Titlebook: Singularities in Fluids, Plasmas and Optics; Russel E. Caflisch,George C. Papanicolaou Book 1993 Springer Science+Business Media Dordrecht

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https://doi.org/10.1007/978-94-011-2022-7Fluid mechanics; Laser; PES; Profil; Tracking; convection; mechanics; optics; porous media; fluid- and aerody

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Singularities in Fluids, Plasmas and Optics978-94-011-2022-7Series ISSN 1389-2185

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Complex Analytic Branching Structures in Porous Media Convectionween the hot and cold fluids. We show how this formalism provides a natural language to describe the proliferation of singularities in the complex plane which was found previously in a joint work with A. Pumir and E.D. Siggia (ref. [2] of this paper).

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The Rayleigh Centrifugal Instability for Vortex Rings with Swirl fluid via the geometrical optics method. In the present paper we solve the geometrical optics equations for vortex rings (without and with swirl) and prove that all of them are unstable with respect to short wavelength perturbations.

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Scaling of a Singularity of EulerSelf-similar scaling in the collapse of perturbed anti-parallel vortex tubes towards a singularity of the three-dimensional, incompressible Euler equations is shown. Histograms of the normalized .-strain have a sharp peak at a positive value of about 0.4.

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Separatrices and SingularitiesSingularities tend to occur near separatrices. Two examples are described in support of this assertion. The first example describes current sheets in coronal plasmas that grow algebraically in time. The second example describes a vortex singularity which develops in finite time in three-dimensional Euler flows.