Bulletin of the American Physical Society
61st Annual Meeting of the APS Division of Fluid Dynamics
Volume 53, Number 15
Sunday–Tuesday, November 23–25, 2008; San Antonio, Texas
Session EU: Vortex Flows III |
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Chair: Gregoire Winckelmans, UCL/EPL/MECA Room: 204B |
Sunday, November 23, 2008 4:10PM - 4:23PM |
EU.00001: Linear stability of relative equilibria of identical point vortices Hassan Aref The linear stability analysis of relative equilibria of $N$ identical point vortices is reconsidered. First, we show that the problem can be reduced to evaluating the eigenvalues and eigenvectors of a certain Hermitean matrix. Then, the exact solution of the linear stability problem for the collinear relative equilibria is given following work by Calogero and Bruschi from the late 1970's. We consider the possibility of extending these largely algebraic results to general configurations, and we explore the class of relative equilibria for which such calculations may be carried through. The regular polygons certainly fall in this class, but the known families of nested, regular polygons may also allow at least a partial analytical stability analysis. The role of the generating polynomial in stability calculations is explored, and also the link between stability of a relative equilibrium and the existence of an axis of symmetry of the configuration. Such a link was suggested to the author by D. L. Vainchtein several years ago. [Preview Abstract] |
Sunday, November 23, 2008 4:23PM - 4:36PM |
EU.00002: Structures in the wake of a long flexible cylinder undergoing vortex-induced vibrations Francisco Huera-Huarte, Anton Vernet An investigation of the vortex structures in the wake of a long flexible cylinder responding at low mode numbers is presented. The experiments consisted of a cylinder model instrumented with strain gauges, with an external diameter of 16 mm and a total length of 1.5 m giving an aspect ratio of about 94. Reduced velocities based on the fundamental natural frequency up to 16 were reached, with Reynolds numbers up to 12000. The mass ratio was 1.8 (mass divided by mass of displaced fluid) and the combined mass-damping parameter was about 0.05. A detailed investigation of the strain signals, focused on cross-flow and in-line amplitudes, x-y trajectories and phase synchronisation, dominant frequencies, modal amplitudes and drag coefficients, has already shown the dynamic response of the model. Particle Image Velocimetry interrogations were done at two different positions along the length of the model, in order to observe the spanwise variation of the vortex structures and here, a fuzzy clustering technique has been used to identify them. [Preview Abstract] |
Sunday, November 23, 2008 4:36PM - 4:49PM |
EU.00003: Velocity statistics distinguish quantum from classical turbulence Matthew S. Paoletti, Michael E. Fisher, Katepalli R. Sreenivasan, Daniel P. Lathrop We present experimental studies of the velocity statistics of decaying quantum turbulence in superfluid $^{4}$He. By analyzing the trajectories of solid hydrogen tracers, we observe velocity distributions with strongly non-Gaussian 1/$v^{3}$ power-law tails. These statistics differ from the near-Gaussian distributions observed in homogenous and isotropic classical turbulence. We attribute the distinction with classical turbulence to quantized vortex dynamics and reconnection, which produces high, atypical velocities. We identify and analyze the dynamics of approximately 40,000 individual reconnection events and show by simple scaling arguments that they produce the observed power-law velocity tails. The potential implications for multifractal models of classical turbulence are discussed. [Preview Abstract] |
Sunday, November 23, 2008 4:49PM - 5:02PM |
EU.00004: Azimuthal Instability of a Vortex Ring Computed by a Vortex Sheet Panel Method Robert Krasny, Hualong Feng, Leon Kaganovskiy A Lagrangian panel method is presented for vortex sheet motion in 3D flow. The sheet is represented by a set of quadrilateral panels with a quadtree structure. The panels have active particles carrying circulation and passive particles used for adaptive panel subdivision. The Biot-Savart kernel is regularized and the particle velocity is computed using a treecode. The method is applied to study the azimuthal instability of a vortex ring. Results are presented showing the following sequence of events: wavy deformation of the ring axis, first collapse of the core, appearance of secondary structures wrapped around the core, second collapse of the core out of phase with first collapse, and radial ejection of ringlets. These events are accompanied by local axial flow in the core. [Preview Abstract] |
Sunday, November 23, 2008 5:02PM - 5:15PM |
EU.00005: Mixing in Oscillatory Flows Generated by Electromagnetic Forcing Aldo Figueroa, Patrice Meunier, Sergio Cuevas, Eduardo Ramos The continuously driven laminar flow produced by an oscillating electromagnetic force in a thin electrolytic fluid layer is studied experimentally and numerically. The flow is generated by the interaction of an injected alternate electric current and a steady magnetic dipole field normal to the layer. Alternate currents with frequencies and amplitudes in the range of 10-50 mHz and 1-5 mA, respectively, are explored. The electromagnetic force stirs the fluid and produces an oscillating dipole vortex that enhances the fluid mixing. A numerical 2D solution of the full MHD equations that considers an analytical expression to model the non-uniform magnetic field is obtained. The mixing efficiency is measured by the use of a new semi-Lagrangian numerical scheme which allows to solve the diffusion of a scalar at very high Peclet numbers (up to infinite). This method gives the scalar field as a function of time and also allows to reconstruct the PDF of the scalar analytically as a measure of the degree of mixing. Numerical results show a good qualitative agreement with the experiments. The mixing can be enhanced even more when an array of magnetic dipole fields is considered. [Preview Abstract] |
