Bulletin of the American Physical Society
63rd Annual Meeting of the APS Division of Fluid Dynamics
Volume 55, Number 16
Sunday–Tuesday, November 21–23, 2010; Long Beach, California
Session CN: Vortex Dynamics and Vortex Flows II |
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Chair: Bartosz Protas, McMaster University Room: Long Beach Convention Center 202C |
Sunday, November 21, 2010 1:00PM - 1:13PM |
CN.00001: Mechanics of Viscous Vortex Reconnection F. Hussain, K. Duraisamy This work builds on our long-standing claim that reconnection of coherent structures is the dominant mechanism of jet noise generation and that reconnection plays a key role in both energy cascade and fine-scale mixing in fluid turbulence. Reconnection of two anti-parallel vortex tubes is studied by direct numerical simulations of the incompressible Navier-Stokes equations over a wide range (250-9000) of the vortex Reynolds number (Re). Reconnection is never complete, leaving behind a part of the initial tubes as ``threads,'' which then undergo successive reconnections (our cascade and mixing scenarios) as the newly formed ``bridges'' recoil from each other by self-advection. We find that the time $t_R$ for orthogonal transfer of circulation scales as $t_R \approx Re^{-3/4}$. The shortest distance $d$ between the tube centroids scales as $d \approx a (Re (t_o-t))^{3/4}$ before reconnection and as $d \approx b(Re(t-t_o))^2$ after reconnection. Bridge repulsion is faster than collision and has less variation as local induction predominates, and is clearly the most intense sound generation phase. The maximum rate of vortex circulation transfer, enstrophy production and dissipation scale as $Re^1, Re^{7/4}, Re^{-1/2}$, respectively. [Preview Abstract] |
Sunday, November 21, 2010 1:13PM - 1:26PM |
CN.00002: Regenerative transient growth on a vortex column Eric Stout, Fazle Hussain Perturbations on a Lamb-Oseen vortex column with a circulation overshoot (due to a sheath of negative axial vorticity, $-\Omega _z $, surrounding the core) are studied by DNS of the incompressible Navier-Stokes equations, for a range (500-12500) of the vortex Reynolds number (Re= circulation/viscosity). Initial perturbation radial (rad.) vorticity is tilted by the mean strain into perturbation azimuthal (az.) vorticity, which generates \textit{positive }Reynolds stress necessary for energy growth. The meridional flow of az. vorticity tilts $-\Omega _z $ into intensifying rad. vorticity, increasing the +Reynolds stress, which results in exponential energy growth. +Reynolds stress also transports azimuthal momentum radially \textit{outward}, reducing the overshoot magnitude, which determines $-\Omega _z $. The resulting decreased rad. vorticity reduces the +Reynolds stress, arresting instability growth (with concomitant increase in viscous dissipation). Outward transport of azimuthal momentum also produces -Reynolds stress, which then transports azimuthal momentum\textit{ inward}. A new circulation peak appears nearer to the column axis, initiating a period of new, regenerative transient growth -- a promising scenario for turbulence generation near the vortex column. [Preview Abstract] |
Sunday, November 21, 2010 1:26PM - 1:39PM |
CN.00003: ABSTRACT WITHDRAWN |
Sunday, November 21, 2010 1:39PM - 1:52PM |
CN.00004: A short wave instability caused by the approach of a vortex pair to a ground plane Daniel M. Harris, Charles H.K. Williamson In the present work, we experimentally study the approach of a counter-rotating vortex pair to a ground plane. The trajectories of the primary vortices in experiment differ quite significantly from the inviscid case, primarily due to the fact that between the vortices and the ground, a boundary layer forms, which can separate to generate secondary vortices of opposite sign; a phenomenon originally discovered by Harvey and Perry (1971). We have developed a novel technique to study this flow that allows us to \textit{principally highlight and visualize the secondary vorticity}, in preference to the primary vorticity. As the secondary vortices rotate around the primary vortices, they begin to develop a three-dimensional instability in the presence of the strain rate field of the primaries, which is characteristically similar to the instability first observed in direct numerical simulation by Luton and Ragab (1997). We outline the origin of the instability by comparing our detailed experimental measurements and observations with prior theoretical considerations (for example, Widnall (1974) and others). We also account for the late stage dynamics through inviscid flow considerations. The study has applications to wake vortex interaction at runways and to turbulent flow transition. [Preview Abstract] |
Sunday, November 21, 2010 1:52PM - 2:05PM |
CN.00005: A unified criterion for the centrifugal instability of vortices and swirling jets Paul Billant, Francois Gallaire It is well known that swirling jets can become centrifugally unstable like pure vortices but with a different azimuthal wavenumber selection. The Leibovich and Stewartson (1983) criterion is a generalization of the Rayleigh criterion to swirling jets: it is a sufficient condition for instability with respect to perturbations with both large axial and azimuthal wavenumbers. We have relaxed the large azimuthal wavenumber assumption in this criterion and obtained a new criterion that is valid whatever the azimuthal wavenumber and whatever the magnitude of the axial flow: from zero (pure vortex) to finite values (swirling jets). The new criterion recovers the Leibovich-Stewartson criterion when the azimuthal wavenumber is large and the Rayleigh criterion when the azimuthal wavenumber is small. The criterion is confirmed by comparisons with numerical stability analyses of various classes of swirling jet profiles. In the case of the Batchelor vortex, it provides more accurate results for perturbations with finite azimuthal wavenumbers than the Leibovich-Stewartson criterion. The criterion shows also that a whole range of azimuthal wavenumbers are destabilized as soon as a non-zero axial velocity component is present in a centrifugally unstable vortex. [Preview Abstract] |
Sunday, November 21, 2010 2:05PM - 2:18PM |
