Electronic Resource
College Park, Md.
:
American Institute of Physics (AIP)
Journal of Mathematical Physics
40 (1999), S. 869-883
ISSN:
1089-7658
Source:
AIP Digital Archive
Topics:
Mathematics
,
Physics
Notes:
In this paper we study an incompressible inviscid fluid when the initial vorticity is sharply concentrated in N disjoint regions. This problem has been well studied when a planar symmetry is present, i.e., the fluid moves in R2. In this case we know that, when the diameter σ of each region supporting the vorticity is very small, the time evolution of the fluid is quite well described by a dynamical system with finite degrees of freedom called the "point vortex model." In particular the connection between this model and the Euler equation has been proved rigorously as σ→0. In the present paper we discuss the "stability" of the point vortex model with respect to a particular small perturbation of the planar symmetry. More precisely we consider a fluid moving in R3 with a cylindrical symmetry without swirl in which each vortex is no longer a straight tube, but a vorticity ring. We prove that large annuli of radii r(approximate)σ−β for any β〉0 remain "localized" and hence we obtain the point vortex model as σ→0. © 1999 American Institute of Physics.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.532691
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