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Transverse dynamics of gravity-capillary periodic water waves

Wednesday, September 26, 2012 - 11:30am - 12:20pm
Keller 3-180
Mariana Haragus (Université de Franche-Comté)
The gravity-capillary water-wave problem concerns the
irrotational flow of a perfect fluid in a domain
bounded below by a rigid bottom and above by a free surface under the
influence of gravity and surface tension. In the case of large surface
tension the system has a family of traveling
two-dimensional periodic waves for which the free surface has a periodic
profile in the direction of propagation and is
homogeneous in the transverse direction. We show that
these periodic waves are linearly unstable under spatially inhomogeneous
perturbations which are periodic in the direction transverse to
propagation. As a consequence, the periodic waves
undergo a dimension-breaking bifurcation
generating a family of spatially three-dimensional solutions which are
periodic in both the direction of propagation and the transverse direction.
MSC Code: 
76B15