Linear stability of finite-amplitude capillary waves on water of infinite depth

Roxana Tiron, Wooyoung Choi

Research output: Contribution to journalArticlepeer-review

13 Scopus citations

Abstract

We study the linear stability of the exact deep-water capillary wave solution of Crapper (J. Fluid Mech., vol. 2, 1957, pp. 532-540) subject to two-dimensional perturbations (both subharmonic and superharmonic). By linearizing a set of exact one-dimensional non-local evolution equations, a stability analysis is performed with the aid of Floquet theory. To validate our results, the exact evolution equations are integrated numerically in time and the numerical solutions are compared with the time evolution of linear normal modes. For superharmonic perturbations, contrary to Hogan (J. Fluid Mech., vol. 190, 1988, pp. 165-177), who detected two bubbles of instability for intermediate amplitudes, our results indicate that Crappers capillary waves are linearly stable to superharmonic disturbances for all wave amplitudes. For subharmonic perturbations, it is found that Crappers capillary waves are unstable, and our results generalize to the highly nonlinear regime the analysis for small amplitudes presented by Chen & Saffman (Stud. Appl. Maths, vol. 72, 1985, pp. 125-147).

Original languageEnglish (US)
Pages (from-to)402-422
Number of pages21
JournalJournal of Fluid Mechanics
Volume696
DOIs
StatePublished - Apr 10 2012

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering

Keywords

  • capillary waves

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