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Instabilities of finite-amplitude gravity waves on water of finite depth

Published online by Cambridge University Press:  20 April 2006

John W. McLean
John W. McLean
Affiliation:
Fluid Mechanics Department, TRW Defense and Space Systems Group, Redondo Beach, CA 90278
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Abstract

A study of the instabilities of finite-amplitude periodic gravity waves has extended recent deep-water results to finite depth. Results are presented for three depths, one greater and two less than the depth for stabilization of two-dimensional long-wave perturbations. The results include those instabilities found by perturbation methods as well as some new types of instability.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 114 , January 1982 , pp. 331 - 341
Copyright
© 1972 Cambridge University Press

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References

Benjamin, T. B. 1967 Instability of periodic wavetrains in nonlinear dispersive systems. Proc. Roy. Soc. A 299, 59–75.Google Scholar
Benjamin, T. B. & Feir, J. E. 1967 The disintegration of wavetrains on deep water. J. Fluid Mech. 27, 417–430.Google Scholar
Benney, D. J. & Roskes, G. J. 1970 Wave instabilities. Studies Appl. Math. 48, 377–385.Google Scholar
Bryant, P. J. 1978 Oblique instability of periodic waves in shallow water. J. Fluid Mech. 86, 783–792.Google Scholar
Cokelet, E. D. 1977 Steep gravity waves in water of arbitrary uniform depth. Proc. Roy. Soc. A 286, 184–230.Google Scholar
Hayes, W. D. 1973 Group velocity and nonlinear dispersive wave propagation. Proc. Roy. Soc. A 332, 199–221.Google Scholar
Isaacson, E. & Keller, H. B. 1966 Analysis of Numerical Methods, pp. 340–341. John Wiley & Sons.
Longuet-Higgins, M. S. 1978 Some new relations between Stokes coefficients in the theory of gravity waves. J. Inst. Math. Applics. 22, 261–273.Google Scholar
Mclean, J. W. 1981 Instabilities of finite amplitude water waves. J. Fluid Mech. 114, 315–330.Google Scholar
Mclean, J. W., Ma, Y. C., Martin, D. U., Saffman, P. G. & Yuen, H. C. 1981 Three dimensional instability of finite amplitude water waves. Phys. Rev. Letters, 46, 817–820.Google Scholar
Saffman, P. G. & Yuen, H. C. 1980 A new type of three-dimensional deep-water wave of permanent form. J. Fluid Mech. 101, 797–808.Google Scholar
Whitham, G. B. 1967 Non-linear dispersion of water waves. J. Fluid Mech. 27, 399–412.Google Scholar
Zakharov, V. E. 1968 Stability of periodic waves of finite amplitude on the surface of a deep fluid. J. Appl. Mech. Tech. Phys. 2, 190–194.Google Scholar
Zakharov, V. E. & Kharitonov, V. G. 1970 Instability of monochromatic waves on the surface of a liquid of arbitrary depth. J. Appl. Mech. Tech. Phys. 11, 747–751.Google Scholar