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58 results

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  • Modulation leading to frequency downshifting of water waves in the vicinity of the Benjamin–Feir transition

  • Daniel James Ratliff, Olga Trichtchenko, Thomas J. Bridges
  • Journal:
    Journal of Fluid Mechanics / Volume 1014 / 10 July 2025
    Published online by Cambridge University Press:
    03 July 2025, A23
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  • For Stokes waves in finite depth within the neighbourhood of the Benjamin–Feir stability transition, there are two families of periodic waves, one modulationally unstable and the other stable. In this paper we show that these two families can be joined by a heteroclinic connection, which manifests in the fluid as a travelling front. By shifting the analysis to the setting of Whitham modulation theory, this front is in wavenumber and frequency space. An implication of this jump is that a permanent frequency downshift of the Stokes wave can occur in the absence of viscous effects. This argument, which is built on a sequence of asymptotic expansions of the phase dynamics, is confirmed via energetic arguments, with additional corroboration obtained by numerical simulations of a reduced model based on the Benney–Roskes equation.

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