Geodesic
Traveling waves from the arclength parameterization: Vortex sheets with surface tension
Benjamin Akers1 ; David M. Ambrose2 ; J. Douglas Wright2
1Air Force Institute of Technology, Wright-Patterson AFB, USA
2Drexel University, Philadelphia, USA
Interfaces and free boundaries, Tome 15 (2013) no. 3, pp. 359-380

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DOI

We study traveling waves for the vortex sheet with surface tension. We use the angle-arclength description of the interface rather than Cartesian coordinates, and we utilize an arclength parameterization as well. In this setting, we make a new formulation of the traveling wave ansatz. For this problem, it should be possible for traveling waves to overturn, and notably, our formulation does allow for waves with multi-valued height. We prove that there exist traveling vortex sheets with surface tension bifurcating from equilibrium. We compute these waves by means of a quasi-Newton iteration in Fourier space; we find continua of traveling waves bifurcating from equilibrium and extending to include overturning waves, for a variety of values of the mean vortex sheet strength.
DOI : 10.4171/ifb/306
Classification : 35-XX, 76-XX
Mots-clés : Arclength, vortex sheet, traveling wave, surface tension

Benjamin Akers  1   ; David M. Ambrose  2   ; J. Douglas Wright  2

1 Air Force Institute of Technology, Wright-Patterson AFB, USA
2 Drexel University, Philadelphia, USA 
Benjamin Akers; David M. Ambrose; J. Douglas Wright. Traveling waves from the arclength parameterization: Vortex sheets with surface tension. Interfaces and free boundaries, Tome 15 (2013) no. 3, pp. 359-380. doi: 10.4171/ifb/306
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     author = {Benjamin Akers and David M. Ambrose and J. Douglas Wright},
     title = {Traveling waves from the arclength parameterization: {Vortex} sheets with surface tension},
     journal = {Interfaces and free boundaries},
     pages = {359--380},
     year = {2013},
     volume = {15},
     number = {3},
     doi = {10.4171/ifb/306},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/306/}
}
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