interaction approximation. The self-consistent equations are solved numerically (using the Garrett-Munk spectrum as input) and the results are compared to parameters obtained in the weak-interaction approximation (WIA). The formalism points out that an extra parameter that is implicitly vanishingly small in the WIA has a significant effect on decay rates when computed self-consistently. We end by mentioning possible future self-consistent calculations that would improve upon our own.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 146 , September 1984 , pp. 253 - 270
Copyright
© 1984 Cambridge University Press

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References

Cairns, T. L. & Williams, G. O. 1976 Internal wave observations from a midwater float, 2. J. Geophys. Res. 81, 1943–1950.Google Scholar
Carnevale, G. F. & Fredericksen, J. S. 1983a A statistical dynamical theory of strongly nonlinear internal gravity waves. Geophys. Astrophys. Fluid Dyn. 23, 175–207.Google Scholar
Carnevale, G. F. & Fredericksen, J. S. 1983b Viscosity renormalization based on direct-interaction closure. J. Fluid Mech. 131, 289–303.Google Scholar
DeWitt, R. J. 1982 Self-consistent effective medium parameters for nonlinear random oceanic internal waves, Ph.D. thesis, Physics Dept, University of Illinois, Urbana.
DeWitt, R. J. & Wright, J. 1983 Self-consistent effective-medium theory of random internal waves. J. Fluid Mech. 115, 283–302.Google Scholar
Fredericksen, J. S., Bell, R. C. 1983 Statistical dynamics of internal gravity waves-turbulence. Geophys. Astrophys. Fluid Dyn. 26, 257–301.Google Scholar
Garrett, C. J. R. & Munk, W. H. 1972 Space-time scales of internal waves. Geophys. Fluid Dyn. 2, 225–264.Google Scholar
Garrett, C. J. R. & Munk, W. H. 1975 Space-time scales of internal waves. A progress report. J. Geophys. Res. 80, 291–297.Google Scholar
Henyey, F. S. & Pomphrey, N. 1983 Eikonal description of internal wave interactions, a non-diffusive picture of induced-diffusion. Dyn. Atmos. Oceans 7, 189–220.Google Scholar
Henyey, F. S., Pomphrey, N. & Meiss, J. D. 1983 Comparison of short-wavelength internal wave transport theories. La Jolla Inst. Preprint LJI-R-783-248.
Holloway, G. 1979 On the spectral evolution of strongly interacting waves. Geophys. Astrophys. Fluid Dyn. 11, 271–287.Google Scholar
Holloway, G. 1980 Oceanic internal waves are not weak waves. J. Phys. Oceanogr. 10, 906–914.Google Scholar
Holloway, G. 1982 On interaction time scales of oceanic internal waves. J. Phys. Oceanogr. 12, 293–296.Google Scholar
Holloway, G. & Hendershott, M. C. 1977 Stochastic closure for nonlinear Rossby waves. J. Fluid Mech. 82, 747–765.Google Scholar
Kraichnan, R. H. 1959 The structure of isotropic turbulence at high Reynolds numbers. J. Fluid Mech. 5, 497–543.Google Scholar
Kraichnan, R. H. 1964 Kolmogorov's hypothesis and Eulerian turbulence theory. Phys. Fluids 7, 1723–1734.Google Scholar
McComas, C. H. 1977 Equilibrium mechanisms within the oceanic internal wave field. J. Phys. Oceanogr. 7, 836.Google Scholar
McComas, C. H. & Bretherton, F. P. 1977 Resonant iteractions of oceanic internal waves. J. Geophys. Res. 82, 1397.Google Scholar
McComas, C. H. & Muller, P. 1981 The dynamic balance of internal waves. J. Phys. Oceanogr. 11, 970–986.Google Scholar
Meiss, J. & Watson, K. M. 1982 Internal-wave interactions in the induced-diffusion approximation. J. Fluid Mech. 117, 315–341.Google Scholar
Meiss, J. D., Pomphrey, N. & Watson, K. M. 1979 Proc. Natl Acad. Sci. USA 76, 2109.
Olbers, D. J. 1974 On the energy balance of small-scale internal waves in the deep sea. Hamburg Geophys. Einzelschr. no. 24. GML Wittenborn Sohnes, Hamburg.
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
Pomphrey, N., Meiss, J. D. & Watson, K. M. 1980 Description of nonlinear internal wave interactions using Langevin methods. J. Geophys. Res. 85, 1085–1094.Google Scholar