Research

Dynamics of three-dimensional gravity-capillary solitary waves in deep water


Reference:

Akers, B. and Milewski, P. A., 2010. Dynamics of three-dimensional gravity-capillary solitary waves in deep water. SIAM Journal on Applied Mathematics, 70 (7), pp. 2390-2408.

Related documents:

[img]
Preview
PDF (SMM002390.pdf) - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader
Download (4MB) | Preview

    Official URL:

    http://dx.doi.org/10.1137/090758386

    Abstract

    A model equation for gravity-capillary waves in deep water is proposed. This model is a quadratic approximation of the deep water potential flow equations and has wavepacket-type solitary wave solutions. The model equation supports line solitary waves which are spatially localized in the direction of propagation and constant in the transverse direction, and lump solitary waves which are spatially localized in both directions. Branches of both line and lump solitary waves are computed via a numerical continuation method. The stability of each type of wave is examined. The transverse instability of line solitary waves is predicted by a similar instability of line solitary waves in the nonlinear Schrödinger equation. The spectral stability of lumps is predicted using the waves' speed energy relation. The role of wave collapse in the stability of these waves is also examined. Numerical time evolution is used to confirm stability predictions and observe dynamics, including instabilities and solitary wave collisions.

    Details

    Item Type Articles
    CreatorsAkers, B.and Milewski, P. A.
    DOI10.1137/090758386
    DepartmentsFaculty of Science > Mathematical Sciences
    Publisher StatementSMM002390.pdf: ©SIAM
    RefereedYes
    StatusPublished
    ID Code26673

    Export

    Actions (login required)

    View Item

    Document Downloads

    More statistics for this item...