Bulletin of the American Physical Society
62nd Annual Meeting of the APS Division of Fluid Dynamics
Volume 54, Number 19
Sunday–Tuesday, November 22–24, 2009; Minneapolis, Minnesota
Session ET: Vortex Dynamics and Vortex Flows III |
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Chair: Stefan Llewellyn Smith, University of California, San Diego Room: 200H |
Sunday, November 22, 2009 4:15PM - 4:28PM |
ET.00001: Quantum turbulence D.P. Lathrop, M.S. Paoletti, M.E. Fisher, K.R. Sreenivasan Long range~quantum~order underlies a number of related physical phenomena including superfluidity, superconductivity, the Higgs mechanism, Bose-Einstein condensates, and spin systems. ~ While superfluidity in Helium-4 was one of the earliest discovered of these, it is not the best understood, owing to the strong interactions (making theoretical progress difficult) and the lack of local experimental probes. Approximately three years ago, our group discovered that micron-sized hydrogen particles may be used to label quantized vortices in flows of superfluid helium. ~Particles not on vortices trace the motion of the normal component of the superfluid. This ability has given a new perspective on an old subject. By directly observing and tracking these particles, we have directly confirmed the two-fluid model, observed vortex rings and reconnection, characterized thermal counterflows, and taken local observations of the very peculiar nature of~quantum~turbulence. [Preview Abstract] |
Sunday, November 22, 2009 4:28PM - 4:41PM |
ET.00002: Velocity statistics in superfluid and classical turbulence K.R. Sreenivasan, D.A. Donzis, M.E. Fisher, D.P. Lathrop, M.S. Paoletti, P.K. Young Past work, summarized in part by Vinen {\&} Niemela (\textit{J. Low Temp. Phys. }\textbf{129}, 213 (2002)) and by Walmsley \textit{et al.} \textit{Phys. Rev. Lett.} \textbf{99}, 265302 (2007))\textbf{,} suggests that similarities exist between superfluid and classical turbulence. Conversely, the more recent work of Paoletti \textit{et al.} (\textit{Phys. Rev. Lett.} \textbf{101}, 154501 (2008)) has highlighted differences: in particular, the probability density function (PDF) of the turbulent superfluid velocity, measured by tracking the trajectories of small hydrogen particles, is strongly non-Gaussian with power-law tails, in contrast to classical homogeneous and isotropic turbulence for which the PDF is nearly Gaussian. Here, we explore this dichotomy. Since the observed power-law exponent of -3 in the superfluid case can be traced to the reconnection of quantized vortices, it is natural to explore the role of vortex reconnection in the classical case. We surmise that the latter, if it is significant at all, must involve vortices of high intensity. Using direct numerical solutions of homogeneous and isotropic turbulence on a grid of linear size 4096, we condition the velocity statistics on the magnitude of vorticity and find that the resulting conditional PDFs, if normalized on their own standard deviation, remain Gaussian for all vorticity magnitudes. [Preview Abstract] |
Sunday, November 22, 2009 4:41PM - 4:54PM |
ET.00003: Dynamics of the Lattice Array Formation in Superfluid Helium Kristina Gaff, Enrico Fonda, Matthew Paoletti, Daniel Lathrop, Katepalli Sreenivasan In 1955, Feynman theorized that the lowest energy state of rotating superfluid helium would result in a lattice structure of quantized vortices. In 1979, Yarmchuk \textit{et. al.} observed a small lattice array of up to eleven vortices using clusters of ions, and later experiments observed the lattice array in superfluid $^{4}$He perpendicular to the axis of rotation using hydrogen ice particles (Bewley \textit{et. al.} 2006). Yet, the formation and dynamics of these arrays remain otherwise unexplored experimentally. Now, by visualizing sub-micron particles trapped on quantized vortices, we characterize the lattice array formation in superfluid helium. Our study investigates the lattice formation by independently varying rotation rate and temperature. [Preview Abstract] |
Sunday, November 22, 2009 4:54PM - 5:07PM |
ET.00004: Visualization of quantized vortices near the $\lambda$-transition using nanoparticles Enrico Fonda, Kristina T. Gaff, Matthew S. Paoletti, Katepalli R. Sreenivasan, Daniel P. Lathrop The dynamics of an irregular tangle of quantized vortices in superfluids, i.e. quantum turbulence, has recently drawn interest for its connections with different areas of research and for the premise of shedding light on classical turbulence. Previous experiments (Bewley et al. 2006, Paoletti et al. 2008) studied the superfluid flows in $^{4}$He using micron-sized solid hydrogen particles as tracers. Because of their size, Stokes drag does not allow them to stay trapped on quantized vortices close to the $\lambda$-transition, where the trapping potential is weaker. A new technique has been discovered to create and visualize sub-micron particles. Several size estimates of these nanoparticles have been made based on both optical and fluid dynamical properties. Being smaller, but not small enough to be influenced by thermal motions, the particles are more passive and are less affected by Stokes drag. Thus they stay trapped closer to transition and on faster moving vortices. Preliminary results from near-transition observations are presented. [Preview Abstract] |
Sunday, November 22, 2009 5:07PM - 5:20PM |
