Bulletin of the American Physical Society
2005 58th Annual Meeting of the Division of Fluid Dynamics
Sunday–Tuesday, November 20–22, 2005; Chicago, IL
Session NG: Vortex Dynamics V |
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Chair: Jeffrey Marshall, University of Iowa Room: Hilton Chicago Williford A |
Tuesday, November 22, 2005 11:01AM - 11:14AM |
NG.00001: 3D vortex breakdown in straight pipes M.A. Herrada, R. Fernandez-Feria Three-dimensional (3D) and axisymmetric numerical simulations of the incompressible Navier-Stokes equations have been conducted to study the occurance of vortex breakdown in a familly of columnar vortex flows in straight pipes. The numerical simulations show that the basic form of breakdown is axisymmetric, and a transition to helical breakdown modes is shown to be caused by a sufficiently large pocket of absolute instability in the wake of the bubble. Depending on the values of the Reynolds and swirl parameters, two distinct eigenfunctions corresponding to azimuthal wavenumbers m=+1 and m=+2 have been found to yield a helical or double-helical breakdown modes, respectively. By means of a simple linear, spatial stability analysis carried out in the sections of the pipe where the basic axisymmetric flow present reverse flow, we have identified the frequencies and the dominant azimuthal wave numbers observed in the 3D simulations. [Preview Abstract] |
Tuesday, November 22, 2005 11:14AM - 11:27AM |
NG.00002: Amplification of Three-Dimensional Perturbations during Nominally Parallel Vortex-Cylinder Interaction Xiongbin Liu, Jeffrey Marshall A computational study is reported which examines the amplification of three-dimensional flow features for nominally parallel vortex-cylinder interaction problems. We consider a helical vortex with small-amplitude perturbations that is advected onto a circular cylinder whose axis is parallel to the nominal vortex axis. The study assesses the applicability of the two-dimensional flow assumption for parallel vortex-body interaction problems in which the body impinges on the vortex core. The computations are performed using an unstructured finite-volume method for an incompressible flow, with periodic boundary conditions along the cylinder axis. Growth of three-dimensional flow features is quantified by use of a proper-orthogonal decomposition of the Fourier-transformed velocity and vorticity fields in the cylinder azimuthal and axial directions. The interaction is examined for different axial wavelengths and amplitudes of the initial helical waves on the vortex core, and the results for cylinder force are compared to the two-dimensional results. [Preview Abstract] |
Tuesday, November 22, 2005 11:27AM - 11:40AM |
NG.00003: A Panel Method for Vortex Sheet Roll-Up in 3D Flow Robert Krasny, Leon Kaganovskiy A panel method is described for computing vortex sheet roll-up in 3D flow. The sheet surface is represented as a set of quadrilateral panels with particles at the vertices and possibly also along the edges. The panels are adaptively subdivided to maintain resolution as the sheet rolls up. The set of all panels has a quadtree structure which is used to perform neighbor searches. The particles are advected by a regularized Biot- Savart integral and the induced velocity is evaluated by a multipole treecode. The panel method improves upon a previous filament representation of the sheet surface. The code is applied to compute the collision of two vortex rings. [Preview Abstract] |
Tuesday, November 22, 2005 11:40AM - 11:53AM |
NG.00004: Moment relations for point vortex equilibria Hassan Aref The analytical solution of the algebraic equations describing relative equilibrium configurations of interacting point vortices appears difficult in general. Even for identical vortices - in which case the configurations in question rotate rigidly - surprisingly little is known analytically about the many configurations found through numerical calculation. Only for very special cases - basically, systems with vortices of the same absolute strength where the configuration is either stationary or translates uniformly - have complete solutions been obtained, and then by quite indirect routes. We discuss a new analytical method that uses moments of the vortex positions and yields particularly simple results for equilibrium configurations consisting of nested regular polygons. A complete determination of all triple-ring equilibria has been given and numerous previously unknown configurations identified. Several equilibria reported in the literature, found by numerical solution, have been characterized analytically. [Preview Abstract] |
Tuesday, November 22, 2005 11:53AM - 12:06PM |
NG.00005: Equilibrium solutions of the Euler equations related to $m = 3$ symmetric vortex merger Paolo Luzzatto Fegiz, Charles H.K. Williamson Motivated by the merger of two corotating vortices, Cerretelli and Williamson (\textit{J. Fluid Mech.} 2003) discovered a family of two-fold symmetric uniform vorticity patches. It was found that this branch of solutions passes through a transcritical bifurcation from the family of Kirchoff ellipses (discovered by Kamm 1987 and Saffman 1988), and that the branch continues up to a limiting $m = 2$ cat's eye shape, which corresponds with the $m > 2$ limiting patches of Wu, Overman and Zabusky (1984). We here extend the analysis to cover the case of three vorticity patches, obtaining a series of equilibria which extend the results of Dritschel (1985). We find that a change in the flow topology allows for solutions where the three patches meet. However, if one continues to uncover further equilibrium shapes, one finds a configuration whereby three ``satellite'' patches are joined to a central vorticity patch, whose size progressively increases, ultimately approaching the limiting shape for $m = 3$ found by Wu \textit{et al.} (1984). The discussion will focus on topological changes and on the relation of these novel solutions to existing ones. [Preview Abstract] |
Tuesday, November 22, 2005 12:06PM - 12:19PM |
NG.00006: Vortex Stretching and Reconnection in a Compressible Fluid Bhimsen Shivamoggi Vortex stretching in a compressible fluid is considered. 2D and axisymmetric cases are considered separately. The flows associated with the vortices are perpendicular to the plane of the uniform straining flows. Compressibility effects are considered to be weak to facilitate an analytic solution. Vortex reconnection in a compressible fluid is briefly discussed. Applications to compressible turbulence are discussed. [Preview Abstract] |
