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Trapped internal waves over undular topography

Published online by Cambridge University Press:  26 April 2006

C. Kranenburg ,
J. D. Pietrzak  and
G. Abraham
C. Kranenburg
Affiliation:
Department of Civil Engineering, Delft University of Technology, PO Box 5048, 2600 GA Delft, The Netherlands
J. D. Pietrzak
Affiliation:
Delft Hydraulics, PO Box 177, 2600 MH Delft, The Netherlands Present address: Department of Oceanography, University of British Columbia, Vancouver, BC. Canada V6T 1W5.
G. Abraham
Affiliation:
Delft Hydraulics, PO Box 177, 2600 MH Delft, The Netherlands
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Abstract

We describe observations of slowly decelerating stratified flow over undular bottom topography in an estuary. The flow, which initially was supercritical with respect to the first internal wave mode, approached a resonance after it had become subcritical. A series of acoustic images showed large-amplitude first-mode trapped waves during this phase of the tide. We derive a criterion for quasi-steady response, and present an extension of Yih's class II linear finite-amplitude solutions that accounts for the waves observed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 226 , May 1991 , pp. 205 - 217
Copyright
© 1991 Cambridge University Press

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References

Baines, P. G.: 1977 Upstream influence and Long's model in stratified flows. J. Fluid Mech. 82, 147.Google Scholar
Baines, P. G.: 1984 A unified description of two-layer flow over topography. J. Fluid Mech. 146, 127.Google Scholar
Bell, T. H.: 1975 Lee waves in stratified flows with simple harmonic time dependence. J. Fluid Mech. 67, 705.Google Scholar
Chatwin, P. C.: 1976 Some remarks on the maintenance of the salinity distribution in estuaries. Estuar. Coast. Mar. Sci. 4, 555.Google Scholar
Dyer, K. R.: 1982 The initiation of sedimentary furrows by standing internal waves. Sedimentology 29, 885.Google Scholar
Geyeh, W. R. & Smith, J. D., 1987 Shear instability in a highly stratified estuary. J. Phys. Oceanogr. 17, 1668.Google Scholar
Grimshaw, R. H. J. & Smyth, N. 1986 Resonant flow of a stratified fluid over topography. J. Fluid Mech. 169, 429.Google Scholar
Huppert, H. E.: 1980 Topographic effects in stratified fluids. In Fjord Oceanography (ed. H. J. Freeland, D. M. Farmer & C. D. Levings) Plenum.
Koop, C. G. & McGee, B., 1986 Measurements of internal gravity waves in a ontinuously stratified shear flow. J. Fluid Mech. 172, 453.Google Scholar
Lansing, F. S. & Maxworthy, T., 1984 On the generation and evolution of internal gravity waves. J. Fluid Mech. 145, 127.Google Scholar
Long, R. R.: 1953 Some aspects of the flow of stratified fluids. I. A theoretical investigation. Tellws 5, 42.Google Scholar
Maxworthy, T.: 1979 A note on the internal solitary waves produced by tidal flow over a three-dimensional ridge. J. Geophys. Res. (C) 84, 338.Google Scholar
McDowell, D. M. & O'Connor, B. A. 1977 Hydraulic Behaviour of Estuaries. Macmillan.
Melville, W. K. & Helfrich, K. R., 1987 Transcritical two-llayer flow over topography. J. Fluid Mech. 178, 31.Google Scholar
Pietrzak, J. D., Abraham, G. & Kranenburg, C., 1989 Field observations of internal waves in the Rotterdam Waterway. Stratified Flows Rep. 6. Rijkswaterstaat, Delft Hydraulics, Delft University of Technology.
Pietrzak, J. D., Kranenburg, C. & Abraham, G., 1990 Resonant internal waves in fluid flow. Nature 344, 844.Google Scholar
Tubnee, J. S.: 1973 Buoyancy Effects in Fluids. Cambridge University Press.
Yni, C. S.: 1980 Stratified Flows. Academic.