Abstract
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.
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Verga, A. (2004). Singularity formation in vortex sheets and interfaces. In: Descalzi, O., Martínez, J., Rica, S. (eds) Instabilities and Nonequilibrium Structures IX. Nonlinear Phenomena and Complex Systems, vol 9. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-0991-1_23
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DOI: https://doi.org/10.1007/978-94-007-0991-1_23
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