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 FN: Rotating Flows |
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Chair: Harry Swinney, University of Texas Room: Hilton Chicago PDR 2 |
Monday, November 21, 2005 8:00AM - 8:13AM |
FN.00001: Rotating flows in an axisymmetric stirred tank. Daniel T. Valentine, Michael Brazell Internal flows induced by a rotating disk in a cylinder are described. Axisymmetric flows of incompressible fluids governed by the Navier-Stokes equations were computed. Steady-state solutions and time-periodic solutions were found by solving initial-value problems computationally. Results are presented for steady and periodic motions predicted for a disk-induced flow in a cylindrical container for the range of rotational- Reynolds number from 1000 to 5000. Solutions for one aspect ratio (viz., height-to-radius ratio of 2.0), one disk size (viz., a thin disk with radius equal to 0.5 of the cylinder radius), and one disk location (viz., one quarter of the height of the cylinder from the bottom) are presented. The three- dimensional trajectories for a group of particles were computed. They are presented to illustrate mixing in the stirred tank. The ``breakdown'' of the primary vortical structure as characterized by breakdown bubbles along the centerline of the upper part of the cylinder are discussed. Side-wall boundary-layer separation and other identifiable flow features that were predicted are also discussed. [Preview Abstract] |
Monday, November 21, 2005 8:13AM - 8:26AM |
FN.00002: On swirling flow in a rotating sectioned cylinder Mats Nigam We consider a rotating fluid in a sectioned cylinder with radial inflow and axial outflow. A reduced model is obtained by assuming a weak variation in the azimuthal direction and applying a Galerkin method. The asymptotic analysis for small Rossby numbers yields a third order ODE for the swirl-velocity. In the limit of infinite Reynolds number, the equation can be solved analytically. The solution shows strong qualitative similarities with the axially symmetric case. The small radial-to-axial flow is given by a stream-function which varies linearly in the axial direction and induces an order one swirl. Finally, estimates of the radial pressure drop and the induced torque are presented for various outlet configurations. [Preview Abstract] |
Monday, November 21, 2005 8:26AM - 8:39AM |
FN.00003: Probing the three-dimensional structure of a rotating turbulent flow Jori E. Ruppert-Felsot, Hepeng Zhang, Harry L. Swinney We study laboratory produced fluid turbulence under the influence of rapid rotation. Three-dimensional turbulence was generated by strong pumping through sources and sinks at the bottom of a deep rotating tank (48.4 cm high, 39.4 cm diameter) filled with water. The resulting flow evolved toward quasi-two-dimensional (quasi-2D) turbulence with increasing height in the tank. The quasi-2D flow near the top of the tank contained many long-lived coherent vortices and jets\footnote{J. E. Ruppert- Felsot, O. Praud, E. Sharon, and H. L. Swinney, Phys. Rev. E \textbf{72}, 016311 (2005)}. Digital particle image velocimetry measurements of the flow field were made using tracer particles illuminated by laser light-sheets. Measurements using two synchronized cameras and vertically separated horizontal light-sheets revealed that the coherent vortices were columnar and vertically extended throughout the tank. We found the simultaneously measured vertically separated horizontal projections of the velocity field to be well correlated even at moderate rotation. Further, a gradual spatial decay was observed in the correlation for increasing vertical separation, rather than a sharp transition. The findings were consistent with the effect of rotation to cause a quasi-2D column-like flow structure aligned along the axis of rotation. [Preview Abstract] |
Monday, November 21, 2005 8:39AM - 8:52AM |
FN.00004: Decaying grid-generated turbulence in a rotating frame Cyprien Morize, Fr\'{e}d\'{e}ric Moisy, Marc Rabaud Decaying turbulence in a rotating frame is experimentally investigated. Turbulence is generated by rapidly towing a grid in a rotating water tank, and the velocity field in a plane perpendicular to the rotation axis is measured by means of particle image velocimetry. A power-law decay of energy is observed up to the Ekman timescale, above which the friction from the Ekman layers become dominant. The value of the decay exponent is found to decreases continuously from $n \simeq 2$ to 1 as the rotation rate is increased. We show that these values can be understood from dimensional analysis, neglecting the anisotropy but including the effect of the confinement. The energy spectrum perpendicular to the rotation axis becomes steeper as the micro Rossby number $Ro_{\omega} = \omega' / 2 \Omega$ (where $\Omega$ is the rotation rate and $\omega'$ the vorticity r.m.s.) decreases below 2, with an exponent that increases from its classical Kolmogorov value 5/3 up to $2.3 \pm 0.1$. Below the same $Ro_{\omega}$ threshold, the velocity derivative skewness decreases as $|S| \propto Ro_{\omega}$, reflecting the inhibition of the energy transfers by the background rotation, with an inverse energy cascade that develops at large scales. [Preview Abstract] |
Monday, November 21, 2005 8:52AM - 9:05AM |
