Bulletin of the American Physical Society
65th Annual Meeting of the APS Division of Fluid Dynamics
Volume 57, Number 17
Sunday–Tuesday, November 18–20, 2012; San Diego, California
Session M14: Rotating Flows II: Taylor-Couette Flow |
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Chair: Patrice Meunier, Aix Marseille University Room: 27B |
Tuesday, November 20, 2012 8:00AM - 8:13AM |
M14.00001: Experimental study of the statistics of a gravity-wave instability in a Taylor-Couette system with free surface Julian Martinez Mercado, Cristobal Arratia, Nicolas Mujica In this work, we study the occurrence of a gravity-wave instability in a turbulent Taylor-Couette system with a free surface. In such configuration the system can bifurcate from an axisymmetric turbulent base state to a $m=1$ gravity wave state, where a wave grows from a resonant mode of the free surface taking the energy from the turbulent base state. We use the Froude number $F_r=(a\omega)^2/gh$ to characterize the bifurcation, where $a$ is the radius of the inner cylinder, $\omega$ its angular velocity, $g$ the gravity acceleration and $h$ the height of the free surface. We show that the observed instability is subcritical, presenting bistability and hysteresis. The measured bifurcation curve can be fitted with the deterministic amplitude equation $\partial_t u = \epsilon u + \nu u ^ 2 - \gamma u^3$, being $u$ the wave's amplitude, although differences are observed due to noise induced by turbulence. The growing rate of the wave's amplitude $\sigma$ varies linearly with $F_r-{F_r}_c$. Moreover, the probability distribution of the wave's amplitude can be expressed as a functional of the form $\ln c_0-c_1u^2+c_2u^3-c_3u^4$, resulting from the use of a Fokker-Planck equation to obtain the probability distribution for this type of bifurcation. [Preview Abstract] |
Tuesday, November 20, 2012 8:13AM - 8:26AM |
M14.00002: Transitions and Reynolds number scaling in quasi-Keplerian Taylor-Couette flow Hansen Nordsiek, Daniel Lathrop Experimental investigations of the Reynolds number dependence of the torque and wallshear stress for Taylor-Couette flow in the quasi-Keplerian regime (Rayleigh stable anticyclonic flow) are presented in the range of $300 < Re < 10^5$. The Taylor-Couette experiment has independently rotating inner and outer cylinders, a radius ratio of 0.724, an aspect ratio of 11.42, and axial boundaries that rotate with the outer cylinder. The torque required to rotate the inner cylinder at a constant angular velocity, and the wall shear stress at the outer boundary are precisely measured as a function of the Reynolds number for several values of the Rossby number, which compares shear to global rotation. We compare our measurements with previous experiments and simulations, and discuss potential implications for the hydrodynamic contribution to angular momentum transport in astrophysical flows. [Preview Abstract] |
Tuesday, November 20, 2012 8:26AM - 8:39AM |
M14.00003: Reynolds Number Effects on Turbulent Characteristics of Taylor-Couette Flow JoonHwi Park, Naoya Fukushima, Masayasu Shimura, Mamoru Tanahashi, Toshio Miyauchi Laminar and turbulent Taylor-Couette flow is of great importance in a wide range of engineering applications, such as viscosity measurement devices, rotating machineries and reactors. In this study, we focus on turbulent Taylor-Couette flow with a fixed outer cylinder and a rotating inner cylinder. Direct numerical simulation (DNS) of turbulent Taylor-Couette flow has been conducted to investigate turbulent characteristics including Reynolds stress budget at Reynolds number from 8000 to 20000. Reynolds number, Re, is defined by gap width and rotating speed of inner cylinder. In this range of Re, turbulent characteristics are expected to change around Re=10000, referring to Wendt's empirical formula. Averaged torque from DNS agrees well with Wendt's empirical formula and torque transition is confirmed around Re=10000. Averaged azimuthal velocity normalized by friction velocity on inner/outer wall increases in logarithmic region with increase in Re. All components of Reynolds stress tensor also increase in all domain. The minute movement of center of Taylor vortices is observed spatially and temporally when Re is over 12000. Finally, Reynolds stress budgets are investigated to figure out Reynolds number effects on turbulent statistics in detail. [Preview Abstract] |
Tuesday, November 20, 2012 8:39AM - 8:52AM |
M14.00004: New considerations for centrifugal buoyancy effects in fast rotating flows Jose Manuel Lopez Alonso, Francisco Marques, Marc Avila Boussinesq type approximations accounting for centrifugal buoyancy are well-known and have been used with remarkable results in problems where a distinguised frame of reference is readily identified. However, it does not consider those flows where different parts may rotate independently, such as Taylor-Couette flows with stratification and/or heating, cylindrical containers with the lids rotating at different angular velocities,etc... In these flows, there is not a unique angular velocity and the differences among them may originate that terms which are not considered by the classical Boussinesq approximation become important. Moreover, this centrifugal effect is not only important when we have rotating walls, but also if a strong vortex appears dynamically in the interior of the domain. We propose a new and easy way to introduce the centrifugal buoyancy into the Navier-Stokes equations which takes into account the previous considerations. We present a linear analysis of stability in an axially periodic Taylor-Couette system subjected to a negative gradient of temperature in order to illustrate the differences of using both approximations when considering the centrifugal effects. [Preview Abstract] |
Tuesday, November 20, 2012 8:52AM - 9:05AM |
