Hostname: page-component-77c89778f8-m8s7h Total loading time: 0 Render date: 2024-07-20T12:13:16.991Z Has data issue: false hasContentIssue false
  • English
  • Français

Scattering of Poincare waves by an irregular coastline. Part 2. Multiple scattering

Published online by Cambridge University Press:  12 April 2006

L. A. Mysak  and
M. S. Howe
L. A. Mysak
Affiliation:
Department of Mathematics and Institute of Oceanography, University of British Columbia, Vancouver
M. S. Howe
Affiliation:
Engineering Department, University of Cambridge Present address: Bolt Beranek and Newman Inc., 50 Moulton Street, Cambridge, Massachusetts 02138.
Get access Rights & Permissions [Opens in a new window]

Abstract

Kelvin and Poincaré waves are generated when an ocean wave arrives at a nominally rectilinear coastline and interacts with coastal irregularities. The discussion of this problem given by Howe & Mysak (1973) is extended in this paper in order to examine the role of multiple scattering of the Kelvin and Poincaré waves. An integro-differential kinetic equation is derived to describe these processes in the limit in which the irregularities are small compared with the characteristic wavelength. In the absence of dissipative mechanisms it is verified that this description of interactions with the coast conserves total wave energy. The theory is applied to a variety of idealized problems which model tidal and storm surge events, including the generation and decay of Kelvin waves by extensive and localized Poincaré-wave forcing, and the influence of multiple scattering on the radiation of Poincaré-wave noise into the open ocean.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 86 , Issue 2 , 29 May 1978 , pp. 337 - 363
Copyright
© 1978 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.)

References

Frisch, U. 1968 Wave propagation in random media. In Probabilistic Methods in Applied Mathematics, vol. 1 (ed. A. T. Bharucha-Reid), p. 75. Academic Press.
Heaps, N. S. 1969 Phil. Trans. Roy. Soc. A 265, 93.
Howe, M. S. 1971 J. Fluid Mech. 45, 769.
Howe, M. S. 1974a Proc. Roy. Soc. A 337, 413.
Howe, M. S. 1974b Quart. J. Mech. Appl. Math. 27, 237.
Howe, M. S. & Mysak, L. A. 1973 J. Fluid Mech. 57, 111.
Lamb, H. 1932 Hydrodynamics, 6th edn. Cambridge University Press.
Lighthill, M. J. 1960 Phil. Trans. Roy. Soc. A 252, 397.
Müller, P. & Olbers, D. J. 1975 J. Geophys. Res. 80, 3848.
Mysak, L. A. & Howe, M. S. 1976 Dyn. Atmos. Ocean 1, 3.
Mysak, L. A. & Tang, C. L. 1974 J. Fluid Mech. 64, 241.
Platzman, G. W. 1971 Ocean tides and related waves. In Mathematical Problems in the Geophysical Sciences. Lectures in Applied Mathematics (ed. Reid W. M.), vol. 14, pp. 239–291. Providence, R.I.: Am. Math. Soc.
Stratonovich, R. L. 1963 Topics in the Theory of Random Noise, vol. 1. Gordon & Breach.
Thomson, R. E. 1970 J. Fluid Mech. 42, 657.