Bulletin of the American Physical Society
68th Annual Meeting of the APS Division of Fluid Dynamics
Volume 60, Number 21
Sunday–Tuesday, November 22–24, 2015; Boston, Massachusetts
Session R15: Vortex Dynamics: Theory |
Hide Abstracts |
Chair: P. J. Morrison, University of Texas at Austin Room: 203 |
Tuesday, November 24, 2015 12:50PM - 1:03PM |
R15.00001: Metriplectic Simulated Annealing P.J. Morrison, G.R. Flierl Metriplectic dynamics [1,2] is a general form for dynamical systems that represent the first and second laws of thermodynamics, energy conservation and entropy production. Entropy production provides asymptotic stability to equilibrium states, which because of constraints need not be trivial. The formalism will be used to perform quasigeostrophic computations, akin to those of [3], for obtaining a variety of vortex states. \\[4pt] [1] P.J.~Morrison, Physica D {\bf18}, 410 (1986).\newline [2] A.M.~Bloch, P.J.~Morrison, and T.S.~Ratiu, in Recent Trends in Dynamical Systems {\bf35}, 371 (2013).\newline [3] G.R.~Flierl and P.J,~Morrison, Physica D {\bf240}, 212 (2011). [Preview Abstract] |
Tuesday, November 24, 2015 1:03PM - 1:16PM |
R15.00002: ABSTRACT WITHDRAWN |
Tuesday, November 24, 2015 1:16PM - 1:29PM |
R15.00003: A high order multi-resolution solver for the Poisson equation with application to vortex methods Mads Mølholm Hejlesen, Henrik Juul Spietz, Jens Honore Walther A high order method is presented for solving the Poisson equation subject to mixed free-space and periodic boundary conditions by using fast Fourier transforms (FFT). The high order convergence is achieved by deriving mollified Green's functions from a high order regularization function which provides a correspondingly smooth solution to the Poisson equation. The high order regularization function may be obtained analogous to the approximate deconvolution method used in turbulence models and strongly relates to deblurring algorithms used in image processing. At first we show that the regularized solver can be combined with a short range particle-particle correction for evaluating discrete particle interactions in the context of a particle-particle particle-mesh (P$^3$M) method. By a similar approach we extend the regularized solver to handle multi-resolution patches in continuum field simulations by super-positioning an inter-mesh correction. For sufficiently smooth vector fields this multi-resolution correction can be achieved without the loss of convergence rate. An implementation of the multi-resolution solver in a two-dimensional re-meshed particle-mesh based vortex method is presented and validated. [Preview Abstract] |
Tuesday, November 24, 2015 1:29PM - 1:42PM |
R15.00004: Coupling of a compressible vortex particle-mesh method with a near-body compressible discontinuous Galerkin solver Philippe Parmentier, Gregoire Winckelmans, Philippe Chatelain, Koen Hillewaert A hybrid approach, coupling a compressible vortex particle-mesh method (CVPM, also with efficient Poisson solver) and a high order compressible discontinuous Galerkin Eulerian solver, is being developed in order to efficiently simulate flows past bodies; also in the transonic regime. The Eulerian solver is dedicated to capturing the anisotropic flow structures in the near-wall region whereas the CVPM solver is exploited away from the body and in the wake. An overlapping domain decomposition approach is used. The Eulerian solver, which captures the near-body region, also corrects the CVPM solution in that region at every time step. The CVPM solver, which captures the region away from the body and the wake, also provides the outer boundary conditions to the Eulerian solver. Because of the coupling, a boundary element method is also required for consistency. The approach is assessed on typical 2D benchmark cases. [Preview Abstract] |
Tuesday, November 24, 2015 1:42PM - 1:55PM |
R15.00005: The Finite Time Lyapunov Exponent Field of N Interacting Vortices in the Zero Viscosity Limit Richard Galvez, Melissa Green We present an analysis of the Finite Time Lyapunov Exponent (FTLE) field of interacting vortices in the potential flow limit. This work is based on an inviscid approximation, but develops a useful tool that will aid in the effort of understanding the interactions of vortices and turbulence in viscous fluids. The FTLE field of N interacting vortices is computed numerically in two dimensions in different physical scenarios: i) orbiting one another with no initial velocities, ii) approaching each other given an initial velocity and iii) as periodically produced behind a circular cylinder. For situation ii) we expand on the cases where the approach velocities of the vortices are less than or greater than a critical capture velocity, that is, the velocity necessary to escape a captured orbit between co-rotating vortices. We focus on the evolution and interaction of the Lagrangian coherent structures (LCS) in these scenarios to determine if there is a way to anticipate the character of vortex interaction by the initial structure of the LCS. Additional remarks will be made on the extrapolation of observations to a large number of interacting vortices (large N). [Preview Abstract] |