Tuesday, November 22, 2005 12:19PM - 12:32PM |
NG.00007: Transient growth of perturbations in a columnar vortex Fazle Hussain, Dhoorjaty Pradeep Linear transient growth is studied in a normal-mode-stable vortex. Energetically ``optimal'' perturbations -- attaining over thousand-fold amplification at moderate Reynolds numbers, $Re \sim 10^4$ -- grow via two inviscid mechanisms: $(a)$ 2-D perturbations with ``positive-tilt'' streamlines (contributing positive Reynolds stress, hence production) grow until the mean swirl transforms the streamlines to ``negative tilt'' (negative stress); $(b)$ 3-D perturbations grow via the tilting and stretching of perturbation radial vorticity. Competition between the amplifying effect of mean strain and growth-arresting effect of mean vorticity, in addition to viscous damping, fixes the optimal radius of initial perturbation. With increasing growth, axisymmetric, $m=0$, modes originate at increasingly larger radii outside the core, whereas $m=\pm1$ modes are localized close to the vortex axis, where they resonantly excite vortex core waves. Resulting strong growth of bending waves appears likely to cause core transition, hence enhanced vortex decay -- a phenomenon of interest in high-$Re$ practical flows, e.g. aircraft wake. [Preview Abstract] |
Tuesday, November 22, 2005 12:32PM - 12:45PM |
NG.00008: Motion of unstable polygonal ring of vortex points on sphere with pole vortices Takashi Sakajo We consider the motion of the $N$-vortex points that are equally spaced along a line of latitude on sphere with fixed pole vortices, which is called the polygonal $N$-ring configuration. We are interested in not only the linear stability, but also the long time evolution of the unstable $N$-ring. In this talk, starting with the linear stability analysis, we characterize the eigenvectors and their corresponding eigenvectors. Then based on the linear stability result, we propose a projection method that reduce the whole system to low-dimensional invariant dynamical system with some symmetry. Thus applying the method to the even vortex points and the $3$-ring cases, we show the existence of the heteroclinic and the homoclinic orbits embedded in the high-dimensional phase space. We also discuss the transition of the topology of these invariatnt structures when the strengths of the pole vortices change. [Preview Abstract] |
Tuesday, November 22, 2005 12:45PM - 12:58PM |
NG.00009: Data Assimilation for Improved Point-Vortex Models Natalie Ross, Elizabeth Bradley, Jean Hertzberg, Thomas Peacock Most flow simulation methods, though accurate, are still too slow for real time applications. In contrast, a point-vortex solver tracks only the vortices in the flow, providing speed at the cost of over-simplification. Periodically correcting the model with observations of the fluid, a process known as data assimilation, could result in a simulation that is both fast \textit{and} accurate if the assimilation is effective and its computational costs are low. Most existing data assimilation methods, however, have been developed in the context of highly complex atmospheric and oceanic applications, such as numerical weather prediction. Results show that one of the simplest of these schemes, Newtonian Nudging, can actually be \textit{detrimental} to a smaller scale point-vortex simulation. We present an alternative assimilation strategy that allows the dynamics of the system to dictate when corrections are required. Data is assimilated \textit{only} in regions where gradients are relatively large, permitting a significant reduction in computational cost as compared to periodic correction. In initial experiments, we were also able to increase the accuracy of the simulation by a factor of two. [Preview Abstract] |
Tuesday, November 22, 2005 12:58PM - 1:11PM |
NG.00010: Kelvin Modes with Nonlinear Critical Layers on a Vortex with a Continuous Velocity Profile Sherwin Maslowe, Nilima Nigam The short wave cooperative instability mechanism is of interest both scientifically and because of its pertinence to the aircraft trailing vortex problem. In the first quantitative investigation of this mechanism [Tsai \& Widnall (1976)], the discontinuous Rankine vortex was employed. Recently, Sipp \& Jacquin [Phys. Fluids (2003)] have shown, however, that for a continuous velocity profile the modes required for the ``Widnall instabilities'' would be damped. The damping is a consequence of viscosity being used to deal with the singular critical point that occurs in the linear, inviscid theory. An alternative approach that is, in fact, more appropriate at high Reynolds numbers is to restore nonlinear terms in a thin critical layer centered on the singular point. With such a nonlinear critical layer, we show that neutral modes exist that would be damped in the linear viscous theory. These modes are non-axisymmetric and the theory is similar mathematically to that for stratified shear flows, where it has been shown that nonlinear modes, not permitted in linear theory, can occur at Richardson numbers larger than 1/4. [Preview Abstract] |
Tuesday, November 22, 2005 1:11PM - 1:24PM |
NG.00011: PIV Measurements for Validation of Self-induction Theory of Vortex Breakdown Brad Thompson, Dana Dabiri, Mitsuru Kurosaka THE PROBLEM: Tail buffeting is a severe operational and maintenance problem in twin-tailed aircraft. Tail buffeting is driven by aerodynamic forces resulting from the wing leading edge produced concentrated vortices and their subsequent abrupt breakdown and radial expansion. The expansion leads to large-diameter helical vortices, which impose lateral forces on the tails. Various brute-force, empirical approaches have provided some ad-hoc fixes, but poor understanding of the underlying physics prevents effective design solutions. It is not yet possible to design buffet-free aircraft from first principles. Preliminary work offers a unique explanation for vortex breakdown called the \textit{azimuthal vorticity gradient theory} ...(Cain 2001). This paper will present and establish experimental evidence using DPIV to validate this recent theory. Cain, C. B. (2001). The Self-Induction Theory of Vortex Breakdown. \underline {Aeronautics Dept}. Seattle, WA, University of Washington. \textbf{Master Thesis}. [Preview Abstract] |
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