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 M12: Vortex VII 
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Chair: Dustin Kleckner, University of Chicago Room: 26B 
Tuesday, November 20, 2012 8:00AM  8:13AM 
M12.00001: Relative equilibria in rotating shallow water layer: a real fluid case of point vortex theory Mohamed Fayed, Hamid Ait Abderrahmane, Hoi Dick Ng, Georgios H. Vatistas The present work deals with the question whether or not the regular equilibrium structures, consisting of two and three vortices in rotating shallow water layer, produced inside a cylindrical container with a revolving disk at the bottom, represent real fluid cases of the old point vortex theory. Despite an attempts made by some researchers to address this question, the answer is yet to be clarified. Based on the data from our experiments we show that the observed vortexpattern do retain the fundamental characteristics of Kevin's equilibria that can be adequately described by the classical idealized point vortex theory. Equivalently, we demonstrate that the experimental results found in recent literature, if properly interpreted, lead to the same conclusion. [Preview Abstract] 

M12.00002: ABSTRACT WITHDRAWN 
Tuesday, November 20, 2012 8:26AM  8:39AM 
M12.00003: Regenerative centrifugal instability on a vortex column Eric Stout, Fazle Hussain The limitation and renewal of centrifugal instability of a vortex column (due to a sheath of negative axial vorticity, \textit{$\Omega $}$_{z}$, surrounding the +\textit{$\Omega $} core, i.e. a circulation overshoot) is studied via the transport dynamics of perturbations to the initially unstable vortex using DNS of the incompressible NavierStokes equations for a range of vortex Reynolds numbers (Re=circulation/viscosity). Any radial perturbation vorticity, \textit{$\omega $'}$_{r}$, is tilted by the column's mean shear to form filaments with azimuthal vorticity, \textit{$\omega $'}$_{\theta }$, generating positive Reynolds stress, +$u'v'$ ($u'$,$ v'$ are the radial and azimuthal perturbation velocities), required for energy growth. This \textit{$\omega $'}$_{\theta }$ in turn tilts \textit{$\Omega $}$_{z}$ to amplify \textit{$\omega $'}$_{r}$ (and consequently \textit{$\omega $'}$_{\theta })$  thus causing instability. Limitation of \textit{$\omega $'}$_{r}$ growth, thus also energy production, occurs as the perturbation transports angular momentum (\textit{rV}) radially outward from the overshoot, moving the overshoot outward, hence lessening and shifting \textit{$\Omega $}$_{z}$, while also transporting core +\textit{$\Omega $}$_{z}$, around the location of the filament. After the overshoot shifts, tilting of \textit{$\Omega $}$_{z}$ reverses \textit{$\omega $'}$_{r}$ (hence reducing \textit{$\omega $'}$_{\theta })$, causing the filament to generate $u'v'$, i.e. energy decay, and hence selflimitation of growth. Associated with $u'v'$ is the filament's radially inward transport of \textit{rV}, which can produce a new circulation overshoot and renewed instability. New overshoot formation and renewed generation of $+u'v'$ is examined using a helical ($m=1)$ mode  a promising scenario for regenerative transient growth and possible turbulence generation on a vortex column. [Preview Abstract] 
Tuesday, November 20, 2012 8:39AM  8:52AM 
M12.00004: Stirring vortices with vorticity holes Oscar Velasco Fuentes A vorticity hole is a region with, in absolute value, significantly lower vorticity than its surroundings. Here we discuss the dynamics of a Rankine vortex with two equal circular holes. If a symmetric initial condition is assumed, the evolution depends on three parameters: the vorticity drop, the hole size and the distance between the holes. We computed the evolution with a contourdynamics model and quantified the stirring of fluid particles using finitetime Lyapunov exponents and Melnikov's method. The vorticity holes evolve similarly to a pair of vortices in an otherwise quiescent fluid, although they are additionally affected by their interaction with the boundary of the Rankine vortex. The strongest stirring occurs when the holes interact elastically and then always in the center of the vortex. This result contradicts the generally accepted notion that vortices are regions of null to weak stirring. [Preview Abstract] 
Tuesday, November 20, 2012 8:52AM  9:05AM 
M12.00005: Threedimensional vortex analysis and aeroacoustic source characterization of jet core breakdown Daniele Violato, Fulvio Scarano The 3D patterns of jet core breakdown are investigated in a jet at \textit{Re}=5,000 by timeresolved tomographic particle image velocimetry in the range between 0 and 10 jet diameters. The characteristic pulsatile motion of vortex ring shedding and pairing culminates with the growth of primary inplane and outofplane azimuthal waves and leads to the formation of streamwise vortices. Vortex ring humps are tilted and ejected along the axial direction as they are subjected to higher axial velocities. By the end of the potential core, this process causes the breakdown of the vortex ring regime and the onset of streamwise filaments oriented at 3045 degrees to the jet axis. A three dimensional modal analysis of velocity and vorticity fields is conducted by proper orthogonal decomposition within the first 10 modes. The decomposed velocity fluctuations describe helical motion in the region of the jet corebreakdown and, further downstream, jet axis flapping and precession motions. By the end of the potential core, vorticity modes show travelling waves of radial and axial vorticity with a characteristic 40 degree inclination to the jet axis. Following Powell's aeroacoustic analogy, the instantaneous spatial distribution of the acoustic source term is mapped. Farfield acoustic predictions are given based on the direct evaluation of Powell's analogy with the tomographic data. [Preview Abstract] 
