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On forced internal waves in a rectangular trench

Published online by Cambridge University Press:  26 April 2006

Francis C. K. Ting
Francis C. K. Ting
Affiliation:
Ocean Engineering Program, Department of Civil Engineering, Texas A & M University, College Station, TX 77843, USA
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Abstract

The generation of internal waves in a submarine rectangular trench by normally incident surface waves has been investigated through laboratory experiments and theory. A linear model was developed for small-amplitude, simple harmonic wave motions. In this model, the fluid outside the trench is homogeneous, and the fluid in the trench is composed of two homogeneous layers of different densities separated by a transition region of linear density variation; viscous dissipation is treated based on the assumption of a laminar boundary layer. In the experiments, the stratification in the trench was created using fresh water and salt water, and a scanning laser beam and detector system was used to measure the amplitude of internal waves. The study shows that, when the frequency of the surface waves corresponds to the natural frequency of internal waves, the amplitude of internal waves becomes large compared to the amplitude of surface waves. The natural frequency of oscillation of internal waves decreases as the thickness of the density interface increases and the depth of the lower fluid decreases. Two distinct classes of internal waves were observed, namely, standing internal waves when the lower fluid was deep, and travelling internal waves when the lower fluid was shallow. The linear model predicted the response curve for internal waves quite well in all the cases investigated. It was also found that the internal waves were strongly damped when the depth of the lower fluid was small compared to the wavelength of internal waves.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 235 , February 1992 , pp. 255 - 283
Copyright
© 1992 Cambridge University Press

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References

Benjamin, T. B. 1966 Internal waves of finite amplitude and permanent forms. J. Fluid Mech. 25, 241–270.Google Scholar
Benjamin, T. B. 1967 Internal waves of permanent form in fluids of great depth. J. Fluid Mech. 29, 559–592.Google Scholar
Dore, B. D. 1969a A contribution to the theory of viscous damping of stratified wave flows. Acta Mech. 8, 25–33.Google Scholar
Dore, B. D. 1969b The decay of oscillations of a non-homogeneous fluid within a container. Proc. Camb. Phil. Soc. 65, 301–307.Google Scholar
Head, M. J. 1983 The use of miniature four-electrode conductivity probes for high resolution measurement of turbulent density or temperature variations in salt-stratified water flows. Ph.D. thesis, University of California, San Diego.
Helal, M. A. & Molines, J. M. 1981 Non-linear internal waves in shallow water. A theoretical and experimental study. Tellus 33, 488–504.Google Scholar
Hunt, J. N. 1961 Interfacial waves of finite amplitude. La Houille Blanche 16, 515–525.Google Scholar
Kirby, J. T. & Dalrymple, R. A. 1983 Propagation of obliquely incident water waves over a trench. J. Fluid Mech. 133, 47–63.Google Scholar
Lee, J. J. & Ayer, R. M. 1981 Wave propagation over a rectangular trench. J. Fluid Mech. 110, 335–347.Google Scholar
Marine Board (National Research Council) 1983 Criteria for the Depths of Dredged Navigational Channels. Washington, DC: National Academy Press.
Mei, C. C. & Liu, L. F. 1973 The damping of surface gravity waves in a bounded liquid. J. Fluid Mech. 59, 239–256.Google Scholar
Miles, J. W. 1982 On surface-wave diffraction by a trench. J. Fluid Mech. 115, 315–325.Google Scholar
Thorpe, S. A. 1968 On standing internal gravity waves of finite amplitude. J. Fluid Mech. 32, 489–528.Google Scholar
Ting, C. K. F. & Raichlen, F. 1986 Wave interaction with a rectangular trench. J. Waterway, Port, Coastal Ocean Engng. Div., ASCE 112, 454–460.Google Scholar
Ting, C. K. F. & Raichlen, F. 1988 Wave interaction with rectangular trench in density-stratified fluid. J. Waterway, Port, Coastal Ocean Engng. Div., ASCE 114, 615–636.Google Scholar
Yih, C. S. 1980 Stratified Flows. Academic.