Bulletin of the American Physical Society
66th Annual Meeting of the APS Division of Fluid Dynamics
Volume 58, Number 18
Sunday–Tuesday, November 24–26, 2013; Pittsburgh, Pennsylvania
Session M12: Vortex Dynamics and Vortex Flows IX |
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Chair: Kamran Mohseni, University of Florida Room: 336 |
Tuesday, November 26, 2013 8:00AM - 8:13AM |
M12.00001: On relation between scalar interfaces and vorticity in inviscid flows O.N. Ramesh, Saurabh Patwardhan A great variety of applications like pollutant mixing in the atmosphere, mixing of reactants in combustion highlight the importance of passive scalar dynamics in fluid flows. The other dynamically important variable in the study of fluid flow is the vorticity. Vorticity though, unlike a passive scalar, does affect the fluid motion. The dynamics of scalar (linear) and vorticity (non-linear) are governed by the equations which inherently have different characteristics. This paper addresses the question of the faithfulness of representation of vorticity by scalar marker and the motivation for this comes from the experiment of Head and Bandyopadhyay (1981) which showed the existence of coherent vortices by using smoke flow visualization in a turbulent boundary layer. We will show analytically in regions where the molecular diffusion effects are negligible, the vorticity and scalar gradients are orthogonal to each other. The iso- surface of scalar follows the vorticity in an inviscid situation. Also, we will demonstrate that in the case of unsteady burgers vortex and vortex shedding behind a finite circular cylinder, the scalar gradient is orthogonal to vorticity and inner product of vorticity and scalar gradients is zero in regions away from the wall. [Preview Abstract] |
Tuesday, November 26, 2013 8:13AM - 8:26AM |
M12.00002: Inviscid Damping of Vortex Asymmetries by a Critical Layer Flux C.F. Driscoll, A.A. Kabantsev, C.Y. Chim, T.M. O'Neil Experiments and theory characterize a novel regime of near-inviscid 2D vortex symmetrization, wherein a weak flux through the critical layer causes algebraic (rather than exponential) damping of azimuthal asymmetries. This is distinct from exponential critical-layer damping (or spiral wind-up), where the damping may cease once the critical-layer vorticity is trapped in cats-eyes.\footnote{D.A. Schecter et al., Phys. Fluids {\bf 12}, 2397 (2000).} Here, weak viscosity causes slow vortex expansion and negligible direct azimuthal-shear damping; but when the weak expansion flux reaches the critical layer, previously un-damped Kelvin waves are rapidly damped to zero. Pure electron plasma experiments have quantitatively characterized this novel damping for $m_\theta=1$ and $m_\theta=2$ waves, obtaining wave amplitudes varying as $A(t) = A_0 - \gamma \, t$. A simple analysis of critical-layer dynamics agrees well with experiments for $m_\theta=1$ waves (with a bounding wall); but suggests a $\gamma \, t^{2/3}$ dependence for $m_\theta=2$ due to the critical-layer width scaling with wave amplitude. Simulations suggest that weak diffusion may obviate this discordant time exponent of 2/3. [Preview Abstract] |
Tuesday, November 26, 2013 8:26AM - 8:39AM |
M12.00003: Point vortex modeling of symmetric four vortex wakes Saikat Basu, Mark Stremler Bluff body wakes frequently display different complex patterns. Our previously disseminated results introduced a point vortex model for the 2P wake configuration, which is one of the most commonly observed wake patterns and consists of two staggered rows of vortex pairs. In this talk, we present our findings for the related case of a symmetric 2P-like wake configuration. The pattern consists of two pairs of counter-rotating vortices placed symmetrically about the wake centerline in a singly-periodic domain. Due to the assumed symmetry of the wake we are able to model the vortex dynamics as an integrable Hamiltonian system. The mathematical analysis reveals some interesting and novel relative vortex motions that we will discuss. The model results will be compared against experimental wakes from the literature. As with our staggered 2P wake analysis, the model results suggest that the classification of these exotic wakes should include more than just the number of vortices shed by the body. [Preview Abstract] |
Tuesday, November 26, 2013 8:39AM - 8:52AM |
M12.00004: Topological Classification of Periodic Solutions to the Point Vortex Model Spencer Smith The point vortex model represents one of the earliest attempts to discretize the field equations of fluid motion. Since the time of Helmholz, it has served as a starting point for the investigation of such disparate phenomena as weak turbulence and negative temperature states. Using this simple and elegant model, we created a large data set of numerically generated periodic orbits for small numbers of identical vortices. We then applied a topological classification scheme based on braid theory to organize and sort the data. This novel approach reveals unexpected and intriguing patterns in the distribution of these solutions in phase and parameter space. [Preview Abstract] |
