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Propagation of obliquely incident water waves over a trench

Published online by Cambridge University Press:  20 April 2006

James T. Kirby  and
Robert A. Dalrymple
James T. Kirby
Affiliation:
Department of Civil Engineering, University of Delaware, Newark, DE 19711
Robert A. Dalrymple
Affiliation:
Department of Civil Engineering, University of Delaware, Newark, DE 19711
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Abstract

The diffraction of obliquely incident surface waves by an asymmetric trench is investigated using linearized potential theory. A numerical solution is constructed by matching particular solutions for each subregion of constant depth along vertical boundaries; the resulting matrix equation is solved numerically. Several cases where the trench-parallel wavenumber component in the incident-wave region exceeds the wavenumber for freely propagating waves in the trench are investigated and are found to result in large reductions in wave transmission; however, reflection is not total owing to the finiteness of the obstacle.

Results for one case are compared with data obtained from a small-scale wave-tank experiment. An approximate solution based on plane-wave modes is derived and compared with the numerical solution and, in the long-wave limit, with a previous analytic solution.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 133 , August 1983 , pp. 47 - 63
Copyright
© 1983 Cambridge University Press

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References

Anderson, E. E. 1971 Modern Physics and Quantum Mechanics. Saunders.
Bartholomeusz, E. F. 1958 The reflexion of long waves at a step Proc. Camb. Phil. Soc. 54, 106–118.Google Scholar
Kreisel, G. 1949 Surface waves Q. Appl. Maths 7, 21–44.Google Scholar
Lamb, H. 1932 Hydrodynamics. Dover.
Lassiter, J. B. 1972 The propagation of water waves over sediment pockets. Ph.D. thesis, Massachusetts Institute of Technology.
Lee, J.-J. & Ayer, R. M. 1981 Wave propagation over a rectangular trench J. Fluid Mech. 110, 335–347.Google Scholar
Lee, J.-J., Ayer, R. M. & Chiang, W.-L. 1980 Interactions of waves with submarine trenches. In Proc. 17th Intl Conf. Coastal Engng, ASCE Sydney, pp. 812–822.
Liu, P. L.-F. & Abbaspour, M. 1982 An integral equation method for the diffraction of oblique waves by an infinite cylinder Int. J. Num. Meth. Engng 18, 1497–1504.Google Scholar
Mei, C. C. & Black, J. L. 1969 Scattering of surface waves by rectangular obstacles in water of finite depth J. Fluid Mech. 38, 499–511.Google Scholar
Miles, J. W. 1967 Surface-wave scattering matrix for a shelf J. Fluid Mech. 28, 755–767.Google Scholar
Miles, J. W. 1982 On surface-wave diffraction by a trench J. Fluid Mech. 115, 315–325.Google Scholar
Newman, J. N. 1965a Propagation of water waves past long two-dimensional obstacles J. Fluid Mech. 23, 23–29.Google Scholar
Newman, J. N. 1965b Propagation of water waves over an infinite step J. Fluid Mech. 23, 399–415.Google Scholar
Raichlen, F. & Lee, J.-J. 1978 An inclined-plate wave generator. In Proc. 16th Intl Conf. Coastal Engng, ASCE, Hamburg, pp. 388–399.Google Scholar
Schwinger, J. & Saxon, D. S. 1968 Discontinuities in Waveguides. Gordon & Breach.
Takano, K. 1960 Effets d'un obstacle parallélépipédique sur la propagation de la houle Houille Blanche 15, 247–267.Google Scholar