Bulletin of the American Physical Society
64th Annual Meeting of the APS Division of Fluid Dynamics
Volume 56, Number 18
Sunday–Tuesday, November 20–22, 2011; Baltimore, Maryland
Session H21: Vortex Dynamics IV |
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Chair: Fabrice Schlegel, Massachusetts Institute of Technology Room: 324-325 |
Monday, November 21, 2011 10:30AM - 10:43AM |
H21.00001: Vorticity Dynamics in Actuated Transverse Jets Fabrice Schlegel, Ahmed F. Ghoniem Transverse jets are important to various industrial applications (film cooling, primary or dilution jets in gas turbines). Our previous results on the impact of the boundary layer detachment on the jet evolution show the sensibility of the overall jet dynamics to the near-nozzle conditions. Small perturbations at the nozzle exit are thus expected to act as powerful tools for control of the jet trajectory, its spanwise spreading, and its mixing properties. In this study, we demonstrate actuation strategies that manipulate the jet via nozzle edge perturbations, helical perturbations and the addition of delta-tabs at the nozzle exit. [Preview Abstract] |
Monday, November 21, 2011 10:43AM - 10:56AM |
H21.00002: Close relative equilibria of identical point vortices Tobias Dirksen, Hassan Aref Via numerical solution of the classical problem of relative equilibria for identical point vortices on the unbounded plane we have found configurations that are very close to the analytically known, centered, symmetrically arranged, nested equilateral triangles. Numerical solutions of this kind were found for $3n+1$ vortices, where $n = 2, 3, \ldots, 30$. A sufficient, although apparently not necessary, condition for this phenomenon of close solutions is that the ``core'' of the configuration is marginally stable, as occurs for a central vortex surrounded by an equilateral triangle. The open, regular heptagon also has this property, and new relative equilibria close to the nested, symmetrically arranged, regular heptagons have been found. The centered regular nonagon is also marginally stable. Again, a new family of close relative equilibria has been found. The closest relative equilibrium pairs occur, however, for symmetrically nested equilateral triangles. The numerical evidence is surveyed and related recent work mentioned. A Letter in {\it Physics of Fluids} {\bf 23} (2011) 051706 is available. [Preview Abstract] |
Monday, November 21, 2011 10:56AM - 11:09AM |
H21.00003: Stability of trailing vortices with radial stratification Jerome Fontane, Laurent Joly, Auriane Audouin We look at the effects of the radial density stratification on the stability of the q-vortex, a commonly accepted model for aircraft trailing vortices. It has been demonstrated that the 2D Lamb--Oseen vortex develops a Rayleigh--Taylor instability when its core is heavier than the surrounding fluid (Joly, Fontane \& Chassaing 2005, Sipp \textit{et al} 2005). The underlying mechanism relies on baroclinic vorticity generation due to any misalignment between the density gradient and the centripetal acceleration field. The instability is triggered provided that the density decreases radially somewhere in the vortex core. This mechanism is also active in the 3D trailing vortex and affects its stability characteristics due to the addition of an axial component in the acceleration field. We show that the unstable center modes of the homogeneous case (Fabre \& Jacquin 2004) are promoted in a q-vortex with a heavy core. Their growth rate increases while their m-spiral structure is preserved. For an Atwood number $At=0.5$, their predicted growth rate can be ten times the ones found in the homogeneous case. Furthermore, the unstable domain is extended far beyond the neutral curve in the homogeneous case, with unstable modes observed for Swirl numbers up to $q=5$. It is argued here that corresponding density perturbations could eventually lead to the development of new and original strategies to decrease the lifespan of aircraft trailing vortices and greatly reduce their unwanted side-effects on contrails persistence and air traffic regulations. [Preview Abstract] |
Monday, November 21, 2011 11:09AM - 11:22AM |
H21.00004: Linear response of a vortex column - singular eigenfunctions and growth mechanisms Anubhab Roy, Abhishek S, Harish N. Dixit, Ganesh Subramanian A vortex column supports oscillations known as Kelvin modes, eigenmodes that are irrotational outside the vortex core. In order to understand the interaction of a vortex with an external vortical disturbance field, we use an extended modal description that incorporates a singular continuous spectrum with eigenmodes that are vortical outside the core. The continuous spectrum eigenfunctions are explicitly evaluated for a Rankine vortex; the description is extended to smooth vorticity profiles based on an analogy with stratified shear flows. Next, in the framework of an initial value problem, we analyze the inviscid resonant interaction between a vortex column and suitably localized initial conditions. It is shown that while a Rankine vortex allows for an unbounded secular growth in response an infinitely localized initial condition, smooth vorticity profiles, with a non-zero critical layer vorticity gradient, exhibit a saturation resulting from a perturbation-vorticity-induced screening mechanism. The effects of an upstream tilt on this novel saturation response are investigated. [Preview Abstract] |
Monday, November 21, 2011 11:22AM - 11:35AM |
H21.00005: Inviscid linear stability of a Vatistas-trailing line vortex Hossein Abdollahi, Hamid Ait Abderrahmane, Georgios H. Vatistas The paper examines the inviscid linear stability of a Vatistas-trailing line vortex using normal mode analysis. The employed numerical method is based on the Riccatti transformation. The stability of Vatistas-trailing line vortex is discussed with respect to the well-known Batchelor's trailing line vortex. The results show that Vatistas' vortex is more stable. [Preview Abstract] |
