The singularity at the crest of a finite amplitude progressive Stokes wave

1973/06/19 by Malcolm A. Grant · 82 citations
Earth and Planetary Sciences · Engineering · Mathematics · #Ocean Waves and Remote Sensing #Wave and Wind Energy Systems #Coastal and Marine Dynamics #Singularity #Crest #Gravitational singularity #Amplitude #Stokes wave #Physics #Mathematical analysis #Singular point of a curve #Stokes flow #Classical mechanics #Mechanics #Wave propagation #Breaking wave #Mathematics #Optics #Flow (mathematics)

paper · doi:10.1017/s0022112073001552

published in Journal of Fluid Mechanics 59(2), 257-262 (Cambridge University Press)

openalex publication_date 1973/06/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Expansions have been given in the past for steady Stokes waves at or near a largest wave with a 120° corner. It is shown here that the solution is more complicated than has been assumed: that the corner is not a regular singular point, and that waves of less than maximum amplitude have singularities of a different order.

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