The dynamic pressure in deep-water extreme Stokes waves

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2 Citations (Scopus)


In this paper, we consider the dynamic pressure in a deep-water extreme Stokes wave. While the presence of stagnation points introduces a number of mathematical complications, maximum principles are applied to analyse the dynamic pressure in the fluid body by means of an excision process. It is shown that the dynamic pressure attains its maximum value beneath the wave crest and its minimum beneath the wave trough, while it decreases in moving away from the crest line along any streamline. This article is part of the theme issue ‘Nonlinear water waves’.

Original languageEnglish
Article number20170095
JournalPhilosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
Issue number2111
Publication statusPublished - 28 Jan 2018


  • Euler’s equation
  • Maximum principles
  • Weak solutions


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