Monday, November 21, 2011 11:35AM - 11:48AM |
H21.00006: On Existence of Relative Equilibria of Two--Dimensional Vortex Sheets Bartosz Protas, Marcel Rodney In this study we consider the existence of relative equilibria of two--dimensional vortex sheets. We focus on open sheets and derive conditions which must be satisfied by equilibrium configurations of such sheets. It is shown that, in contrast to the time--dependent case, such sheets must be everywhere orthogonal to the velocity field of the coordinate system in which they are stationary. Finally, we provide a rigorous demonstration that for vortex sheets arising from desingularization of translating (counter--rotating) and corotaing pairs of point vortices such equilibrium configuration do not in fact exist. The argument is based on classical results concerning existence of solutions of singular integral equations. [Preview Abstract] |
Monday, November 21, 2011 11:48AM - 12:01PM |
H21.00007: Stability of a helical vortex tube with axial flow Yuji Hattori, Yasuhide Fukumoto The stability of a helical vortex tube with axial flow is studied analytically. The base flow is obtained by solving the Euler equation perturbatively assuming small ratio of core to curvature radius, which is denoted by $\varepsilon $, and Rankine vortex with uniform axial flow at the leading order. We apply both local and modal stability analysis. By local stability analysis we show that the flow is subject to not only curvature instability but also Coriolis instability, both having the same resonance condition. The unstable growth rate is $O\left( \varepsilon \right)$ and given by the magnitude of a sum of the complex numbers corresponding to the two instabilities. Combined effects of the axial flow and the torsion of the helical vortex tube appear as $O\left( {\varepsilon ^2} \right)$ modification. These results are confirmed by the modal stability analysis. [Preview Abstract] |
Monday, November 21, 2011 12:01PM - 12:14PM |
H21.00008: Inertial dynamics of chains: slack, stress, and convective instabilities James Hanna, Christian Santangelo Inertial chains may be thought of as one-dimensional incompressible/inextensible fluids or solids moving in three dimensions. Incompressibility is enforced by a stress screened by the chain's curvature (slack). The nature of the stress--- tensile or compressive, uniform or spatially varying--- governs the stability of the motion. The most stable motions, characterized by a uniform tensile stress, belong to a wide class that includes travelling waves of curvature and torsion. Convective instabilities exist in the presence of stress gradients; we present a striking example from a tabletop experiment involving a growing arch in a straightening chain. This work adds to a large body of literature on locally arc length preserving dynamics of curves arising in the study of thin objects such as elastic rods, vortex filaments, and oceanic jets. [Preview Abstract] |
Monday, November 21, 2011 12:14PM - 12:27PM |
H21.00009: The bifurcation and stability of vortex flow states at near-crtical swirl ratios Lei Xu, Zvi Rusak, Shixiao Wang A theoretical and computational study of the bifurcation and stability of vortex flow states at near-critical swirl levels is presented. The theoretical analysis is based on a nonlinear model problem of the dynamics of small perturbations on a columnar flow. The model is first used to study the bifurcation of additional branches of equilibrium states and the stability of these states. The response of the columnar flow to various initial conditions is also studied. A frequency response analysis to inlet perturbations at various amplitudes and initial conditions is conducted and demonstrates the ability to control the growth of the perturbations when certain oscillations are imposed. However, this approach is limited to relatively small-amplitude initial perturbations. A bang-bang control approach where swirl is changed as a function of outlet centerline axial speed shows the ability to induce limit-cycle oscillations on the flow and control the growth of perturbations at a wider range of swirl levels and initial conditions. [Preview Abstract] |
Monday, November 21, 2011 12:27PM - 12:40PM |
H21.00010: The global nonlinear stability of a swirling flow in a pipe Zvi Rusak, Shixiao Wang, Lei Xu, Steve Taylor The dynamics of a perturbed axisymmetric, near-critical swirling flow in a long, finite-length, straight, circular pipe is studied through a weakly nonlinear analysis. The flow is subjected to non-periodic inlet and outlet conditions. Examples of flow dynamics at various near-critical swirl levels in response to different initial perturbations demonstrate the important role of the nonlinear steepening terms in perturbations' dynamics. Results reveal the evolution of explosive, faster-than-exponential, shape-changing modes as perturbations grow into a vortex breakdown process. Further analysis of the model problem shows the important role of the nonlinear evolution in (i) the transfer of perturbation's kinetic energy between the boundaries and flow bulk, (ii) the evolution of perturbations in practical concentrated vortices, and (iii) the design of control methods to stabilize vortex flows. A robust feedback control method to stabilize a solid-body rotation flow in a pipe at a wide range of swirl levels above critical is developed. Applicability of this method to stabilize medium and small core-size vortices is also discussed. [Preview Abstract] |
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