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Dynamics of gravity–capillary solitary waves in deep water


Reference:

Wang, Z. and Milewski, P. A., 2012. Dynamics of gravity–capillary solitary waves in deep water. Journal of Fluid Mechanics, 708, pp. 480-501.

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    Official URL:

    http://dx.doi.org/10.1017/jfm.2012.320

    Abstract

    The dynamics of solitary gravity-capillary water waves propagating on the surface of a three-dimensional fluid domain is studied numerically. In order to accurately compute complex time-dependent solutions, we simplify the full potential flow problem by using surface variables and taking a particular cubic truncation possessing a Hamiltonian with desirable properties. This approximation agrees remarkably well with the full equations for the bifurcation curves, wave profiles and the dynamics of solitary waves for a two-dimensional fluid domain, and with higher-order truncations in three dimensions. Fully localized solitary waves are then computed in the three-dimensional problem and the stability and interaction of both line and localized solitary waves are investigated via numerical time integration of the equations. There are many solitary wave branches, indexed by their finite energy as their amplitude tends to zero. The dynamics of the solitary waves is complex, involving nonlinear focusing of wavepackets, quasi-elastic collisions, and the generation of propagating, spatially localized, time-periodic structures akin to breathers.

    Details

    Item Type Articles
    CreatorsWang, Z.and Milewski, P. A.
    DOI10.1017/jfm.2012.320
    DepartmentsFaculty of Science > Mathematical Sciences
    Publisher StatementMilewski_J_Fluid_Mech_2012.pdf: © Cambridge University Press 2012
    RefereedYes
    StatusPublished
    ID Code32104

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