Showing papers by "Philip Geoffrey Saffman published in 1995"
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TL;DR: In this article, the Squire-Long equation is used to investigate the dependence of solutions on upstream, or inlet, and downstream, or outlet, boundary conditions and flow geometry.
Abstract: The steady axisymmetric Euler flow of an inviscid incompressible swirling fluid
is described exactly by the Squire-Long equation. This equation is studied numerically
for the case of diverging flow to investigate the dependence of solutions
on upstream, or inlet, and downstream, or outlet, boundary conditions and flow
geometry. The work is performed with a view to understanding how the phenomenon
of vortex breakdown occurs. It is shown that solutions fail to exist or,
alternatively, that the axial flow ceases to be unidirectional, so that breakdown
can be inferred, when a parameter measuring the relative magnitude of rotation
and axial flow (the Squire number) exceeds critical values depending upon the geometry
and inlet profiles. A 'quasi-cylindrical' simplification of the Squire-Long
equation is compared with the more complete Euler model and shown to be able
to account for most of the latter's behaviour. The relationship is examined between
'failure' of the quasi-cylindrical model and the occurrence of a 'critical'
flow state in which disturbances can stand in the flow.
65 citations