Hostname: page-component-6b989bf9dc-g5k2d Total loading time: 0 Render date: 2024-04-14T22:05:18.376Z Has data issue: false hasContentIssue false
  • English
  • Français

On interfacial solitary waves over slowly varying topography

Published online by Cambridge University Press:  20 April 2006

Karl R. Helfrich ,
W. K. Melville  and
John W. Miles
Karl R. Helfrich
Affiliation:
Ralph M. Parsons Laboratory, Massachusetts Institute of Technology, Cambridge, MA 02139
W. K. Melville
Affiliation:
Ralph M. Parsons Laboratory, Massachusetts Institute of Technology, Cambridge, MA 02139
John W. Miles
Affiliation:
Institute of Geophysics and Planetary Physics, University of California, San Diego, La Jolla, CA 92093
Get access Rights & Permissions [Opens in a new window]

Abstract

The propagation of long, weakly nonlinear interfacial waves in a two-layer fluid of slowly varying depth is studied. The governing equations are formulated to include cubic nonlinearity, which dominates quadratic nonlinearity in some parametric neighbourhood of equal layer depths. Numerical solutions are obtained for an initial profile corresponding to either a single solitary wave or a rank-ordered pair of such waves incident in a monotonic transition between two regions of constant depth. The numerical solutions, supplemented by inverse-scattering theory, are used to investigate the change of polarity of the incident waves as they pass through a ‘turning point’ of approximately equal layer depths. Our results exhibit significant differences from those reported by Knickerbocker & Newell (1980), which were based on a model equation. In particular, we find that more than one wave of reversed polarity may emerge.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 149 , December 1984 , pp. 305 - 317
Copyright
© 1984 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

Apel, J. R., Byrne, H. M., Proni, J. R. & Charnell, R. L. 1975 Observation of oceanic internal and surface waves from the Earth Resources Technology Satellite. J. Geophys. Res. 80, 865–881.Google Scholar
Dahlquist, G. & Björck, A. 1974 Numerical Methods. Prentice-Hall.
Djordjevic, V. D. & Redekopp, L. G. 1978 The fission and disintegration of internal solitary waves moving over two-dimensional topography. J. Phys. Oceanogr. 8, 1016–1024.Google Scholar
Fornberg, B. & Whitham, G. B. 1978 A numerical and theoretical study of certain nonlinear wave phenomena. Phil. Trans. R. Soc. Lond. A 289, 373–404.Google Scholar
Kakutani, T. & Yamasaki, N. 1978 Solitary waves on a two-layer fluid. J. Phys. Soc. Japan 45, 674–679.Google Scholar
Kaup, D. J. & Newell, A. C. 1978 Solitons as particles, oscillators, and in slowly changing media: a singular perturbation theory. Proc. R. Soc. Lond. A 361, 413–446.Google Scholar
Keulegan, G. H. 1953 Characteristics of internal solitary waves. J. Res. Natl Bur. Standards 51, 133–140.Google Scholar
Knickerbocker, C. J. & Newell, A. C. 1980 Internal solitary waves near a turning point. Phys. Lett. 75 A, 326–330.Google Scholar
Lamb, H. 1932 Hydrodynamics. Cambridge University Press.
Lee, C. Y. & Beardsley, R. C. 1974 The generation of long nonlinear internal waves in a weakly stratified shear flow. J. Geophys. Res. 79, 453–462.Google Scholar
Long, R. R. 1956 Solitary waves in one- and two-fluid systems. Tellus 8, 460–471.Google Scholar
Maxworthy, T. 1979 A note on the internal solitary waves produced by tidal flow over a three-dimensional ridge. J. Geophys. Res. 84, 338–346.Google Scholar
Miles, J. W. 1979 On internal solitary waves. Tellus 31, 456–462.Google Scholar
Miles, J. W. 1980 Solitary waves. Ann. Rev. Fluid Mech. 12, 11–43.Google Scholar
Miles, J. W. 1981 On internal solitary waves, II. Tellus 33, 397–401.Google Scholar
Osborne, A. R. & Burch, T. L. 1980 Internal solitons in the Andaman Sea. Science 208, 451–460.Google Scholar
Whitham, F. B. 1974 Linear and Nonlinear Waves. Academic.
Wilkinson, J. H. 1965 The Algebraic Eigenvalue Problem. Clarendon.