Tuesday, November 24, 2015 1:55PM - 2:08PM |
R15.00006: New Vortex Shedding Criteria for Low Order Models of Unsteady Plate Motion Field Manar, Anya Jones A complex potential flow model with a small number of point vortices of time-varying strength is developed to evaluate the flow around an infinitely thin flat plate undergoing arbitrary unsteady motion. Vortex strengths are determined using the Kutta condition, and vortex convection takes place according to an impulse-matching scheme. Previous work has had only limited success due to vortices not being properly shed from the plate and acquiring too much circulation. In this work, a new vortex shedding criterion based on the dynamics of the shear layer is investigated. This criterion seeks to approximate the occurrence of vortex pinch off by observing the tangential velocities in the shear layer. The effect of the new vortex-shedding criteria on the evolution of the flow are evaluated with respect to previous shedding criteria and experimental PIV results. One motivation for the development of this model is to predict the unsteady forces on a wing quickly, and at low computational cost. Given the velocity field computed via the complex potential model, the forces on the plate are computed by taking the time derivative of the total flow momentum, and are evaluated with respect to experimental measurements. [Preview Abstract] |
Tuesday, November 24, 2015 2:08PM - 2:21PM |
R15.00007: Vorticity Curvature Criterion for the Identification of Two-Dimensional Vortex Structures Jos\'e Hugo Elsas, Luca Moriconi Systematic procedures for the identification of vortices/coherent structures have been proposed as a way to address their kinematical and dynamical roles in structural formulations of turbulence. As a general rule, all of the known vortex detection algorithms are plagued with shortcomings. In this work, we focus on one of the most popular methods - the swirling strength criterion - and investigate how it performs in controled Monte-Carlo tests. We, then, emphasize its main problematic issues: (i) vortex deformation and suppression due to near presence of intense vortical structures; (ii) vortex merging; (iii) spuriuos vortices created in many-vortex configurations and (iv) in the presence of background shear. The inner layer of turbulent boundary layer flows is, in particular, the region where the swirling strength criterion looses accuracy in a dramatic way. We propose an alternative vortex detection criterion, based on the curvature properties of the vorticity profile, which clearly improves over the results obtained with the swirling strength criterion in a number of relevant two-dimensional case studies. [Preview Abstract] |
Tuesday, November 24, 2015 2:21PM - 2:34PM |
R15.00008: A higher-order asymptotic formula for velocity of a viscous vortex pair Yasuhide Fukumoto, Ummu Habibah We establish a general formula for the traveling speed of a counter-rotating vortex pair, being valid for thick cores, moving in an incompressible fluid with and without viscosity. Two-dimensional motion of vortices with finite cores, interacting with each other, has been extensively studied both analytically and numerically. Mathematical methods and numerical schemes have been highly developed for dealing particularly with vortices of uniform vorticity, called vortex patches. In contrast, this is not the case with vortices with distributed vorticity. We extend, to a higher order, the method of matched asymptotic expansions developed by Ting and Tung (1965 Phys. Fluids Vol. 8 pp. 1039-1051). The solution of the Navier-Stokes equations is constructed in the form of a power series in a small parameter, the ratio of the core radius to the distance between the core centers. A correction due to the effect of finite thickness of the vortices to the traveling speed makes its appearance at the 5th order. We manipulate a tidy formula of this correction term for a general vorticity distribution at the leading order. An alternative route to reach the same formula is also sought. We devise a two-dimensional counterpart of Helmholtz-Lamb's formula which is applicable to vortex rings. [Preview Abstract] |
Tuesday, November 24, 2015 2:34PM - 2:47PM |