CN.00006: Secondary Flows Within 3D Vortices Suyang Pei, Pedram Hassanzadeh, Philip Marcus Control volume analyses, analytic scaling arguments, and numerical modeling can all be used to show that in a dissipationless flow that there are classes of 3D vortices in which the fluid velocity is purely 2D. That is, in cylindrical coordinates the vortex occupies a finite region in $z$ so that the vortex has a definite top and bottom, but the velocity in only in the $r$ and $\phi$ directions. However, control volume analyses and scaling arguments show that if dissipation is present, these 3D vortices must have a 3D meridional, or secondary, circulation. The dissipation can be due to viscosity, or if the flow is temperature- or salt-stratified, the dissipation can be due to the diffusion of heat or salt. The best known secondary circulation in a 3D vortex is Ekman pumping, which requires that the 3D vortex is confined between upper and lower solid boundaries. We present numerical results of secondary flows within several classes of 3D vortices, including vortices that are not bound above and below by solid walls. We relate these results to geophysical vortices, including ocean meddies and planetary vortices. [Preview Abstract] |
Sunday, November 21, 2010 2:18PM - 2:31PM |
CN.00007: How Do 3D Vortices Spin Down, or Do They? Pedram Hassanzadeh, Suyang Pei, Philip Marcus It is well known that laminar 3D vortices sandwiched between upper and lower boundaries in a rapidly rotating flow will rapidly spin down due to Ekman pumping. The pumping transports angular momentum and energy out of the vortex and into thin boundary layers where viscosity acts efficiently. On the other hand the Great Red Spot of Jupiter and laboratory models of the Red Spot, which are 3D vortices sandwiched between upper and lower boundaries in a rapidly rotating tank, do not spin down. Those 3D vortices maintain themselves indefinitely. The longevity of the Red Spot has been attributed to angular momentum transfer from its surrounding shearing flow, from its mergers with smaller vortices, and to a number of other processes, none of which have been verified and all of which lack plausibility. The reasons behind the longevity of ``Red Spots'' in the laboratory have never been examined. We present numerical results that show how a laboratory model of the Red Spot maintains itself and does not spin down. [Preview Abstract] |
Sunday, November 21, 2010 2:31PM - 2:44PM |
CN.00008: Control of vortex breakdown in a contracting pipe Francois Gallaire, Philippe Meliga We investigate numerically the vortex breakdown of a viscous, swirling jet developing in an axisymmetric contracting pipe. When the swirl number, i.e. the ratio of the maximum azimuthal to streamwise velocity, exceeds a certain threshold value, such flows are known to undergo a violent transition from the so-called columnar state to the breakdown state, the latter being characterized by a large recirculation region. We show first that breakdown occurs through a saddle-node bifurcation, owing to the destabilization of an axisymmetric global mode. We also address the question of control by means of a small annular jet, whose position is allowed to vary at the pipe wall. Such a control technique can be easily implemented in practice and is originally designed to restore the linear stability of the bifurcating mode close to threshold. Results issuing from fully nonlinear simulations will be presented. In particular, it will be shown that vortex breakdown can be suppressed over a large range of swirl numbers, even for low-flow-rate jets representing only a few per cent of the flow rate in the inlet section. [Preview Abstract] |
Sunday, November 21, 2010 2:44PM - 2:57PM |
CN.00009: Structure of a Steady Bathtub Vortex Anders Andersen, Lasse B{\O}hling, David Fabre Bathtub vortex flows constitute an important class of concentrated vortex flows which are characterised by intense axial down-flow and stress free surface. We use direct numerical simulations to explore the flow structure of a steady bathtub vortex in a cylindrical tank with a central drain-hole. We find that the qualitative structure of the meridional flow does not depend on the radial Reynolds number, whereas we observe a weak overall rotation at low radial Reynolds number and a concentrated vortex above the drain-hole at high radial Reynolds number. We present a simple analytical model which shows the same qualitative dependence on the radial Reynolds number as the simulations and which compares favourably with the results for the radial velocity and the azimuthal velocity at the surface. Finally, we describe the height dependence of the radius of the vortex core and the maximum of the azimuthal velocity at high radial Reynolds number, and we show that the data on the radius of the vortex core and the maximum of the azimuthal velocity as functions of height collapse on single curves by appropriate scaling. [Preview Abstract] |
Sunday, November 21, 2010 2:57PM - 3:10PM |
CN.00010: Vortex Behavior in Fully-Oscillating Low-Speed Jet Flows Preston Jones, John Baker Vortex formation associated with a fully oscillating low-speed jet was studied to better understand the fundamental nature of such flows. It has been hypothesized that vortices produced by sinusoidal flow from a nozzle will behave in a manner different from that observed for typical piston-cylinder generated vortices. A variable speed reciprocating pump, designed to produce sinusoidal flow fields at the nozzle exit, was used to examine vortex characteristics as a function of Reynolds number and dynamic vortex formation number. The behavior was visualized using a passive scalar dye. Video recording were used to examine the nature of the flows for the above-mentioned dimensionless parameters. Flows corresponding to Reynolds numbers in the range of 244 to 2708 and dynamic vortex formation numbers in the range of 0.82 to 62.92 were considered. The fully oscillating jets flows produced vortices that appear to not exhibit the critical vortex formation number of 4, commonly observed for pulsating jets. Reynolds number was shown to have an impact on physical vortex detachment. [Preview Abstract] |
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