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 G19: Vortex Dynamics: Vortex Identification and Mechanisms |
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Chair: Piotr Surowka, Harvard University Room: 207 |
Monday, November 23, 2015 8:00AM - 8:13AM |
G19.00001: Information geometry and phase transitions of fluids with global anomalies Piotr Surowka Fluid helicity is an important observable that captures topological properties of hydrodynamics. It naturally emerges in the context of parity-breaking fluids with knotted vortex lines. If the fluid constituents exhibit quantum anomalies the topological nature of fluid helicity can be elucidated using microscopic physics. In this case the helicity is given by a polynomial function of temperature and chiral chemical potential and completely fixed by the anomalies. We explain this relation and address the question of phase structure of such fluids using methods of information geometry. We introduce the metric on a parameter space and show that a non-zero vorticity leads to a curvature on the statistical manifold. We calculate the curvature invariant and analyze its divergences, which contain the information about phase transitions of the system. The transition points are universal and expressed in terms of ratios of anomaly coefficients. [Preview Abstract] |
Monday, November 23, 2015 8:13AM - 8:26AM |
G19.00002: Analysis of Vortex Line Cutting and Reconnection by a Blade Curtis Saunders, Jeffrey Marshall The essence of vortex reconnection involves the cutting of vortex lines originating from one region and reconnecting to vortex lines originating from another region via the diffusion-regulated annihilation of vorticity. Vortex cutting by a blade is a special case of the more general class of vortex reconnection problems, with an important difference being that vorticity is generated at the reconnection site. In this study, a series of Navier-Stokes simulations of orthogonal vortex cutting by a blade with different values of vortex strength are reported. The three phases of vortex reconnection identified in the literature are found to have counterparts for the vortex cutting problem. However numerous differences between the mechanics of vortex cutting and reconnection within each phase are discussed. In addition, comparisons are made between the temporal changes of the maximum and minimum components of vorticity for vortices of differing strength but still within the vortex cutting regime. The vortex cutting results are also compared with predictions of a simple analytical model that incorporates the key elements of a stretched vorticity field interacting with a solid surface, which is representative of the vortex cutting mechanism near the blade leading edge. [Preview Abstract] |
Monday, November 23, 2015 8:26AM - 8:39AM |
G19.00003: Hairpin Vortex Regeneration Threshold Daniel Sabatino, Rijan Maharjan A free surface water channel is used to study hairpin vortex formation created by fluid injection through a narrow slot into a laminar boundary layer. Particle image velocimetry is used to calculate the circulation of the primary hairpin vortex head which is found to monotonically decrease in strength with downstream distance. When a secondary hairpin vortex is formed upstream of the primary vortex, the circulation strength of the head is comparable to the strength of the primary head at the time of regeneration. However, the legs of the primary vortex strengthen up to the moment the secondary hairpin is generated. Although the peak circulation in the legs is not directly correlated to the strength of the original elongated ring vortex, when the circulation is scaled with the injection momentum ratio it is linearly related to scaled injection time. It is proposed that the injection momentum ratio and nondimensionalized injection time based on the wall normal penetration time can be used to identify threshold conditions which produce a secondary vortex. [Preview Abstract] |
Monday, November 23, 2015 8:39AM - 8:52AM |
G19.00004: A Mathematical Proof of the Vortex Shedding Mechanism Michael Boghosian, Kevin Cassel A novel mechanism leading to vortex splitting and subsequent shedding that is valid for both inviscid or viscous flows and external, internal, or wall-bounded flows is described. The mechanism, termed the Vortex-Shedding Mechanism (VSM), is simple and intuitive, requiring only two coincident conditions in the flow: (1) the existence of a location with zero momentum and (2) the presence of a net force having a positive divergence. Previous simulations of various flows have demonstrated the VSM numerically. Here, we present a mathematical proof of the VSM that is shown to be both a necessary and sufficient condition for a vortex splitting event in any two-dimensional, incompressible flow. The proof includes relating the positive divergence of the net force, condition (2) above, with the second invariant of the velocity gradient tensor, i.e. the Q-criterion. It is shown that the Q-criterion is identical to the determinant of the Hessian matrix for the streamfunction. As a result, the second-partial-derivative test on this Hessian matrix can provide a qualitative description on the behavior of the streamfunction, and thus vortices or recirculation regions, near critical points. [Preview Abstract] |
Monday, November 23, 2015 8:52AM - 9:05AM |
G19.00005: Swirling flow states in diverging or contracting pipes Zvi Rusak, Yuxin Zhang, Harry Li, Shixiao Wang We study the dynamics of inviscid and incompressible swirling flows in diverging or contracting long circular pipes. The inlet flow is described by the circumferential and axial velocity profiles together with a fixed azimuthal vorticity while the outlet flow is characterized by a zero radial velocity state. We first solve the Squire-Long PDE for steady-state flows in a pipe and determine the bifurcation diagram of the various possible flow states as a function of pipe geometry. These include states with a decelerated axial velocity along the pipe center line, an accelerated axial velocity along the pipe center line, vortex breakdown states with a stagnation zone around the pipe center line, and wall-separation states. Then, we establish a correlation between the outlet state of these solutions and solutions of the columnar ($x$-independent) Squire-Long ODE. Numerical simulations based on the unsteady stream function-circulation equations shed light on the stability of the various steady states and their domain of attraction in terms of initial conditions. The results show that pipe divergence promotes the appearance of vortex breakdown states while pipe contraction induces the formation of wall-separation states. [Preview Abstract] |
