Author:
SHTERN VLADIMIR,HUSSAIN FAZLE
Abstract
A new stability approach is developed for a wide class of strongly
non-parallel
axisymmetric flows of a viscous incompressible fluid. This approach encompasses
all
conical flows, and all steady and weakly unsteady disturbances, while prior
studies
were limited to specific flows and particular disturbances. A specially
derived form of
the Navier–Stokes equations allows the exact reduction of the linear
stability problem
to a system of ordinary differential equations. We found that disturbances
originating
at the boundaries of a similarity region cause a variety of steady bifurcations.
Consideration of the still fluid allows disturbances to be classified into
inner, outer and
global modes, depending on the boundary conditions perturbed. Then we identify
and
study modes which cause bifurcation as the Reynolds number increases. The
study
provides improved understanding of (a) azimuthal symmetry
breaking, (b) genesis of swirl, (c) onset of heat convection,
(d) hydromagnetic dynamo, (e) hysteretic
transitions, and (f) jump flow separation. We also discover and
analyse two new
bifurcations: (g) fold catastrophes and (h)
appearance of radial oscillations in swirl-free
jets. The stability analysis reveals that bifurcations (a),
(c) and (f) are caused by inner
perturbations, bifurcations (b), (d), (e) and
(g) by outer perturbations, and bifurcation
(h) by global perturbations. We deduce amplitude equations to
describe the nonlinear
spatiotemporal development of disturbances near the critical Reynolds numbers
for (b)
and (g). Disturbances switching between the basic and secondary
steady states are
found to grow monotonically with time.
Publisher
Cambridge University Press (CUP)
Subject
Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics
Cited by
12 articles.
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