ET.00005: Elementary vortex processes in thermal superfluid turbulence Demosthenes Kivotides, Louise Wilkin By solving pertinent mathematical models with numerical and computational methods, we analyze the formation of superfluid vorticity structures in a turbulent normal fluid with an inertial range exhibiting Kolmogorov scaling. We demonstrate that mutual friction forcing causes quantum vortex instabilities whose signature is spiral vortical configurations. The spirals expand until they accidentally meet metastable, intense normal fluid vorticity tubes of similar curvature and vorticity orientation that trap them by driving them towards low mutual friction sites where superfluid bundles are formed. The bundle formation sites are located within the tube cores, but, due to tube curvature and many-tube interaction effects, are displaced by variable distances from the tube centerlines as they follow the contours of the latter. We analyze possible implications of these processes in fully developed thermal superfluid turbulence dynamics. [Preview Abstract] |
Sunday, November 22, 2009 5:20PM - 5:33PM |
ET.00006: Scaling and symmetry breaking in a vortex dipole M. Duran-Matute, F. Fontenele Araujo, R.R. Trieling, G.J.F. van Heijst A vortex dipole is experimentally studied in a layer of salt water driven by time independent electromagnetic forcing. In particular, we characterize the flow along the dipole axis by measuring the Reynolds number $Re$ as a function of the Chandrasekhar number $Ch$ (the ratio of Lorentz to viscous forces). We find $Re \sim Ch^{\alpha}$, with the scaling exponent $\alpha$ ranging from $\alpha=1$ (viscous regime) to $\alpha = 1/2$ (advective regime). The underlying transition emerges as a symmetry breaking of the axial flow, which we quantify via the skewness of the axial velocity profile. [Preview Abstract] |
Sunday, November 22, 2009 5:33PM - 5:46PM |
ET.00007: Three-dimensional stability of dipole-wall interactions Christopher Subich The interaction of a dipole colliding with a no-slip boundary has been well studied in two dimensions at both low (Orlandi, 1990) and moderate (Kramer, 2007) Reynolds numbers, and just such a case is advocated as a benchmark for numerical simulations (Clercx, 2006). However, in three-dimensional flow the vortex pair has a short-wavelength elliptic instability (Leweke, 1997) that ultimately destroys the two-dimensional character of the vortex pair. For small enough perturbations, however, a dipole can complete a partial rebound from a no-slip wall before the elliptic instability dominates its evolution. The small-scale vorticity generated in the collision creates a different character to the instability. This work presents the results of three-dimensional pseudospectral numerical simulations of the instability at a Reynolds Number of 1,250. [Preview Abstract] |
Sunday, November 22, 2009 5:46PM - 5:59PM |
ET.00008: Computing vortex states with Dirac constraints P.J. Morrison, G.R. Flierl A procedure for calculating vortex states that uses Dirac constraint theory will be described. Several examples will be given, including V-states, rigidly rotating m-fold symmetric vortex patches. The technique is general and applies to both nonconvex and convex contours, and both barotropic and baroclinic vortex dynamics. [Preview Abstract] |
Sunday, November 22, 2009 5:59PM - 6:12PM |
ET.00009: Vortex Dipoles with Prescribed Nonlinear Profiles Alan Elcrat, Ken Miller, Trenton Albrecht We obtain translating vortex pairs using a generalization of the method used in Elcrat,Fornberg,Horn and Miller JFM2000 409 for vortex patches in flow past a cylinder. When the profile function $F$ in $\Delta \psi =\omega F(\psi -\alpha )$, $\psi$ the stream function for the flow, is piecewise constant the flows obtained are the Translating V-States found in Wu,Overman and Zabusky JCP1984 53. When the vortex support attaches to the symmetry axis the flows are called dipoles, and when $F$ is linear we retrieve the Lamb-Chaplygin pair. The solution procedure that we use in which $\psi$ is obtained from an iteration $\Delta \psi _{n+1}=F(\psi _n)$ where the area of the vortex support is fixed in an inner iteration, allows general $F$. We have computed solutions for $F$ that have 2 continuous derivatives at $\psi=0$. These lead to ``smooth'' dipoles, and the solutions obtained have elliptical shapes of the sort obtained recently in Kizner and Khvoles Reg.Chaotic Dyn. 2004 9. The methods that we use extend naturally to translating dipoles in the $\beta$ -plane approximation for flow over a rotating sphere. [Preview Abstract] |
Sunday, November 22, 2009 6:12PM - 6:25PM |
ET.00010: Oscillatory boundary layer in a dipole vortex driven by a periodic electromagnetic force Sergio Cuevas, Aldo Figueroa, Eduardo Ramos The laminar boundary layer flow driven by an oscillatory Lorentz force in a shallow electrolytic layer is analyzed experimentally and theoretically. The force is produced by the interaction of an injected alternate electric current and the magnetic field of a small dipole magnet, externally attached to the bottom wall of a plexiglass container. Alternate currents with frequencies and amplitudes in the range of 10-200 mHz and 1-80 mA, respectively, are explored. In planes parallel to the bottom wall, the flow displays an oscillating dipole vortex, while in planes normal to this wall shows an oscillatory boundary layer that resembles the oscillating Stokes layer. PIV measurements reveal that in each cycle vortices are created in the boundary layer in regions where the non-uniformity of the magnetic field is stronger. An approximate analytical solution of the oscillatory boundary layer, that considers the decay of the magnetic field in the normal direction, is obtained through a balance of viscous, inertial and electromagnetic forces. Additionally, a quasi-two dimensional numerical solution that reproduces the main features of the vortex flow, is presented. [Preview Abstract] |
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