M14.00005: Symmetry-breaking Hopf bifurcations to 1-, 2-, and 3-tori in small-aspect-ratio counter-rotating Taylor-Couette flow Sebastian Altmeyer, Younghae Do, Francisco Marques, Juan M. Lopez Taylor-Couette flow in a small aspect-ratio wide-gap annulus in the counter-rotating regime is investigated by solving the full 3D Navier-Stokes equations. The system is invariant under rotations about the axis, reflection about the mid-plane, and time translations. A systematic investigation is presented, both in terms of the flow physics, the numerical simulations and from a dynamical systems perspective. The dynamics are primarily associated with the behavior of the jet of angular momentum that emerges from the inner cylinder boundary layer at about the mid-plane. The sequence of bifurcations as the rotation is increased consists of a Hopf bifurcation breaking the reflection symmetry and leading to an axisymmetric limit cycle associated to an invariant one-torus manifold with a spatio-temporal symmetry. This undergoes a Hopf bifurcation breaking axisymmetry, leading to quasi-periodic solutions evolving on a 2-torus that is only setwise symmetric due to precesion. These undergo a further Hopf bifurcation introducing a third incommensurate frequency leading to a 3-torus. On it,as the rotation is further increased, a SNIC bifurcation happens, destroying the 3-torus and leaving a pair of symmetrically related 2-tori states on which all symmetries of the system have been broken. [Preview Abstract] |
Tuesday, November 20, 2012 9:05AM - 9:18AM |
M14.00006: Influence of Rotation Number to Coherent Structures and Torque Scaling in Turbulent Taylor-Couette Flow Sedat Tokgoz, Gerrit Elsinga, Rene Delfos, Jerry Westerweel Flow between two coaxial cylinders is called Taylor-Couette flow and has been studied extensively over the years. Due to the closed and well controlled character of the system, experimental studies with different measurement techniques mostly focused on the turbulent flow. Torque measurements performed at the turbulent range of Reynolds numbers showed change of the torque scaling with relative rotation speeds of the cylinders (i.e. rotation number). In this study, we use tomographic PIV to capture instantaneous three-dimensional flow structures in turbulent Taylor-Couette flow in order to study the mechanism that is responsible for the change of the torque. Time-averaging and auto-correlation of the data confirm the change of coherent structures with the rotation number in the mean flow. Spatial filtering of the instantaneous vector fields enables separating the contributions of small and large scale motions to the Reynolds stress. We show that combination of large scale azimuthal-small scale radial and large scale azimuthal-large scale radial motions are the dominant ones that are effecting the torque. Additionally, we observe change of the organisation of the coherent large scale structures with the rotation number, in relation to the change of the torque scaling. [Preview Abstract] |
Tuesday, November 20, 2012 9:18AM - 9:31AM |
M14.00007: Experimental studies of turbulence lifetimes in differentially rotating flows E.M. Edlund, Z. Yan, E.J. Spence, A.H. Roach, J. Rhoads, H. Ji Inference of accretion rates from observations of stellar systems suggests inward mass fluxes which can only be reasonably explained by a turbulent transport process. While the magneto-rotational instability (MRI) is likely active in systems above a critical ionization, there remains some question as to whether the MRI can be active in cooler bodies such as proto-planetary systems, and if not, what mechanism is then responsible for angular momentum transport? Keplerian rotation profiles are hydrodynamically linearly stable in the inviscid limit, however, it is not known if there exists a subcritical transition. A series of studies in the Hydrodynamic Turbulence Experiment (HTX), a modified Taylor-Couette device, have explored quiescent flows in the quasi-Keplerian regime. Operating in the wide-gap limit and with split axial boundaries to control the Ekman circulation, azimuthal flows in HTX can be brought very close to ideal Couette. These flows are subjected to external perturbations to test their ability to sustain incompressible hydrodynamic turbulence. Under no circumstances has a subcritical transition to turbulence been observed. Turbulence decay lifetimes are measured and compared to theoretical models. [Preview Abstract] |
Tuesday, November 20, 2012 9:31AM - 9:44AM |
M14.00008: Bifurcation, thin film structure and collapse in Newton's bucket Shomeek Mukhopadhyay, Joshua Dijksman, Tom Witelski, Richard Mclaughlin, Roberto Camassa, Bob Behringer The understanding of rotating thin film flows is of great fundamental and practical (spin coating, geophysical flows) importance. In this talk we will present our ongoing work with the second generation of a spin coating apparatus that we call ``Newton's bucket,'' extending on previous work [Mukhopadhyay and Behringer (J. Phys, 2009) and Mukhopadhyay et. al. (Phys. Rev. E, 2011)]. We study the bifurcation of the `non-classical' dry spot that develops above a critical rotation rate. We observe a nontrivial fine structure in the contact line that connects the dry spot with the fluid reservoir and measure the collapse dynamics of the fluid reservoir by means of high speed imaging. We compare our observations to numerical solutions of the lubrication approximation. [Preview Abstract] |
Tuesday, November 20, 2012 9:44AM - 9:57AM |
M14.00009: Stability of solution branches in infinite rotating disk flow Kevin van Eeten, John van der Schaaf, Gert-Jan van Heijst, Jaap Schouten The stability of steady solutions of the Navier-Stokes equations for the problem of viscous flow between an infinite rotating disk and an infinite stationary disk is investigated. A random disturbance is applied to five velocity profiles at $t=0$, after which the disturbance propagation, $\Delta(t)$, defined as the squared difference of the azimuthal velocity at time $t$ with the steady state azimuthal velocity, is determined. From this propagation data, the Lyapunov exponents are obtained as a function of the Reynolds number. It was found that four of the five solution branches (including the Batchelor solution) are Lyapunov stable. The Stewartson solution, on the other hand, was found to have a positive Lyapunov exponent and diverged from its initial state to a Batchelor type of flow. The mechanism with which the non-viscous core obtains its angular momentum during this transition was identified as being dominated by radial convection from larger radii towards the axis of rotation. [Preview Abstract] |
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