On the Cauchy Problem for Axi-Symmetric Vortex Rings
نویسندگان
چکیده
منابع مشابه
On the Cauchy problem for axi-symmetric vortex rings
We consider the classical Cauchy problem for the 3d Navier-Stokes equation with the initial vorticity ω0 concentrated on a circle, or more generally, a linear combination of such data for circles with common axis of symmetry. We show that natural approximations of the problem obtained by smoothing the initial data satisfy good a-priori estimates which enable us to conclude that the original pro...
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An axi-symmetric and swirling vortex sheet is investigated as the simplest ow in which there is non-trivial vortex stretching and as a possible setting for studying vortex cancellation and singularity formation. Rayleigh's criterion indicates linear stability of a single sheet but instability for other conngurations of sheets. Due to the simplicity of vortex sheet problems, the linear modes and...
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Studies of the formation of ne structures on free-surfaces in liquids, such as curvature singularities or interface pinching, demand that the motion of the interface must be computed very accurately. Boundary integral techniques are a popular choice in such studies because they reduce the dimension of the problem by one. On the other hand, the boundary integrals are singular, and their accurate...
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The present study involves a novel computational technique, regarding simultaneous use of the pseudo particle method, Poisson integral method and a special-purpose computer originally designed for molecular dynamics simulations (MDGRAPE-3). In the present calculations, the dynamics of two colliding vortex rings have been studied using the vortex method. The present acceleration technique allows...
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ژورنال
عنوان ژورنال: Archive for Rational Mechanics and Analysis
سال: 2014
ISSN: 0003-9527,1432-0673
DOI: 10.1007/s00205-014-0775-4