Change is coming to MEMOCS:
This journal is becoming a
subscription journal with select diamond open-access articles.
Read more about it.
Abstract
|
We discuss the effect of curvature on the dynamics of a two-dimensional
inviscid incompressible fluid with initial vorticity concentrated in
small
disjoint regions, that is, the classical point vortex system. We recall some results
about point vortex dynamics on simply connected surfaces with constant curvature
, that
is, plane, spherical, and hyperbolic surfaces. We show that the effect of curvature can
be treated as a smooth perturbation to the Green’s function of the equation related
to the stream function in the planar case. Then we obtain as a main result that the
localization property of point vortices, already proved for the plane, is preserved also
under the effect of curvature perturbation.
|
Keywords
point vortex dynamics, mathematical fluid mechanics, ideal
fluid
|
Mathematical Subject Classification 2010
Primary: 76B47
|
Milestones
Received: 27 February 2012
Revised: 14 March 2012
Accepted: 17 April 2012
Published: 6 February 2013
Communicated by Carlo Marchioro
|
|