Bulletin of the American Physical Society
64th Annual Meeting of the APS Division of Fluid Dynamics
Volume 56, Number 18
Sunday–Tuesday, November 20–22, 2011; Baltimore, Maryland
Session D17: Taylor Couette Instability |
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Chair: Matt Paoletti, University of Texas at Austin Room: 320 |
Sunday, November 20, 2011 2:10PM - 2:23PM |
D17.00001: Axial velocimetry and torque scaling in turbulent Taylor-Couette flow with independently rotating cylinders Hansen Nordsiek, Matthew Paoletti, Daniel Lathrop We present experimental studies investigating axial flow velocities and torque scaling in the turbulent flow of water between two independently rotating cylinders. The Taylor-Couette system is capable of both strong turbulence ($Re > 2 \times 10^6$) and rapid rotation. The axial velocity profile near one end (via ultrasound doppler velocimetry), the torque required to rotate the inner cylinder, and the wall shear stress at one point on the outer cylinder are precisely measured as a function of the angular velocities of the two cylinders. We compare our measurements with previous experiments and discuss the potential relevance to angular momentum transport in astrophysical flows. [Preview Abstract] |
Sunday, November 20, 2011 2:23PM - 2:36PM |
D17.00002: Exchange of Stabilities in Couette Flow between Cylinders with Navier-Slip Conditions Pablo Suarez, Isom Herron Viscous Couette flow is derived for flow between two infinitely long concentric rotating cylinders with Navier slip on both. Its axisymmetric linear stability is studied within a regime that would be hydrodynamically stable according to Rayleigh's criterion: opposing gradients of angular velocity and specific angular momentum, based on the rotation rates and radii of the cylinders. Stability conditions are analyzed, by methods based on those of Synge and Chandrasekhar. For sufficiently small slip length on the outer cylinder no instability occurs with arbitrary slip length on the inner cylinder. As a corollary, slip on the inner cylinder is shown to be stabilizing, with no slip on the outer cylinder. Two slip configurations are investigated numerically, first with slip only on the outer cylinder, then second with equal slip on both cylinders. It is found that instability does occur (for large outer slip length), and the principle of exchange of stabilities emerges. The instability disappears for sufficiently large slip length in the second case; Rayleigh's criterion provides an explanation for these phenomena. [Preview Abstract] |
Sunday, November 20, 2011 2:36PM - 2:49PM |
D17.00003: Wavy toroidal and helicoidal vortices in Taylor-Couette with axial and radial through-flows Denis Martinand, Eric Serre, Nils Tilton, Richard Lueptow Based on previous stability analyses of a Taylor-Couette cell with superimposed axial and/or radial through-flows, a weakly non-linear approach is used to determine the saturated states of the toroidal or helicoidal marginal instabilities above their relevant thresholds. These saturated states are then used to compute secondary instabilities in the form of wavy vortices by Floquet analysis. Different scenarios for this secondary transition are assessed, involving harmonic or subharmonic, convective or absolute, secondary modes. The effects of the axial and radial through-flows on these secondary modes and their critical conditions are then addressed. The analytical results are compared to direct numerical simulations of supercritical flows using spectral methods. [Preview Abstract] |
Sunday, November 20, 2011 2:49PM - 3:02PM |
D17.00004: Stability and angular momentum transport of flows between co-rotating cylinders Marc Avila The flow of gas in astrophysical disks is characterized by radially decreasing angular velocity and radially increasing angular momentum. In principle, disk-like flows can be obtained in experiments of fluid between co-rotating cylinders and so these are often used to extrapolate momentum transport and stability of accretion disks. Recent results from experimental setups in Princeton and Maryland reach, however, opposite conclusions as whether keplerian flows remain laminar or become turbulent at high Reynolds numbers. In this contribution direct numerical simulations of flows with the precise geometry and boundary conditions of the Princeton and Maryland experiments will be reported. It is found that in both cases the flows become turbulent at moderate Reynolds numbers. The underlying instabilities are due to axial boundary conditions in the experiments. [Preview Abstract] |
Sunday, November 20, 2011 3:02PM - 3:15PM |
D17.00005: Linear Analysis of Oscillations in Free Surface Taylor-Couette Flows M. Pretko, E.M. Edlund, E. Spence, A.H. Roach, H. Ji Determining the mechanism of angular momentum transport in accretion disks is a long-standing problem in astrophysics. In addition to the magnetorotational instability, another possible mechanism is hydrodynamic turbulence. Previous experimental work made use of a bounded Taylor-Couette system and found no transition to turbulence even at Reynolds numbers of order $10^6$. However, a free surface adds another degree of freedom and allows for modes which are absent in the bounded case. Therefore, a free surface may lead to instabilities which could not be observed in previous experiments. As preparations for experiments with a free surface Taylor-Couette device are made, we perform a linear analysis of oscillations in such a system and search for unstable modes. As a first approximation, surface tension is neglected and effects of viscosity are dealt with as small corrections. The experimental apparatus has a split endcap in order to minimize Ekman circulation. Thus, in this analysis, it is assumed that the background flow is strictly azimuthal. Analytic and numerical work is currently in progress and will ultimately be compared with experiment. [Preview Abstract] |
Sunday, November 20, 2011 3:15PM - 3:28PM |