FN.00005: The cyclone-anticyclone asymmetry in decaying rotating turbulence Frederic Moisy, Cyprien Morize, Marc Rabaud, Joel Sommeria The statistics of the vorticity fluctuations in decaying rotating turbulence is experimentally investigated by means of particle image velocimetry. Two series of experiments have been carried out, one in a small-scale rotating water tank (FAST, Paris), with an aspect ratio $\sim O(1)$, and the other one in the large-scale `Coriolis' plateform (LEGI, Grenoble), with an aspect ratio $\sim O(10)$. In both experiments, turbulence is generated by rapidly towing a grid through the fluid, providing an initial state which is approximately homogeneous and isotropic. The asymmetry between cyclones and anticyclones is characterized by the vorticity skewness $S_\omega = \langle \omega_z^3 \rangle / \langle \omega_z^2 \rangle^{3/2}$ ($\omega_z$ is the vorticity component along the rotation axis). During the decay, for times up to the Ekman timescale, a growth of the asymmetry towards cyclonic vorticity is observed as $S_\omega \sim (\Omega t)^{0.6 \pm 0.1}$. For larger times, a re-symmetrization of the vorticity fluctuations take place, due to the non-linear Ekman pumping which preferentially affects the cyclonic vorticity. While the power-law growth is generic of both experiment, the maximum value of $S_\omega$ is shown to depend on the experiment size. [Preview Abstract] |
Monday, November 21, 2005 9:05AM - 9:18AM |
FN.00006: Toroidal vortex development in a swirl-driven cavity Richard Hewitt, Tom Mullin, Simon Tavener We present the results of a combined experimental and numerical (axisymmetric, finite-element) investigation into steady secondary vortex flows in swirl-driven annular cavities. The flow is driven by the symmetric rotation of both end walls and an inner cylindrical boundary. In all cases the outer boundary of the flow domain is a stationary circular cylinder. At moderate Reynolds numbers, toroidal vortex structures arise either through the creation of stagnation points (in the meridional plane) at the inner bounding cylinder, or on the mid-plane of symmetry. A detailed description of the flow regimes is presented, suggesting that a cascade of such vortices can be created. Experimental results are reported that visualize some of the new states and confirm the prediction that they are stable to (mid-plane) symmetry breaking perturbations. We also consider how the minimum Reynolds number for such non-trivial flow structures behaves in the limit of small aspect ratios. [Preview Abstract] |
Monday, November 21, 2005 9:18AM - 9:31AM |
FN.00007: WITHDRAWN: Rotating Polygons on a Fluid Surface Tomas Bohr, Thomas Jansson, Martin Haspang, Kaare Jensen, Pascal Hersen The free surface of a rotating fluid will, due to the centrifugal force, be pressed radially outward. If the fluid rotates as a rigid body in a cylindrical container the surface will assume a parabolic shape. If, however, the flow is driven by rotating the bottom plate, the axial symmetry can break spontaneously and the surface can take the shape of a rigidly rotating polygon. With water we have observed polygons with up to 6 corners. The rotation speed of the polygons does not coincide with that of the plate, but it is often mode-locked, such that the polygon rotates by one corner for each complete rotation of the plate. It has been known for many years that such flows are prone to symmetry breaking. The creation of rotating waves inside the container was observed for Reynolds numbers up to around 3000, where the free surface remains essentially flat (see J. M. Lopez and F. Marques and A. H. Hirsa and R. Miraghaie, ``Symmetry breaking in free-surface cylinder flows,'' {\em J. Fluid Mech.}, {\bf 502}, 99 (2004)). The polygons occur at much larger Reynolds numbers, for water around 500.000. Correspondingly, the dependence on viscosity is rather small. [Preview Abstract] |
Monday, November 21, 2005 9:31AM - 9:44AM |
FN.00008: Poloidal-toroidal decomposition applied to the MHD equations in a finite cylindrical geometry Piotr Boronski, Laurette Tuckerman Motivated by the recent international research effort to create an experimentally self-sustained dynamo, we have developed a numerical code for solving the three-dimensional MHD equations for a conducting fluid in a finite cylindrical geometry. The flow configuration corresponds to the VKS (von Karman sodium) dynamo experiment carried out by experimentalists at CEA-Saclay, ENS-Paris, and ENS-Lyon. The configuration corresponds to the cylindrical container filled with a conducting fluid whose motion is driven by the counter-rotating disks. Our pseudospectral code uses a toroidal-poloidal decomposition to ensure the divergence-free velocity and magnetic fields. We propose a novel approach, based on the influence matrix technique, for imposing the condition of the continuity of the magnetic field at the boundary between the conducting fluid and a vacuum. Using this code we investigate a recently discovered phenomenon observed experimentally (Ravelet et al., {\sl Phys. Rev. Lett.}, 2004): transition between states of a highly turbulent flow. This transition seems to correspond to the bifurcation of the time-averaged mean flow. [Preview Abstract] |
Monday, November 21, 2005 9:44AM - 9:57AM |
FN.00009: Using Liquid Helium to Observe Rotating and Superfluid Turbulence Gregory Bewley, Daniel P. Lathrop, K.R. Sreenivasan We report on observations of grid generated turbulence in rotation and in a superfluid. We use cryogenic liquid helium, because it has a small viscosity, allowing high Reynolds numbers and rotation rates simultaneously, and because it becomes a superfluid when it is cooled. We generate decaying turbulence by pulling a square grid of bars through the fluid. In these experiments, the mesh Reynolds number is up to 500,000, and the rotation rate, $\Omega$, is up to 2 Hz. This condition corresponds to a Taylor-scale Reynolds number of about 425 and an inverse Rossby number, $\Omega L/U$, of about 10 (where $\Omega$ is the system rotation rate, $L$ is the width of the channel, and $U$ is the RMS velocity of the fluid.) The large scales of the flow are observed using PIV, and a novel technique to trace the fluid motions using micron sized solid hydrogen particles. We find that the rotating flow is dominated by standing inertial waves, whose characteristics are determined by the geometry of the boundary. [Preview Abstract] |
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