Tuesday, November 20, 2012 9:05AM  9:18AM 
M12.00006: Partial reconnection of orthogonal vortices Louis Dufresne, Guillaume Beardsell, Guy Dumas In this work, we use DNS to study the reconnection of two orthogonal vortices following the approach of Boratav et al.\ (1992). For equal circulation vortices we observe the classical reconnection process (Hussain \& Duraisamy, 2011). Our main interest though is on the interaction of unequal strength vortices for which only partial reconnection can occur. Typically in these latter cases, the weak vortex ($\Gamma_2$) is seen to deform and wrap itself around the strong one ($\Gamma_1$) to (partially) reconnect in an antiparallel configuration similar to what is observed in Marshall et al.\ (2001). Each branch of the broken weak vortex then forms a spiral structure around the main one; the weaker the vortex, the stronger the spiral. This results in two ``circulation jumps'' on the main vortex that propagate away from each other, leaving behind them an altered main vortex with reduced circulation. For Reynolds numbers ($\Gamma_1/\nu$) in the order of $10^3$ and circulation ratios $0.1 \leq \Gamma_2/\Gamma_1 \leq 0.9$, we look at the internal struture of the main vortex with a particular attention to the propagating vorticity structures. These structures are very similar to what has been previously observed in the evolution of fourvortex systems (Dufresne \& Winckelmans, 2005). [Preview Abstract] 
Tuesday, November 20, 2012 9:18AM  9:31AM 
M12.00007: Phase space pattern formation: the singlewave model P.J. Morrison, N.J. Balmforth, J.L. Thiffeault Pattern formation in physical systems has received considerable attention, much of which is based on GinzburgLandau type systems with advective and diffusive nonlinearity and dispersion. In contrast, the singlewave model (SWM), a Hamiltonian meanfield model, arises in many physical contexts that share common pattern forming behavior. Although the SWM was originally derived in nonlinear plasma theory, where it describes the behavior near threshold and subsequent nonlinear evolution of unstable plasma waves, it arises in fluid mechanics, specifically vortex dyanmics, and also applies to galactic dynamics, the XY and Potts models of condensed matter physics, and general longrange Hamiltonian mean field models. The SWM is a normal form equation for systems that transition to instability with modes emerging from a continuous spectrum (critical layers) and it describes there subsequent nonlinear behavior and pattern formation. This talk surveys SWM phenomena as described in a recent review article.\footnote{N. Balmforth, P. J. Morrison, and JL. Thiffeault, Reviews of Modern Physics, to appear (2012).} [Preview Abstract] 
Tuesday, November 20, 2012 9:31AM  9:44AM 
M12.00008: Creation and Dynamics of Knotted Vortices Dustin Kleckner, Martin Scheeler, William Irvine Fluid vortex loops linked together or tied into knots are the basis of a topological interpretation of fluid mechanics. In perfect fluids, the linking of vortex lines is preserved indefinitely and associated with a conserved quantity known as helicity. The situation is considerably more complicated in real fluids  even superfluids  because the vortex topology can change through local reconnections whose dynamics are not well understood. Previous attempts to study these phenomena in experiments have failed because no controlled method existed for making vortex knots in the laboratory. We will describe a method we recently developed for making knotted and linked vortices using 3Dprinted hydrofoils. We measure the subsequent evolution of the vortex structures using highspeed laser scanning tomography. We observe that they spontaneously untie/unlink themselves through a series of local reconnections, which we resolve in detail. [Preview Abstract] 
Tuesday, November 20, 2012 9:44AM  9:57AM 
M12.00009: The Formation Number of Accelerating and Variable Diameter Jet Flows, and a Review of PinchOff Criteria Mike Krieg, Kamran Mohseni This study analyzes vortex ring formation from starting jets with variable jet velocity and diameter and the underlying mechanisms of separation from the feeding shear flow. We assume that the conditions necessary for a vortex ring to separate from the driving shear flow can be identified by a relationship between characteristic velocities of the jet and the vortex ring along the axis of symmetry, and examine multiple pinchoff criteria. A wide variety of jet driving conditions are examined to validate the relationship between pinchoff and characteristic velocities under different constraints, including nozzle type (inclusion of converging radial velocity), acceleration of the jet velocity, and dynamic contraction/expansion of the shear layer diameter. All of these parameters are examined and adjusted independently of each other so that the effect of each jetting parameter can be observed without being affected by the other parameters. Accelerating the jet velocity to compensate for the growing vortex ring substantially increased the formation number of both parallel and converging jet flows. Different definitions of formation time (different time scaling) are also investigated as they pertain to the final vortex ring configuration and the physics of vortex ring formation. It is observed that new definitions of formation time result in jet formation numbers more closely aligned with previous results, suggesting that the new definition corresponds to the physics of vortex ring formation. [Preview Abstract] 
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