Bulletin of the American Physical Society
70th Annual Meeting of the APS Division of Fluid Dynamics
Volume 62, Number 14
Sunday–Tuesday, November 19–21, 2017; Denver, Colorado
Session F10: Vortex Evolution & StabilityVortexes

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Chair: Bartosz Protas, McMaster University Room: 503 
Monday, November 20, 2017 8:00AM  8:13AM 
F10.00001: Stabilization of Inviscid Vortex Sheets Bartosz Protas, Takashi Sakajo In this study we investigate the problem of stabilizing inviscid vortex sheets via feedback control. Such models, expressed in terms of the BirkhoffRott equation, are often used to describe the KevinHelmholtz instability of shear layers and are known to be strongly unstable to smallscale perturbations. First, we consider the linear stability of a straight vortex sheet in the periodic setting with actuation in the form of an array of point vortices or sources located a certain distance away from the sheet. We establish conditions under which this system is controllable and observable. Next, using methods of the linear control theory, we synthesize a feedback control strategy which stabilizes a straight vortex sheet in the linear regime. Given the poor conditioning of the discretized problem, reliable solution of the resulting algebraic Riccati equation requires the use of highprecision arithmetic. Finally, we demonstrate that this control approach also succeeds in the nonlinear regime, provided the magnitude of the initial perturbation is sufficiently small. [Preview Abstract] 
Monday, November 20, 2017 8:13AM  8:26AM 
F10.00002: Numerical simulations of vortex breakdown in lowReynoldsnumber swirling flow Joseph Chung, Xiao Zhang, Ryan Houim, Elaine Oran Numerical simulations of lowReynoldsnumber vortex breakdown were carried out by solving the unsteady, threedimensional, compressible, NavierStokes (NS) equations on a Cartesian mesh. The fluxcorrected transport algorithm was used to solve for the inviscid fluxes and highorder central differencing for the viscous terms. BoxLib, an adaptive meshrefinement library, was used for spatial refinement near the core of the vortex. The molecular weight and temperature were scaled to relax the timestep constraints imposed by the sound speed. The results confirm threedimensional vortex breakdown in qualitative and quantitative agreement with previous incompressible simulations. Application of the barely implicit correction (BIC) algorithm further relaxed the timestep constraint by solving for a pressure correction to the energy and momentum equations. [Preview Abstract] 
Monday, November 20, 2017 8:26AM  8:39AM 
F10.00003: Axisymmetric contour dynamics for buoyant vortex rings Ching Chang, Stefan Llewellyn Smith Vortex rings are important in many fluid flows in engineering and environmental applications. A family of steady propagating vortex rings including thincore rings and Hill’s spherical vortex was obtained by Norbury (1973). However, the dynamics of vortex rings in the presence of buoyancy has not been investigated yet in detail. When the core of a ring is thin, we may formulate reduced equations using momentum balance for vortex filaments, but that is not the case for “fat” rings. In our study, we use contour dynamics to study the time evolution of axisymmetric vortex rings when the density of the fluid inside the ring differs from that of the ambient. Axisymmetry leads to an almostconserved material variable when the Boussinesq approximation is made. A set of integrodifferential equations is solved numerically for these buoyant vortex rings. The same physical settings are also used to run a DNS code and compare to the results from contour dynamics. [Preview Abstract] 
Monday, November 20, 2017 8:39AM  8:52AM 
F10.00004: Transient Growth on a HighReynoldsnumber Oseen Vortex Leading to Breakup Eric Stout, Fazle Hussain Incompressible vortexturbulence interaction and vortex perturbation transient growth are explored at Reynolds numbers (\textit{Re}$\equiv $vortex circulation/viscosity) much higher than the current computational maximum of \textit{Re}$=$10,000, via Large Eddy Simulation (LES) using the Smagorinsky model. At \textit{Re}$=$10,000, LES results agree closely with Direct Numerical Simulation (DNS) results for the perturbation energy, peak azimuthal velocity, and core radius (radius of peak azimuthal velocity)  thus validating the LES scheme. Our previous studies have shown that turbulence, strained into external spiral filaments, induces axial flow on an initially rectilinear Oseen vortex column. Axial flow comparable to the swirl destabilizes a vortex; however, at \textit{Re}$=$10000, viscous decay of the filaments limits the axial flow. We study a vortex column at \textit{Re}$=$50,000 using LES to achieve stronger axial flow, thus triggering instability and transition of the vortex into turbulence. This transition is compared with DNS of an unstable vortex at \textit{Re}$=$10000  both simulations showing transition of the vortex column into a bundle of numerous spiraling axial vortex threads. Details of the initial transient growth, transition process and turbulence evolution will be explained. [Preview Abstract] 
Monday, November 20, 2017 8:52AM  9:05AM 
F10.00005: The growth and breakdown of a vortexpair in a stably stratified fluid. Advaith S, Aashay Tinaikar, Manu K V, Saptarshi Basu 
Monday, November 20, 2017 9:05AM  9:18AM 
F10.00006: Abstract Withdrawn Evolution of vortex rings in isodensity and isoviscosity fluid have been studied analytically using a novel mathematical model. The model predicts spatiotemporal variation in peak vorticity, circulation, vortex size and spacing based on instantaneous vortex parameters. This proposed model is quantitatively verified using experimental measurements. Experiments are conducted using highspeed Particle Image Velocimetry (PIV) and Laser Induced Fluorescence (LIF) techniques. A transitional theory is also framed using force balance equations which seamlessly integrate short and long time asymptotic theories. It also explain differences observed in structural evolution of thin and thick core vortex rings. Proposed theory explains the spatiotemporal evolution of vortex rings for a wide range of Reynolds number from 100 to 5500. 
