Singularity formation in vortex sheets and interfaces

  • Alberto Verga
Part of the Nonlinear Phenomena and Complex Systems book series (NOPH, volume 9)


One of the paradigms of nonlinear science is that patterns result from instability and bifurcation. However, another pathway is possible: self-similar evolution, singularity formation, and form. One example of this process is the formation of spherical drops throngh the pinch off of a cylindrical thread of liquid. Other example is given by the evolution of a vortex sheet, which from an initial regular shape, develops a finite time singularity of the curvature, resulting in the generation of a spiraling vortex. We investigate some simple systems, a stretched vortex sheet, the free surface of a perfect fluid driven by a vortex dipole, and the splash produced by a convergent capillary wave, in order to illustrate some specific scenarios to the appearance of a “form” through a singularity.


Stagnation Point Froude Number Vortex Core Perfect Fluid Point Vortex 
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Copyright information

© Springer Science+Business Media Dordrecht 2004

Authors and Affiliations

  • Alberto Verga
    • 1
    • 2
  1. 1.Institut de Recherche sur les Phénomènes Hors ÉquilibreMarseilleFrance
  2. 2.Université d’Aix-Marseille, CNRSFrance

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