386 research outputs found
The Geometry of Axisymmetric Ideal Fluid Flows with Swirl
The sectional curvature of the volume preserving diffeomorphism group of a
Riemannian manifold can give information about the stability of inviscid,
incompressible fluid flows on . We demonstrate that the submanifold of the
volumorphism group of the solid flat torus generated by axisymmetric fluid
flows with swirl, denoted by , has positive sectional
curvature in every section containing the field iff
. This is in sharp contrast to the situation on
, where only Killing fields have nonnegative
sectional curvature in all sections containing it. We also show that this
criterion guarantees the existence of conjugate points on
along the geodesic defined by .Comment: 8 page
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