The superharmonic normal mode instabilities of nonlinear deep-water capillary waves

S. J. Hogan

doi:10.1017/S0022112088001260

The superharmonic normal mode instabilities of nonlinear deep-water capillary waves

S. J. Hogan^*

^*Corresponding author for this work

Research output: Contribution to journal › Article (Academic Journal) › peer-review

9 Citations (Scopus)

Abstract

We present results of the calculation of superharmonic normal mode perturbations to the exact nonlinear deep-water capillary wave solution of Crapper (1957). By using the method of Longuet-Higgins (1978a) we are able for the first time to consider all waveheights up to and including the maximum for two-dimensional perturbations. We find agreement with the recent asymptotic analysis of Hogan, Gruman & Stiassnie (1988). Superharmonic instabilities are found at various waveheights less than the maximum.

Original language	English
Pages (from-to)	165-177
Number of pages	13
Journal	Journal of Fluid Mechanics
Volume	190
DOIs	https://doi.org/10.1017/S0022112088001260
Publication status	Published - 1 Jan 1988

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AB - We present results of the calculation of superharmonic normal mode perturbations to the exact nonlinear deep-water capillary wave solution of Crapper (1957). By using the method of Longuet-Higgins (1978a) we are able for the first time to consider all waveheights up to and including the maximum for two-dimensional perturbations. We find agreement with the recent asymptotic analysis of Hogan, Gruman & Stiassnie (1988). Superharmonic instabilities are found at various waveheights less than the maximum.

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