Theory of weakly damped free-surface flows: A new formulation based on potential flow solutions

F. Dias, A. I. Dyachenko, V. E. Zakharov

Research output: Contribution to journalArticlepeer-review

98 Citations (Scopus)

Abstract

Several theories for weakly damped free-surface flows have been formulated. In this Letter we use the linear approximation to the Navier-Stokes equations to derive a new set of equations for potential flow which include dissipation due to viscosity. A viscous correction is added not only to the irrotational pressure (Bernoulli's equation), but also to the kinematic boundary condition. The nonlinear Schrödinger (NLS) equation that one can derive from the new set of equations to describe the modulations of weakly nonlinear, weakly damped deep-water gravity waves turns out to be the classical damped version of the NLS equation that has been used by many authors without rigorous justification.

Original languageEnglish
Pages (from-to)1297-1302
Number of pages6
JournalPhysics Letters A
Volume372
Issue number8
DOIs
Publication statusPublished - 18 Feb 2008
Externally publishedYes

Keywords

  • Free surface
  • Navier-Stokes equations
  • Potential flow
  • Viscosity

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