Bulletin of the American Physical Society
2005 58th Annual Meeting of the Division of Fluid Dynamics
Sunday–Tuesday, November 20–22, 2005; Chicago, IL
Session FT: Taylor-Couette Flow |
Hide Abstracts |
Chair: Juan Lopez, Arizona State University Room: Hilton Chicago Stevens 5 |
Monday, November 21, 2005 8:00AM - 8:13AM |
FT.00001: Linear stability of circular Couette flow in the limit of small radius ratio Arne J. Pearlstein, Florent B. Petteini In the context of a detailed study of the linear stability of spiral Poiseuille flow at small radius ratio (Cotrell and Pearlstein, $J. Fluid Mech.$, in press), we have shown that in the limiting case of no rotation, annular Poiseuille flow is linearly stable at all $Re$, provided that the radius ratio lies below a critical value. Here, we consider the other limiting case, of no axial flow, and report a numerical investigation of the stability of circular Couette flow for small radius ratio. The results are compared to experimental work of Theodorsen for a whirling shaft in an unbounded, otherwise quiescent fluid. [Preview Abstract] |
Monday, November 21, 2005 8:13AM - 8:26AM |
FT.00002: Symmetry breaking via global bifurcations in Taylor-Couette flow F. Marques, J.M. Lopez, J. Abshagen, G. Pfister A combined experimental and numerical study finds a complex mechanism of Z2 symmetry breaking involving global bifurcations. In addition to symmetry breaking via pitchfork bifurcation, the Z2 symmetry of a rotating wave that occurs in Taylor-Couette flow is broken by a global saddle-node-infinite-period (SNIP) bifurcation after it has undergone a Neimark-Sacker bifurcation to a Z2-symmetric modulated rotating wave. Unexpected complexity in the bifurcation structure arises as the curves of cyclic pitchfork, Neimark-Sacker, and SNIP bifurcations are traced towards their apparent merging point. The complex mechanism of Z2 symmetry breaking involves nonsymmetric two-tori undergoing saddle-loop homoclinic bifurcations in the vicinity of this global bifurcation. As the Reynolds number is increased beyond the SNIP bifurcation, the transition involves period-doubling cascades, period-adding cascades, and a blue-sky catastrophe. The excellent agreement between the experiments and the numerical simulations demonstrates the robustness of these exotic bifurcations in a physically realized system. [Preview Abstract] |
Monday, November 21, 2005 8:26AM - 8:39AM |
FT.00003: Wide-Gap Taylor-Couette Flow Experiments with Astrophysical Relevance M.J. Burin, J. Goodman, H. Ji, E. Schartman, W. Liu Most astrophysical accretion disks are thought to be turbulent due to magnetohydrodynamic effects. For cool disks however, such as those around protostars, purely hydrodynamic turbulence may be essential. It is claimed that turbulence could occur in these centrifugally-stable shear flows at a sufficiently high Reynolds number (\textit{Re}) via subcritical instabilities. However, with \textit{Re}-limited simulations and only a handful of relevant experiments to date, there is current uncertainty on both the truth and significance of this claim. Laboratory Taylor-Couette flows may in principle be able to provide an avenue for investigating this issue. Towards this end, a Taylor-Couette apparatus having an aspect ratio near 2 has recently been constructed that generates centrifugally-stable (co-rotating) flows with \textit{Re} up to $\sim $ 10$^{7}$. To obtain velocity profiles similar to gravitationally-bound systems, the Ekman circulation typical of wide gap flows had to be reduced substantially. This was accomplished with increased boundary controls, namely a novel differential end cap design, whose efficacy we discuss. Initial experimental data comes from two primary diagnostics: Laser Doppler Velocimetry, providing average and r.m.s. velocity information, and motor-drive torque, providing a gross measure of angular momentum transport. [Preview Abstract] |
Monday, November 21, 2005 8:39AM - 8:52AM |
FT.00004: Pattern Dynamics in Taylor Vortex Flow with Double Hourglass Geometry Richard Wiener, Nicholas Carroll, Matthew McCord, Thomas Olsen In previous investigations \footnote{Wiener {\it et al}., Phys. Rev. E {\bf 55}, 5489 (1997) \& Phys. Rev. Lett. {\bf 83}, 2340 (1999)} we have demonstrated experimentally that Taylor vortex flow in an hourglass geometry undergoes a period-doubling cascade to chaotic pattern dynamics that can be controlled by proportional feedback with small perturbations. The hourglass geometry creates a spatial ramp in the Reynolds number. This results in a region of supercritical vortex flow between regions of subcritical structureless flow that provide the pattern with soft boundaries that allow for persistent dynamics. For a range of reduced Reynolds numbers, the Taylor vortex pattern exhibits persistent dynamics consisting of drifting and stretching vortices punctuated with phase slips. Each phase slip corresponds to the generation of a new vortex pair. We are currently investigating the phase dynamics of Tayor vortex flow with a double hourglass geometry which consists of two regions of supercritical flow in which phase slips occur, separated by a narrow region of subcritical flow. Initial results indicate that at some reduced Reynolds numbers there is synchronization between the vortex dynamics in the two regions, both in the temporal occurrence of the phase slips as well as the drift directions of the vortices. [Preview Abstract] |
