150 research outputs found
Wave-number dependence of the transitions between traveling and standing vortex waves and their mixed states in the Taylor-Couette system
Previous numerical investigations of the stability and bifurcation properties
of different nonlinear combination structures of spiral vortices in a
counterrotating Taylor-Couette system that were done for fixed axial
wavelengths are supplemented by exploring the dependence of the vortex
phenomena waves on their wavelength. This yields information about the
experimental and numerical accessability of the various bifurcation scenarios.
Also backwards bifurcating standing waves with oscillating amplitudes of the
constituent traveling waves are found.Comment: 4 pages, 5 figure
Bifurcation of standing waves into a pair of oppositely traveling waves with oscillating amplitudes caused by a three-mode interaction
A novel flow state consisting of two oppositely travelling waves (TWs) with
oscillating amplitudes has been found in the counterrotating Taylor-Couette
system by full numerical simulations. This structure bifurcates out of axially
standing waves that are nonlinear superpositions of left and right handed
spiral vortex waves with equal time-independent amplitudes. Beyond a critical
driving the two spiral TW modes start to oscillate in counterphase due to a
Hopf bifurcation. The trigger for this bifurcation is provided by a nonlinearly
excited mode of different symmetry than the spiral TWs. A three-mode coupled
amplitude equation model is presented that captures this bifurcation scenario.
The mode-coupling between two symmetry degenerate critical modes and a
nonlinearly excited one that is contained in the model can be expected to occur
in other structure forming systems as well.Comment: 4 pages, 5 figure
Non-axisymmetric Magnetorotational Instabilities in Cylindrical Taylor-Couette Flow
We study the stability of cylindrical Taylor-Couette flow in the presence of
azimuthal magnetic fields, and show that one obtains non-axisymmetric
magnetorotational instabilities, having azimuthal wavenumber m=1. For
Omega_o/Omega_i only slightly greater than the Rayleigh value (r_i/r_o)^2, the
critical Reynolds and Hartmann numbers are Re_c ~ 10^3 and Ha_c ~ 10^2,
independent of the magnetic Prandtl number Pm. These values are sufficiently
small that it should be possible to obtain these instabilities in the PROMISE
experimental facility.Comment: final version as accepted by Phys Rev Let
Controlling the stability transfer between oppositely traveling waves and standing waves by inversion-symmetry-breaking perturbations
The effect of an externally applied flow on symmetry degenerated waves
propagating into opposite directions and standing waves that exchange stability
with the traveling waves via mixed states is analyzed. Wave structures that
consist of spiral vortices in the counter rotating Taylor-Couette system are
investigated by full numerical simulations and explained quantitatively by
amplitude equations containing quintic coupling terms. The latter are
appropriate to describe the influence of inversion symmetry breaking
perturbations on many oscillatory instabilities with O(2) symmetry.Comment: 4 pages, 4 figure
Competition between Traveling Fluid Waves of Left and Right Spiral Vortices and Their Different Amplitude Combinations
Stability, bifurcation properties, and the spatiotemporal behavior of
different nonlinear combination structures of spiral vortices in the counter
rotating Taylor-Couette system are investigated by full numerical simulations
and by coupled amplitude equation approximations. Stable cross-spiral
structures with continuously varying content of left and right spiral modes are
found. They provide a stability transferring connection between the initially
stable, axially counter propagating wave states of pure spirals and the axially
standing waves of so-called ribbons that become stable slightly further away
from onset of vortex flow.Comment: 4 pages, 5 figure
Spiral vortices traveling between two rotating defects in the Taylor-Couette system
Numerical calculations of vortex flows in Taylor-Couette systems with counter
rotating cylinders are presented. The full, time dependent Navier-Stokes
equations are solved with a combination of a finite difference and a Galerkin
method. Annular gaps of radius ratio and of several heights are
simulated. They are closed by nonrotating lids that produce localized Ekman
vortices in their vicinity and that prevent axial phase propagation of spiral
vortices. Existence and spatio temporal properties of rotating defects, of
modulated Ekman vortices, and of the spiral vortex structures in the bulk are
elucidated in quantitative detail.Comment: 9 pages, 9 figure
Resonance bifurcations from robust homoclinic cycles
We present two calculations for a class of robust homoclinic cycles with
symmetry Z_n x Z_2^n, for which the sufficient conditions for asymptotic
stability given by Krupa and Melbourne are not optimal.
Firstly, we compute optimal conditions for asymptotic stability using
transition matrix techniques which make explicit use of the geometry of the
group action.
Secondly, through an explicit computation of the global parts of the Poincare
map near the cycle we show that, generically, the resonance bifurcations from
the cycles are supercritical: a unique branch of asymptotically stable period
orbits emerges from the resonance bifurcation and exists for coefficient values
where the cycle has lost stability. This calculation is the first to explicitly
compute the criticality of a resonance bifurcation, and answers a conjecture of
Field and Swift in a particular limiting case. Moreover, we are able to obtain
an asymptotically-correct analytic expression for the period of the bifurcating
orbit, with no adjustable parameters, which has not proved possible previously.
We show that the asymptotic analysis compares very favourably with numerical
results.Comment: 24 pages, 3 figures, submitted to Nonlinearit
Broken symmetries and pattern formation in two-frequency forced Faraday waves
We exploit the presence of approximate (broken) symmetries to obtain general
scaling laws governing the process of pattern formation in weakly damped
Faraday waves. Specifically, we consider a two-frequency forcing function and
trace the effects of time translation, time reversal and Hamiltonian structure
for three illustrative examples: hexagons, two-mode superlattices, and two-mode
rhomboids. By means of explicit parameter symmetries, we show how the size of
various three-wave resonant interactions depends on the frequency ratio m:n and
on the relative temporal phase of the two driving terms. These symmetry-based
predictions are verified for numerically calculated coefficients, and help
explain the results of recent experiments.Comment: 4 pages, 6 figure
Towards an experimental von Karman dynamo: numerical studies for an optimized design
Numerical studies of a kinematic dynamo based on von Karman type flows
between two counterrotating disks in a finite cylinder are reported. The flow
has been optimized using a water model experiment, varying the driving
impellers configuration. A solution leading to dynamo action for the mean flow
has been found. This solution may be achieved in VKS2, the new sodium
experiment to be performed in Cadarache, France. The optimization process is
described and discussed, then the effects of adding a stationary conducting
layer around the flow on the threshold, on the shape of the neutral mode and on
the magnetic energy balance are studied. Finally, the possible processes
involved into kinematic dynamo action in a von Karman flow are reviewed and
discussed. Among the possible processes we highlight the joint effect of the
boundary-layer radial velocity shear and of the Ohmic dissipation localized at
the flow/outer-shell boundary
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