Tuesday, November 26, 2013 8:52AM - 9:05AM |
M12.00005: Desingularized propagating vortex equilibria Stefan Llewellyn Smith The correction to the propagation velocity of point vortex equilibria is calculated by allowing the vortices to have finite core size. A matched asymptotic expansion in the small parameter $\epsilon$, given by the ratio of the core size to the dimension of the configuration, is carried out. The resulting velocity correction is found to be of order $\epsilon^4$ and comes from the interaction of terms in the inner expansion. The results are compared to the known cases of propagating hollow vortex and vortex patch dipoles. [Preview Abstract] |
Tuesday, November 26, 2013 9:05AM - 9:18AM |
M12.00006: Extreme Vortex States and the Growth of Palinstrophy in Two Dimensions Diego Ayala, Bartosz Protas We probe the sharpness of analytic estimates for the instantaneous rate of growth and the finite-time growth of palinstrophy in 2D viscous incompressible flows on periodic domains. This effort is part of a broader research program concerning a systematic search for extreme vortex states which is intrinsically related to the finite-time ``blow-up'' problem in 3D incompressible flows. Evidence is presented for the existence of a family of 2D vorticity fields parametrized by their energy and palinstrophy which saturate an estimate characterizing the finite-time growth of palinstrophy. The family of such ``optimal'' vortex states is obtained by solving suitable optimization problems in which the rate of growth of palinstrophy is maximized under constraints. Although found as a solution of an instantaneous problem, vortex states from this family also saturate the finite-time estimates. This intriguing finding leads to some open questions about the 3D case, namely, whether extreme vortex states with prescribed energy and enstrophy may exhibit a larger growth of enstrophy than the previously found fields in which only enstrophy was fixed and whose growth of enstrophy was too weak to produce a singularity in finite time. [Preview Abstract] |
Tuesday, November 26, 2013 9:18AM - 9:31AM |
M12.00007: Why is the Karman vortex street so stable to the pairing instability? Cristobal Arratia, Saviz Mowlavi, Francois Gallaire An infinite double row of staggered point vortices was proposed by von Karman as a simplified model for the alternating vortex street forming in the wake of blunt bodies. This model, however, was found to be always unstable except against infinitesimal disturbances when the aspect ratio of the vortex street has a precise value, a puzzling result in clear contradiction with experience. Several authors including Saffman, Kida and Jimenez studied extensions to Karman's point vortex model, but it turned out that instability for all but a specific value of the parameters is generic in these inviscid models (Jimenez, JFM 1987). Here, we revisit this classical problem from a spatio-temporal instability perspective, which is required for taking into account the propagation speed of the vortex street. We show that the instability of the point vortex model is convective for a large range of parameters, and comparison of the model with different physically relevant cases will be shown. We also consider the absolute/convective nature of the pairing instability in a single row of inviscid point vortices. In both cases we study the effect of confining walls which can be taken into account as an infinite series of image vortices. [Preview Abstract] |
Tuesday, November 26, 2013 9:31AM - 9:44AM |
M12.00008: Coherent Lagrangian vortices: The black holes of turbulence George Haller We discuss a simple variational principle for coherent material vortices in two-dimensional turbulence. Vortex boundaries are sought as closed stationary curves of the averaged Lagrangian strain. We find that solutions to this problem are mathematically equivalent to photon spheres around black holes in cosmology. The fluidic photon spheres satisfy explicit differential equations whose outermost limit cycles are optimal Lagrangian vortex boundaries. As an application, we uncover super-coherent material eddies in the South Atlantic, which yield specific Lagrangian transport estimates for Agulhas rings. We also describe briefly coherent Lagrangian vortex detection to three-dimensional flows. [Preview Abstract] |
Tuesday, November 26, 2013 9:44AM - 9:57AM |
M12.00009: The life of a vortex knot (in experiment) Dustin Kleckner, Martin Scheeler, Davide Proment, William T.M. Irvine In recent experiments on linked and knotted vortices in classical fluids, we have found that they undergo a spontaneous change in topology: they untie themselves through a series of local reconnections. This outcome is at odds with the notion that fluid helicity (knottedness) should be conserved, as it should be for a dissipation-less fluid. Remarkably similar behavior is found for simulations of superfluid knots using the Gross-Pitaevskii equation. We will discuss our search for the missing helicity and the possibility of a universal driving mechanism for reconnections in topological vortices. [Preview Abstract] |
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