Monday, November 21, 2005 8:52AM - 9:05AM |
FT.00005: Effective axial diffusivities for wavy vortex flow from numerical particle tracking: dependence on radius ratio and flow state Gregory P. King, Murray Rudman, Katie Coughlin, George Rowlands The mixing characteristics of wavy Taylor vortex flow have been studied. In a previous work [Rudman, \textit{AIChE J.}, \textbf{44}, 1998) we demonstrated that inter-vortex mixing could be modelled as a one-dimensional diffusion process along the length ($z$) of the cylinders and determined, through particle tracking experiments in numerical fields, that the (non-dimensional) effective axial diffusion coefficient ($D_z$) is a non-monotonic function of the Reynolds number. In a subsequent work (\textit{Phys. Fluids}, \textbf {13} 2001) we showed that $D_z$ correlated with the product of space-averaged Eulerian symmetry measures -- quantities that measure the deviation from two-dimensional flow. Those results were for one radius ratio ($\eta = 0.875$) and one particular wavy vortex flow state (six waves, axial wavelength = 2.33 gap widths). To determine if this result was `coincidental', we have carried out an extensive investigation of the dependence of $D_z$ on Reynolds number, radius ratio and flow state. We find that the excellent correlation of the original study deteriorates only modestly when the radius ratio is decreased from 0.875 to 0.700. On the other hand, $D_z$ shows a more interesting dependence on flow state. [Preview Abstract] |
Monday, November 21, 2005 9:05AM - 9:18AM |
FT.00006: Hysteretic Gravity-Wave Bifurcation in a Highly Turbulent Swirling Flow Nicol\'{a}s Mujica, Daniel Lathrop We report on experimental observations of a gravity-wave instability forced by a highly turbulent free-surface Taylor--Couette flow. Bistability and hysteresis are observed at the bifurcation from a turbulent base state, with an axisymmetric mean flow, to a turbulent gravity-wave state, with an azimuthal $m=1$ pattern to the mean flow and free surface. We show that the critical Reynolds number at which the wave state appears is not sharply defined as it depends on turbulent fluctuations. [Preview Abstract] |
Monday, November 21, 2005 9:18AM - 9:31AM |
FT.00007: WITHDRAWN: On the Taylor-Couette problem in the continuum limit Itzchak Frankel, Avshalom Manela We study the Taylor-Couette problem for a perfect gas which is
situated
between a rotating inner cylinder and a concentric stationary
cylinder, both
of which are maintained at the same temperature. A linear
temporal
stability analysis is carried for small Knudsen numbers
using a ``slip-flow" model assuming axisymmetric perturbations.
At small Mach numbers ($Ma$) the resulting neutral curve
initially coincides
with the critical-Reynolds-number ($Re$) curve ($Re\propto
Ma/Kn$)
obtained in the corresponding incompressible-flow problem. With
increasing
$Ma$, the neutral curve deviates to larger values of $Re$
demonstrating that, contrary to some statements in the
literature,
compressibility effects are stabilizing. Furthermore,
our results indicate that there is an upper bound for the
Knudsen
number, $Kn_m$, above which
the system is stable for all Mach numbers.
Thus, owing to compressibility there also
exists (for all $Kn |
Monday, November 21, 2005 9:31AM - 9:44AM |
FT.00008: Formation of polygonal flow pattern between two corotating disks in an enclosure Tomohito Miura, Jiro Mizushima Pattern formation and transitions of flow between two corotating disks in a cylindrical enclosure is investigated numerically and experimentally. The outer cylindrical boundary of the flow field is assumed to being fixed, whereas the inner cylinder rotates together with the two disks. The flow is not only symmetric with respect to the inter-disk midplane but also axisymmetric around the axis of rotation at small Reynolds numbers. The axisymmetry of the flow field is broken due to instability at high Reynolds numbers. Such an instability occurs for small gap ratios, the ratio of the gap between two disks to the radius of the annulus, and yields a polygonal flow pattern in a plane normal to the rotation axis. We identified two kinds of three-dimensional (3D) unsteady flow by numerical simulations, one of which is asymmetric with respect to the inter-disk midplane and the other has a shift-and-reflect symmetry with the midplane, and compared them with those obtained by experiment. We evaluated the critical Reynolds number at which the axisymmetric flow makes a transition to 3D unsteady flow and found that the axisymmetry is broken due to Hopf bifurcation. [Preview Abstract] |
Follow Us |
Engage
Become an APS Member |
My APS
Renew Membership |
Information for |
About APSThe American Physical Society (APS) is a non-profit membership organization working to advance the knowledge of physics. |
© 2024 American Physical Society
| All rights reserved | Terms of Use
| Contact Us
Headquarters
1 Physics Ellipse, College Park, MD 20740-3844
(301) 209-3200
Editorial Office
100 Motor Pkwy, Suite 110, Hauppauge, NY 11788
(631) 591-4000
Office of Public Affairs
529 14th St NW, Suite 1050, Washington, D.C. 20045-2001
(202) 662-8700