2,431 research outputs found
Free Surface Flow in Vertical Taylor-Couette System
Vertical Taylor-Couette flow with a free surface at its top has been examined by numerical and experimental approaches. Being compared with the ideal case with infinite length cylinders, this system has effects of the finite lengths, the gravitational acceleration and the surface tension. The inner cylinder rotates and the outer cylinder and the bottom wall are stationary. The numerical approach uses the VOF method to model the free surface. In the experiment, the flow patterns are observed from the top and the meridional views, and the displacement of the free surface is measured. The flow modes are classified by the number of vortices appearing in the meridional plane and the radial flow directions at the top and the bottom. The power spectra of the displacement of the free surface and the bulk energy are numerically evaluated and the bulk energy tends to give favorable agreement with the spectra of the displacement obtained experimentally. The transition from the secondary mode flow appearing at higher Reynolds number to the primary mode flow at lower Reynolds number is examined and comparison between the numerical and experimental results are made
Temporal Modulation of Traveling Waves in the Flow Between Rotating Cylinders With Broken Azimuthal Symmetry
The effect of temporal modulation on traveling waves in the flows in two
distinct systems of rotating cylinders, both with broken azimuthal symmetry,
has been investigated. It is shown that by modulating the control parameter at
twice the critical frequency one can excite phase-locked standing waves and
standing-wave-like states which are not allowed when the system is rotationally
symmetric. We also show how previous theoretical results can be extended to
handle patterns such as these, that are periodic in two spatial direction.Comment: 17 pages in LaTeX, 22 figures available as postscript files from
http://www.esam.nwu.edu/riecke/lit/lit.htm
Standard and helical magnetorotational instability: How singularities create paradoxal phenomena in MHD
The magnetorotational instability (MRI) triggers turbulence and enables
outward transport of angular momentum in hydrodynamically stable rotating shear
flows, e.g., in accretion disks. What laws of differential rotation are
susceptible to the destabilization by axial, azimuthal, or helical magnetic
field? The answer to this question, which is vital for astrophysical and
experimental applications, inevitably leads to the study of spectral and
geometrical singularities on the instability threshold. The singularities
provide a connection between seemingly discontinuous stability criteria and
thus explain several paradoxes in the theory of MRI that were poorly understood
since the 1950s.Comment: 25 pages, 10 figures. A tutorial paper. Invited talk at SPT 2011,
Symmetry and Perturbation Theory, 5 - 12 June 2011, Otranto near Lecce
(Italy
Momentum transport and torque scaling in Taylor-Couette flow from an analogy with turbulent convection
We generalize an analogy between rotating and stratified shear flows. This
analogy is summarized in Table 1. We use this analogy in the unstable case
(centrifugally unstable flow v.s. convection) to compute the torque in
Taylor-Couette configuration, as a function of the Reynolds number. At low
Reynolds numbers, when most of the dissipation comes from the mean flow, we
predict that the non-dimensional torque , where is the cylinder
length, scales with Reynolds number and gap width , . At larger Reynolds number, velocity
fluctuations become non-negligible in the dissipation. In these regimes, there
is no exact power law dependence the torque versus Reynolds. Instead, we obtain
logarithmic corrections to the classical ultra-hard (exponent 2) regimes: These predictions are found to be in excellent agreement with
available experimental data. Predictions for scaling of velocity fluctuations
are also provided.Comment: revTex, 6 Figure
The linear instability of the stratified plane Couette flow
We present the stability analysis of a plane Couette flow which is stably
stratified in the vertical direction orthogonally to the horizontal shear.
Interest in such a flow comes from geophysical and astrophysical applications
where background shear and vertical stable stratification commonly coexist. We
perform the linear stability analysis of the flow in a domain which is periodic
in the stream-wise and vertical directions and confined in the cross-stream
direction. The stability diagram is constructed as a function of the Reynolds
number Re and the Froude number Fr, which compares the importance of shear and
stratification. We find that the flow becomes unstable when shear and
stratification are of the same order (i.e. Fr 1) and above a moderate
value of the Reynolds number Re700. The instability results from a
resonance mechanism already known in the context of channel flows, for instance
the unstratified plane Couette flow in the shallow water approximation. The
result is confirmed by fully non linear direct numerical simulations and to the
best of our knowledge, constitutes the first evidence of linear instability in
a vertically stratified plane Couette flow. We also report the study of a
laboratory flow generated by a transparent belt entrained by two vertical
cylinders and immersed in a tank filled with salty water linearly stratified in
density. We observe the emergence of a robust spatio-temporal pattern close to
the threshold values of F r and Re indicated by linear analysis, and explore
the accessible part of the stability diagram. With the support of numerical
simulations we conclude that the observed pattern is a signature of the same
instability predicted by the linear theory, although slightly modified due to
streamwise confinement
On self-sustaining processes in Rayleigh-stable rotating plane Couette flows and subcritical transition to turbulence in accretion disks
Subcritical transition to turbulence in Keplerian accretion disks is still a
controversial issue and some theoretical progress is required in order to
determine whether or not this scenario provides a plausible explanation for the
origin of angular momentum transport in non-magnetized accretion disks.
Motivated by the recent discoveries of exact nonlinear steady self-sustaining
solutions in linearly stable non-rotating shear flows, we attempt to compute
similar solutions in Rayleigh-stable rotating plane Couette flows and to
identify transition mechanisms in such flows by combining nonlinear
continuation methods and asymptotic theory. We obtain exact nonlinear solutions
for Rayleigh-stable cyclonic regimes but show that it is not possible to
compute solutions for Rayleigh-stable anticyclonic regimes, including Keplerian
flow, using similar techniques. We also present asymptotic descriptions of
these various problems at large Reynolds numbers that provide some insight into
the differences between the non-rotating and Rayleigh-stable anticyclonic
regimes and derive some necessary conditions for mechanisms analogous to the
non-rotating self-sustaining process to be present in flows on the Rayleigh
line. Our results demonstrate that subcritical transition mechanisms cannot be
identified in wall-bounded Rayleigh-stable anticyclonic shear flows by
transposing directly the phenomenology of subcritical transition in cyclonic
and non-rotating wall-bounded shear flows. Asymptotic developments, however,
leave open the possibility that nonlinear self-sustaining solutions may exist
in unbounded or periodic flows on the Rayleigh line. These could serve as a
starting point to discover solutions in Rayleigh-stable flows, but the
nonlinear stability of Keplerian accretion disks remains to be determined.Comment: 16 pages, 12 figures. Accepted for publication in A&
- …