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Waves on Wednesday Seminar Series

Wednesday, December 7,  2005, 10:00 am
Cullimore 611
New Jersey Institute of Technology

Transverse instability of gravity-capillary solitary waves and formation of lumps

B. Kim

Department of Mathematics

Massachusetts Institute of Technology

Abstract

Using perturbation methods, the stability to long-wave transverse perturbations is discussed of gravity-capillary solitary waves for B (Bond number)<1/3 on water of finite or infinite depth. Consistent with Bridges (2001), if the total energy happens to be a decreasing function of wave speed, transverse instability occurs. Solitary waves of depression, although stable to longitudinal perturbations, are thus unstable to transverse perturbations, and this instability apparently results in the formation of gravity-capillary lumps (Kim & Akylas JFM 2005). These lumps are shown to bifurcate in the form of wavepackets with a nonzero wavenumber at which the extremum of phase speed is attained: in the weakly nonlinear limit, the envelope turns out to be the lump type solution of the elliptic Davey-Stewartson equations when B<1/3. Generalization of the stability analysis and the formation of lumps to interfacial gravity-capillary solitary waves is also discussed.