Monday, November 23, 2015 9:05AM - 9:18AM |
G19.00006: Twist Helicity in Classical Vortices Martin W. Scheeler, Hridesh Kedia, Dustin Kleckner, William T. M. Irvine Recent experimental work has demonstrated that a partial measure of fluid Helicity (the sum of linking and writhing of vortex tubes) is conserved even as those vortices undergo topology changing reconnections. Measuring the total Helicity, however, requires additional information about how the vortex lines are locally twisted inside the vortex core. To bridge this gap, we have developed a novel technique for experimentally measuring twist Helicity. Using this method, we are able to measure the production and eventual decay of twist for a variety of vortex evolutions. Remarkably, we observe twist dynamics capable of conserving total Helicity even in the presence of rapidly changing writhe. [Preview Abstract] |
Monday, November 23, 2015 9:18AM - 9:31AM |
G19.00007: Hollow vortices in weakly compressible flows Vikas Krishnamurthy, Darren Crowdy In a two-dimensional, inviscid and steady fluid flow, hollow vortices are bounded regions of constant pressure with non-zero circulation. It is known that for an infinite row of incompressible hollow vortices, analytical solutions for the flow field and the shape of the hollow vortex boundary can be obtained using conformal mapping methods. In this talk, we show how to derive analytical expressions for a weakly compressible hollow vortex row. This is done by introducing a new method based on the Imai-Lamla formula. We will also touch upon how to extend these results to a von-Karman street of hollow vortices. [Preview Abstract] |
Monday, November 23, 2015 9:31AM - 9:44AM |
G19.00008: Sadovskii vortex in strain Daniel Freilich, Stefan Llewellyn Smith Sadovskii vortices are patches of fluid with uniform vorticity surrounded by a vortex sheet. They were first constructed as models for wakes behind bluff objects. We investigate the Sadovskii vortex in a straining field and examine limiting cases to validate our computational method. One limit is the patch vortex in strain (Moore \& Saffman, \emph{Aircraft wake turbulence and its detection} 1971), where there is no vortex sheet. We solve this as a free-boundary problem, and show that a simple method using the Biot-Savart law quickly gives solutions for stable shapes. When used for the more elongated (stronger straining field) situations, the method also leads to new vortex shapes. In the hollow vortex case, where there is no vortex patch and the circulation is entirely due to the vortex sheet (Llewellyn Smith and Crowdy, \emph{J.\ Fluid Mech}.\ \textbf{691} 2012), we use the Birkhoff-Rott equation to calculate the velocity of the fluid on the vortex boundary. The combination of these two methods can then be used to calculate the shape and velocity field of the Sadovksii vortex in strain. [Preview Abstract] |
Monday, November 23, 2015 9:44AM - 9:57AM |
G19.00009: Correlating Velocity Information in the Vicinity of Lagrangian Saddle Points to the Spatially and Temporally Resolved Static Pressure Distribution on a Circular Cylinder Matthew Rockwood, Melissa Green The locations of Lagrangian saddle points found as the intersections of positive and negative-time Lagrangian coherent structures (LCS) can be used to determine the location and behavior of von Karman vortices shed in the wake of bluff bodies. Correlating the Lagrangian saddle point locations to physical quantities measurable in real-time is critical to the development of a novel input for closed-loop flow control. As a first step towards finding this correlation, the velocity fluctuations in the vicinity of the Lagrangian saddle point are correlated to the fluctuating static pressure at multiple locations on the cylinder surface to determine the lag time between the two quantities at these locations. This offers insight into the specific location and time of past events on the cylinder that influenced the flow field in the vicinity of the Lagrangian saddle point. [Preview Abstract] |
Monday, November 23, 2015 9:57AM - 10:10AM |
G19.00010: Helical vortex systems: linear instability analysis and nonlinear dynamics Can Selçuk We investige the stability properties of helical vortices. Instabilities in such vortex systems have mainly been studied theoretically (Widnall 1972, Okulov and Sørensen 2007) in an inviscid framework for small core size vortices. The aim of the present study is to generalize these works to the viscous framework for arbitrary core sizes and vorticity profiles. The base flows considered here are helically symmetric: fields are invariant through combined axial translation of distance $\Delta z$ and rotation of angle $\Delta \theta = \Delta z/L$ around the $z$-axis, where $2\pi L$ denotes the helix pitch. We first perform a linear temporal stability analysis of these base flows, using an Arnoldi procedure coupled to two different codes: (i) a linearised version of the helical DNS code HELIX, (ii) another linear code called HELIKZ, which computes the dynamics of {arbitrary perturbations} in the vicinity of a helically symmetric base flow. These two codes permit the investigation of different types of instability modes: (i) modes having the same helical symmetry as the base flow which generalize the Okulov modes ; (ii) modes depending on $z$ as $\exp{\mathrm{i}kz}$ which generalize the Widnall modes. [Preview Abstract] |
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