158 research outputs found
Four-vortex motion around a circular cylinder
The motion of two pairs of counter-rotating point vortices placed in a
uniform flow past a circular cylinder is studied analytically and numerically.
When the dynamics is restricted to the symmetric subspace---a case that can be
realized experimentally by placing a splitter plate in the center plane---, it
is found that there is a family of linearly stable equilibria for same-signed
vortex pairs. The nonlinear dynamics in the symmetric subspace is investigated
and several types of orbits are presented. The analysis reported here provides
new insights and reveals novel features of this four-vortex system, such as the
fact that there is no equilibrium for two pairs of vortices of opposite signs
on the opposite sides of the cylinder. (It is argued that such equilibria might
exist for vortex flows past a cylinder confined in a channel.) In addition, a
new family of opposite-signed equilibria on the normal line is reported. The
stability analysis for antisymmetric perturbations is also carried out and it
shows that all equilibria are unstable in this case.Comment: 27 pages, 13 figures, to be published in Physics of Fluid
Gravitating Opposites Attract
Generalizing previous work by two of us, we prove the non-existence of
certain stationary configurations in General Relativity having a spatial
reflection symmetry across a non-compact surface disjoint from the matter
region. Our results cover cases such that of two symmetrically arranged
rotating bodies with anti-aligned spins in () dimensions, or
two symmetrically arranged static bodies with opposite charges in 3+1
dimensions. They also cover certain symmetric configurations in
(3+1)-dimensional gravity coupled to a collection of scalars and abelian vector
fields, such as arise in supergravity and Kaluza-Klein models. We also treat
the bosonic sector of simple supergravity in 4+1 dimensions.Comment: 13 pages; slightly amended version, some references added, matches
version to be published in Classical and Quantum Gravit
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