The nonlinear damping of parametrically excited two-dimensional gravity waves

S.P. Decent

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    10 Citations (Scopus)

    Abstract

    Parametrically excited waves are usually modelled with a nonlinear amplitude equation. It has recently been demonstrated that the behaviour of these waves depends critically upon the coefficient of the cubic damping term in the nonlinear amplitude equation, and especially upon the sign of this coefficient (see Decent and Craik [J. Fluid Mech. 293 (1995) 237]. However, very little work has been carried out on theoretically determining the value of this coefficient. This paper derives the coefficient of cubic damping for the single-mode nonlinear amplitude equation which models two-dimensional gravity waves in a narrow rectangular container. Energy dissipation in the main body of the fluid and in boundary layers at the sidewalls and at the surface is considered. Theoretical results agree fairly well with an experiment carried out by Decent and Craik (1995).
    Original languageEnglish
    Pages (from-to)201-217
    Number of pages17
    JournalFluid Dynamics Research
    Volume19
    Issue number4
    DOIs
    Publication statusPublished - Apr 1997

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