The Pressure in a Deep-Water Stokes Wave of Greatest Height

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14 Citations (Scopus)


In this paper we investigate the qualitative behaviour of the pressure function beneath an extreme Stokes wave over infinite depth. The presence of a stagnation point at the wave-crest of an extreme Stokes wave introduces a number of mathematical difficulties resulting in the irregularity of the free surface profile. It will be proven that the pressure decreases in the horizontal direction between a crest-line and subsequent trough-line, except along these lines themselves where the pressure is stationary with respect to the horizontal coordinate. In addition we will prove that the pressure strictly increases with depth throughout the fluid body.

Original languageEnglish
Pages (from-to)209-218
Number of pages10
JournalJournal of Mathematical Fluid Mechanics
Issue number2
Publication statusPublished - 01 Jun 2016
Externally publishedYes


  • Euler’s equation
  • fluid pressure
  • maximum principles
  • weak solutions


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