R15.00009: Classification and transitions of streamline topologies of structurally stable incompressible flows Takashi Sakajo, Tomoo Yokoyama We consider Hamiltonian vector fields with a dipole singularity satisfying the slip boundary condition in two-dimensional multiply connected domains. An example of such Hamiltonian vector fields is an incompressible and inviscid flow in exterior multiply connected domains with a uniform flow, whose Hamiltonian is called the stream function. Here, we are concerned with streamline topologies of incompressible fluid flows, which are the level sets of the Hamiltonian. We first provide a classification procedure to assign a unique sequence of words, called the maximal words, to every structurally stable streamline pattern. Owing to this procedure, we can identify every streamline pattern with its representing sequence of words up to topological equivalence. In addition, based on the theory of word representations, we propose a combinatorial method to provide a list of possible transient structurally unstable streamline patterns between two different structurally stable patterns by simply comparing their maximal word representations without specifying any Hamiltonian. It reveals the existence of many non-trivial global transitions in a generic sense. We also demonstrate how the present theory is applied to fluid flow problems with vortex flows. [Preview Abstract] |
Tuesday, November 24, 2015 2:47PM - 3:00PM |
R15.00010: Construction of initial vortex-surface fields and Clebsch potentials for flows with high-symmetry using first integrals Pengyu He, Yue Yang We develop a systematic methodology to construct the explicit, general form of vortex-surface fields (Yang and Pullin, J. Fluid Mech., 661, 2010) and Clebsch potentials based on first integrals of the characteristic equation of a given three-dimensional velocity-vorticity field. This methodology is successfully applied to the initial fields with the zero helicity density and high symmetry, e.g., initial fields with the Taylor-Green and the Kida-Pelz symmetries. [Preview Abstract] |
Tuesday, November 24, 2015 3:00PM - 3:13PM |
R15.00011: Contour surgery in multiply-connected domains Rhodri Nelson In this talk we present a new method for computing the motion of vortex patches in multiply connected domains. The method works by first solving for the velocity field owing to an unbounded vortex at appropriate points on the boundaries (as if the boundaries were not present). Following this, a suitable modified Schwarz-problem is solved to give a 'correction' velocity such that the sum of this field and that due to the 'unbounded' vortex satisfy the no-normal flow boundary condition on all boundaries present. For flows in which complex distributions of vorticity evolve, the algorithm performs contour surgery (allowing vortices to split or merge) to allow accurate, long time integration of such systems. [Preview Abstract] |
(Author Not Attending)
|
R15.00012: Added mass and critical mass in vortex induced vibration Efstathios Konstantinidis The critical mass phenomenon is the observation that a circular cylinder suspended freely in a fluid stream without a mechanical restoring force exhibits significant vortex induced vibration if its mass is below some value whereas insignificant vibration occurs if the mass is above this value. While the phenomenon is known, its origin remains largely unknown. Furthermore, there are several outstanding questions regarding this phenomenon which cannot be explained on the basis of the existing theoretical framework. In this work, a new formulation of the added mass in the context of potential flow is presented. This leads to a new expression for the potential force, which is more complex than the classical one, that is subsequently employed in simplified form in order to analytically model the flow-structure interaction by decomposing the fluid force into potential and vortex components via the equation of cylinder motion. It is found that the model predicts a significant increase in the amplitude response of a freely suspended cylinder in sharp contrast to predictions using the classical formulation of the added mass. Finally, the model equations are employed to exemplify the phenomenology of the critical mass in real flows. [Preview Abstract] |
Follow Us |
Engage
Become an APS Member |
My APS
Renew Membership |
Information for |
About APSThe American Physical Society (APS) is a non-profit membership organization working to advance the knowledge of physics. |
© 2024 American Physical Society
| All rights reserved | Terms of Use
| Contact Us
Headquarters
1 Physics Ellipse, College Park, MD 20740-3844
(301) 209-3200
Editorial Office
100 Motor Pkwy, Suite 110, Hauppauge, NY 11788
(631) 591-4000
Office of Public Affairs
529 14th St NW, Suite 1050, Washington, D.C. 20045-2001
(202) 662-8700