D17.00006: Recent results from the Princeton MRI experiment Erik Spence, Austin Roach, Eric Edlund, Christophe Gissinger, Peter Sloboda, Hantao Ji The magnetorotational instability (MRI) is widely expected to be responsible for the observationally inferred accretion rates of astrophysical disks. The Princeton MRI experiment is a Taylor-Couette device used to generate conditions under which the MRI should be unstable: an externally applied magnetic field, and a radially decreasing angular velocity profile. The apparatus' unique feature is independently-rotating endcap rings, which are used to reduce Ekman circulation. The working fluid is GaInSn; its velocity field is measured using an ultrasonic Doppler velocimetry system. Though an ideal-Couette angular rotation profile can almost be attained, through careful choice of end-cap ring speeds, residual Ekman circulation remains. The instability's identification is complicated by this secondary circulation, since it moves in the same radial direction as the flow expected from the instability. Comparison of radial flows in MRI-stable and MRI-unstable regimes is used to search for the instability's signature, as determined by numerical simulations. An update on the search for the instability will be presented. [Preview Abstract] |
Sunday, November 20, 2011 3:28PM - 3:41PM |
D17.00007: Observation of a magnetically enabled instability in the Princeton MRI Experiment A.H. Roach, E.J. Spence, C. Gissinger, E.M. Edlund, P. Sloboda, H. Ji The Princeton MRI Experiment is a modified Taylor-Couette device with a GaInSn working fluid used for the study of rotating MHD flows. An Ultrasound Doppler Velocimetry (UDV) system is used to measure the velocity field. It has revealed an instability causing large-amplitude velocity fluctuations when an axial magnetic field is applied to both hydrodynamically stable and hydrodynamically unstable background flow states with the split axial endcaps rotating differentially. The azimuthal velocity has a characteristic spiral mode structure at saturation, with an azimuthal mode number m=1. This instability appears in a region of parameter space distinct from that where the magnetorotational instability is expected to be present. Nonlinear 3D simulations have shown an instability of the Shercliff layer that forms at the split endcaps when a magnetic field is applied, and the resultant azimuthal flow patterns are largely consistent with experimental observations. Work is ongoing to measure the Shercliff layer in the experiment, and to identify the precise mechanism for the instability in the simulations. Results from experiments and simulations will be presented. Supported by DOE contract DE-AC02-09CH11466. [Preview Abstract] |
Sunday, November 20, 2011 3:41PM - 3:54PM |
D17.00008: Study of Magnetorotational Instability in a Swirling Plasma Hantao Ji, Kyle Kremer, Eric Edlund, Erik Spence Fast angular momentum transport in accretion disks has been an outstanding problem in astrophysics for more than three decades. The magnetorotational instability (MRI) has been identified as a powerful mechanism to transport angular momentum. Experiments using liquid metal are underway to study the MRI in incompressible MHD limit. A new frontier in accretion disk research is to explore physics beyond incompressible MHD. Possible new effects include compressibility, multiple-fluid effects, kinetic effects, ion-neutral collisions, radiation pressure, and dust grains. A swirling gas flow with quasi-Keplerian profiles, which are characterized by radially increasing angular momentum with decreasing angular velocity, is set up by an injection-pumping system. Spiral antennas are used to transmit RF power into the experiment through the helicon mode of discharge to ionize the gas with a desirable degree of ionization. A wide range of outstanding issues can be studied in such device, including: nonlinear hydrodynamic instability, baroclinic instability with axial or azimuthal temperature gradient, MRI in weakly ionized plasmas with Hall effect and ambipolar diffusion. Theoretical analyses and experimental explorations will be presented. [Preview Abstract] |
Sunday, November 20, 2011 3:54PM - 4:07PM |
D17.00009: Searching for a subcritical transition in quasi-Keplerian flows E.M. Edlund, M. Pretko, A. Roach, P. Sloboda, E.J. Spence, H. Ji Angular momentum transport in hot accretion disks in binary star systems and in active galactic nuclei is likely governed by the presence of the magneto-rotational instability (MRI) which can be effective in the presence of very weak magnetic fields. Colder, proto-planetary accretion disks with negligible ionization may not be able to support the MRI and consequently, a hydrodynamic path to turbulence may be needed to enhance the frictional forces and the transport of angular momentum. Hydrodynamic experiments in Taylor-Couette devices with controlled boundary conditions have shown that quasi-Keplerian flows are quiescent with very low levels of fluctuations. Yet there remains the possibility that these prior studies either have not accessed a nonlinear or subcritical transition to turbulence. We report here on recent studies in the Hydrodynamic Turbulence eXperiment (HTX), an order unity aspect ratio Taylor- Couette device, at the Princeton Plasma Physics Laboratory where quasi-Keplerian flows at Reynolds numbers of order $10^6$ are probed with active perturbations to search for a subcritical transition. The role and regulation of secondary circulation in these experiments will be discussed. [Preview Abstract] |
Sunday, November 20, 2011 4:07PM - 4:20PM |
D17.00010: Tomographic PIV Observations of Turbulent Structures in Transitional Taylor-Couette Flow Daniel Borrero, Michael Schatz Theoretical and numerical studies have suggested that unstable, exact solutions of the Navier-Stokes equations known as Exact Coherent Structures (ECS) may provide a foundation for a simplified dynamical description of turbulence. Taylor-Couette flow (TCF) is an ideal system to make experimental connections to current ECS theory since it maintains some of its assumptions (streamwise periodic boundary conditions and plane Couette flow (in the small-gap limit)), but also includes realistic effects (no-slip spanwise boundary conditions). Furthermore, when only the outer cylinder is allowed to rotate, the system exhibits a subcritical transition to turbulence much like the one that the systems used to develop ECS theory undergo. We have developed a Taylor-Couette system with a series of jets built into the inner cylinder wall, which we can use to make small, local perturbations to the flow. We use tomographic particle image velocimetry to measure the structures that form when the flow is perturbed and how these structures affect the stability of the laminar flow in the transitional regime. [Preview Abstract] |
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