Sunday, November 23, 2008 5:15PM - 5:28PM |
EU.00006: Three-dimensional vortex dynamics in oscillatory flow separation Miguel Canals, Geno Pawlak The three-dimensional (3D) dynamics of coherent vortices and their interactions in an oscillatory flow past an obstacle are examined experimentally. The main focus is in the low Keulegan-Carpenter number range (KC $<$ 5), and for moderate Reynolds numbers (2000 $<$ Re $<$ 10000). This parameter space corresponds to the vortex pairing regime, in which vortex dipoles can propagate away from the boundary and provide a direct mechanism for the transfer of momentum and enstrophy to the outer region. The vortex breakdown mechanisms are elucidated via flow visualizations and digital particle image velocimetry (DPIV). Volumetric dye visualizations reveal complex 3D vortex interactions and explosive vortex breakdown. These visualizations suggest that the initial instability of the spanwise vortices is an elliptical instability of the strained vortex cores. This is confirmed by detailed DPIV measurements which have identified the elliptical instability eigenmode. The periodic features of the flow, including the energetics and enstrophy dynamics, are examined using phase-averaging. The phase-averaged dynamics are then interpreted in light of the results obtained from the time domain observations of the vortex instabilities. [Preview Abstract] |
Sunday, November 23, 2008 5:28PM - 5:41PM |
EU.00007: Unstable vortical flow produced by an oscillatory non-uniform magnetic field Alberto Beltran, Sergio Cuevas, Eduardo Ramos We report two-dimensional numerical simulations of an electromagnetically forced flow, produced by the interaction of an imposed direct electrical current and a localized time-dependent magnetic field. The field is produced by a permanent dipolar magnet that oscillates harmonically along a direction parallel to the injected current with fixed frequency and amplitude. When the magnet remains steady, the localized Lorentz force produces a vortex dipole with a jet-like flow along the symmetry line in the direction of the force, perpendicular to both the injected current and the normal magnetic field. For certain oscillation frequencies of the magnet, the jet-like flow is destabilized and local vortical structures, formed in the neighborhood of the magnet, are swept away periodically by the base flow. Numerical results show a qualitative agreement with preliminary experiments performed in a shallow electrolitic fluid layer. [Preview Abstract] |
Sunday, November 23, 2008 5:41PM - 5:54PM |
EU.00008: The Breakdown of Compressible Vortex Flows Zvi Rusak, Jung J. Choi The theoretical foundation for the global analysis of the dynamics of vortex flows is extended to the case of subsonic compressible swirling flows in a finite-length, straight, circular pipe. A novel nonlinear partial differential equation for the solution of the flow stream function is developed in terms of the incoming specific total enthalpy, specific entropy, and circulation functions. Solutions of the resulting nonlinear ordinary differential equation for the columnar case together with a newly derived flow-force condition describe the flow outlet state. These solutions are used to form the bifurcation diagrams of steady, compressible flows with swirl as the swirl level is increased. These provide theoretical predictions of the critical swirl ratio for the first appearance of vortex breakdown as function of Mach number. [Preview Abstract] |
Sunday, November 23, 2008 5:54PM - 6:07PM |
EU.00009: Radiative instability of a stratified Lamb-Oseen vortex Xavier Riedinger, Stephane Le Diz\`es, Patrice Meunier Le Diz\`{e}s and Billant have shown that a Lamb-Oseen vortex with a strong stratification along the vortex axis is inviscidly unstable. The unstable modes are radiative and extend far from the vortex core. In this work, our objective is to analyse the effects of viscosity and stratification on these unstable modes. A linear temporal stability analysis is performed using a Chebychev collocation spectral code. The equations are the linearized Navier-Stokes equations with Boussinesq approximation. We show that the instability is the strongest for a Froude number around one and that the vortex remains unstable for all Reynolds numbers. We shall explain that the stabilization for small Froude number is due to the scaling in $\frac{1}{F}$ of the most unstable wavenumber and that the stabilization for large Froude number is linked to the appearance of a critical layer. For intermediate Froude numbers, another instability mechanism due to resonances between radiative modes and Kelvin modes has been discovered . [Preview Abstract] |
Sunday, November 23, 2008 6:07PM - 6:20PM |
EU.00010: Searching for Euler Singularities Through Vortex Filaments Michael Brenner Numerical simulations over the past decade have suggested that if a singularity of the Euler equation exists, it is likely to be unstable. The question therefore becomes how to devise schemes for searching for unstable singular solutions of the initial value problem. I will summarize our recent efforts to carry out such searches using interacting vortex filaments. [Preview Abstract] |
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