86 research outputs found
Complex eigenvalues for the stability of Couette flow
The eigenvalue problem for the linear stability of Couette flow between rotating concentric cylinders to axisymmetric disturbances is considered. It is shown by numerical calculations and by formal perturbation methods that when the outer cylinder is at rest there exist complex eigenvalues corresponding to oscillatory damped disturbances. The structure of the first few eigenvalues in the spectrum is discussed. The results do not contradict the principle of exchange of stabilities, namely, for a fixed axial wavenumber the first mode to become unstable as the speed of the inner cylinder is increased is nonoscillatory as the stability boundary is crossed
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
Pattern selection in the absolutely unstable regime as a nonlinear eigenvalue problem: Taylor vortices in axial flow
A unique pattern selection in the absolutely unstable regime of a driven,
nonlinear, open-flow system is analyzed: The spatiotemporal structures of
rotationally symmetric vortices that propagate downstream in the annulus of the
rotating Taylor-Couette system due to an externally imposed axial through-flow
are investigated for two different axial boundary conditions at the in- and
outlet. Unlike the stationary patterns in systems without through-flow the
spatiotemporal structures of propagating vortices are independent of parameter
history, initial conditions, and system's length. They do, however, depend on
the axial boundary conditions, the driving rate of the inner cylinder and the
through-flow rate. Our analysis of the amplitude equation shows that the
pattern selection can be described by a nonlinear eigenvalue problem with the
frequency being the eigenvalue. Approaching the border between absolute and
convective instability the eigenvalue problem becomes effectively linear and
the selection mechanism approaches that one of linear front propagation.
PACS:47.54.+r,47.20.Ky,47.32.-y,47.20.FtComment: 15 pages (LateX-file), 8 figures (Postscript
Boundary Limitation of Wavenumbers in Taylor-Vortex Flow
We report experimental results for a boundary-mediated wavenumber-adjustment
mechanism and for a boundary-limited wavenumber-band of Taylor-vortex flow
(TVF). The system consists of fluid contained between two concentric cylinders
with the inner one rotating at an angular frequency . As observed
previously, the Eckhaus instability (a bulk instability) is observed and limits
the stable wavenumber band when the system is terminated axially by two rigid,
non-rotating plates. The band width is then of order at small
() and agrees well with
calculations based on the equations of motion over a wide -range.
When the cylinder axis is vertical and the upper liquid surface is free (i.e.
an air-liquid interface), vortices can be generated or expelled at the free
surface because there the phase of the structure is only weakly pinned. The
band of wavenumbers over which Taylor-vortex flow exists is then more narrow
than the stable band limited by the Eckhaus instability. At small
the boundary-mediated band-width is linear in . These results are
qualitatively consistent with theoretical predictions, but to our knowledge a
quantitative calculation for TVF with a free surface does not exist.Comment: 8 pages incl. 9 eps figures bitmap version of Fig
Spectral theory of Taylor vortices
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46192/1/205_2004_Article_BF00252461.pd
Spatial and temporal spectra of noise driven stripe patterns
Spatial and temporal noise power spectra of stripe patterns are investigated,
using as a model a Swift-Hohenberg equation with a stochastic term. In
particular, the analytical and numerical investigations show: 1) the temporal
noise spectra are of 1/f^alpha form, where alpha=1+(3-D)/4 with D the spatial
dimension of the system; 2) that the stochastic fluctuations of the stripe
position are sub-diffusive.Comment: Submitted to PR
Prototype Design and Feasibility Analysis for Self-Levitated Conveying
In order to avoid friction and scratching when conveying object, an acoustic levitation prototype was designed to verify the feasibility. The modal shapes and the forced harmonic shapes of the prototype are obtained by an ANSYS coupled field computation with a one-quarter symmetry model and the levitation capacity was assessed by the use of groups of simulation and physical testing. The simulation results showed that the pure flexural and mixed flexural wave shapes with different wave numbers existed at some specific frequency. The amplitude in the central point of an aluminum plate having four piezo-electric discs glued to the bottom surface was simulated for a frequency spectrum. The experimental results confirmed the theoretical results and the feasibility of the prototype and confirm that objects can be floated at several resonant frequencies under forced vibrating condition. The system can provide largest bearing capacity when both the piezoelectric disc and the plate resonances coincide
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