Monday, November 20, 2017 9:18AM  9:31AM 
F10.00007: Swirling flow states of compressible supercritical fluids Nguyen Ly, Zvi Rusak, Shixiao Wang Steady states of axisymmetric swirling flows of a supercritical fluid in a rotating finitelength pipe are studied. The fluid thermodynamic behavior is modeled by the Van der Waals equation of state. A nonlinear partial differential equation for the solution of the flow stream function is derived in terms of the inlet flow total enthalpy, entropy, and circulation functions. This equation reflects the nonlinear thermophysical interactions in the flows, specifically when the inlet state temperature and density vary around the thermodynamic critical point, flow compressibility is significant, and inlet swirl ratio is high. The approach is applied to an inlet flow described by a solidbody rotation with uniform profiles of the axial velocity and temperature. Bifurcation diagrams of steady compressible flows of real fluids are formed as the inlet swirl level and the centerline inlet density are increased. Focus is on fluids with low values of R/Cv. Computed results provide predictions of the critical swirl levels for the loss of stability of the columnar state and for the appearance of noncolumnar states and of vortex breakdown states as a function of inlet centerline density. The difference in the dynamical behavior between that of a perfect gas and of a real gas is explored. [Preview Abstract] 
Monday, November 20, 2017 9:31AM  9:44AM 
F10.00008: Identification of key flow for vortex generation in terms of local flow geometry Katsuyuki Nakayama The flow transition into a vortical flow in terms of the invariant local geometry (topology) specified by the velocity gradient tensor is analysed with the swirlity that is a physical quantity to represent the unidirectionality and intensity of the azimuthal flow extracted from the local flow. The velocity gradient tensor is represented in a specific coordinate system where these components are given by invariant quantities and related to the flow topology. While the swirlity specifies the transition process into a vortical flow and predicts its generation, the tensor components are traced. Then the key flow that contributes the vortex generation is identified as an invariant shear (or strain) flow, where its effect is evaluated. This analysis of the flow transition with statistical analysis in an isotropic homogeneous turbulence in a low Reynolds number shows that the key flow is the shear flow in the predicted swirl plane (after vortex transition) orthogonal to one eigenvector. This particular characteristic is similar irrespective of decomposed flow scales in this turbulence (using the band pass filter of the Fourier coefficient of the velocity), with the feature of the swirlity. [Preview Abstract] 
Monday, November 20, 2017 9:44AM  9:57AM 
F10.00009: Effect of the local geometry on the motion of a filamentary vortex Oscar Velasco Fuentes In his seminal paper on vortex motion Helmholtz (1858) showed that a curved vortex moves within the fluid whereas a straight one remains stationary. Schwedoff (1887) later claimed that the velocity of a vortex increases with the curvature and is perpendicular to the plane of curvature. This conjecture, mathematically formalized by Da Rios (1906), is now known as the local induction approximation (LIA). Here we use a higherorder FrenetSerret representation of the vortex centerline in order to study the effect of curvature, torsion and their derivatives on the motion of a filamentary vortex. We found that, to leading order, the curvature induces a vortex velocity in the binormal direction, the torsion induces velocity in the tangential direction and the changes in curvature and torsion along the vortex induce velocity in the normal direction. We verify these results by studying, separately, the evolution of a helical vortex and an elliptical vortex ring, whose motion is also calculated using different analytic/numerical methods. [Preview Abstract] 
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