Bulletin of the American Physical Society
71st Annual Meeting of the APS Division of Fluid Dynamics
Volume 63, Number 13
Sunday–Tuesday, November 18–20, 2018; Atlanta, Georgia
Session Q18: Vortex Dynamics and Instability 
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Chair: Arnab Samanta, Indian Institute of Science Banglore Room: Georgia World Congress Center B305 
Tuesday, November 20, 2018 12:50PM  1:03PM 
Q18.00001: Trailing Vortices in the FarWake of a Delta Wing Sarah Morris, C. H. K. Williamson In this research we study the trailing vortices behind a 30° apex delta wing at 15° angle of attack. The delta wing is towed in an XYTowing Tank, generating a spatially developing vortex pair with streamwise (axial) flow in the vortex cores. PIV using a transverse light sheet is used to find the transverse velocity field, and to characterize the vortices using the superposition of two LambOseen vortices. The axial flow is captured using a longitudinal light sheet; to ensure we capture the vortex core, the light sheet is set such that it is slightly oblique to the length of the vortex. This technique was first developed by Miller & Williamson (1995) and allows the streamwise velocity profiles to be captured over 20 chordlengths downstream. When the vortex pair is in ground effect, the boundary layer that forms between the vortices and the wall separates, generating secondary vorticity and causing the vortex pair to ‘rebound’. The maximum axial velocity and vortex core size are analyzed in and out of ground effect, and a wakelike deficit in axial velocity (flow upstream) is observed. We also trigger the longwavelength instability (Crow 1970) in the vortices by introducing perturbations in the towing velocity, and compare the measured growth rate of the instability to theory. 
Tuesday, November 20, 2018 1:03PM  1:16PM 
Q18.00002: Global Stability Analysis of Vortex Breakdown in Misaligned Compressible Swirling Jet Kento Yamada, Yuya Ohmichi, Kojiro Suzuki A vortex breakdown is an important phenomenon for many engineering applications and contains a complicated mechanism of transition from a bubble vortex breakdown to several types such as spiral, double helix, and turbulent vortex breakdowns. Many of global stability analyses on the transition have been conducted and revealed instability mechanisms and wavemaker regions. In the previous studies, an incompressible flow was considered and a base flow was an axisymmetric bubble obtained from an axisymmetric profile of a longitudinal vortex. However, for more practical cases, the base flow is not limited to be axisymmetric. Also, the compressibility should be taken into consideration. At this work, an asymmetic bubble for a compressible flow was obtained as the base flow by introducing an offset between the axis of a swirling flow and the axis of a jet flow. Based on this base flow, we conducted the global stability analysis on the transition from the bubble vortex breakdown to the spiral vortex breakdown. From this analysis, we examine differences in a growth rate, a frequency, and the threedimensional structure of an unstable mode.

Tuesday, November 20, 2018 1:16PM  1:29PM 
Q18.00003: Secondary Instability of Streamwise Vortices in a Turbulent Convex Wall Jet Anshuman Pandey, James W. Gregory The outer part of a wall jet flowing over a convex wall satisfies the centrifugal instability criterion. Such a configuration has been studied in this work with a wall jet of air flowing over the exterior surface of a 0.91m long circular cylinder. This flow scenario has found practical use in NOTAR helicopters for side force generation and in airfoil trailing edge designs for lift augmentation. As the convex wall jet evolves, centrifugal instability manifests itself in the form of unsteady streamwise vortices whose spanwise wavelength scales with wall jet thickness. These vortices enhance mixing between the wall jet and ambient flow and can be used as a control mechanism through appropriate use of secondary instability affecting them. In this work, microvortex generators are positioned at the wall jet nozzle lip in order to force stronger disturbances and preset the wavelength. Planar, stereo and TRPIV have been conducted to characterize the evolution of the vortices. The coherent streamwise vortices undergo breakdown into noncoherent turbulence at a downstream location that depends on the preset vortex wavelength. Various decomposition techniques such as spatial FFT, POD and DMD have been used to study the modes of secondary instability leading to the breakdown process. 
Tuesday, November 20, 2018 1:29PM  1:42PM 
Q18.00004: Simulations of compressible swirling flows in a circular pipe Noah Cyr, Zvi Rusak, Shixiao Wang The dynamics of inviscid, compressible and axisymmetric swirling flow of a perfect gas in a straight finitelength circular pipe is studied by numerical simulations. The flow solver is based on integration in time of the flow parameters using an explicit, firstorder accurate finitedifference scheme with a secondorder accurate difference formulation in the axial and radial directions. Perturbed flow evolution at various levels of the incoming flow swirl ratio and at various subsonic flow Mach numbers is described, including decaying dynamics of perturbations when the swirl ratio is below the critical level and evolution to vortex breakdown states when the swirl ratio is below the critical level. Computed results are compared with the theoretical predictions from the studies of Rusak, Choi & Lee (2007) and Rusak, Choi, Bourguard & Wang (2015). 
Tuesday, November 20, 2018 1:42PM  1:55PM 
Q18.00005: On the stability mechanism of a swirling flow confined in an enclosed cylindrical container Weimin Yuan, Zhenhua Wan, Shixiao Wang, Zvi Rusak The instability mechanism of a swirling flow confined in an enclosed cylindrical container, driven by the rotation of one endwall is studied by DNS and stability analysis. A case study where the cylinder aspect ratio H/R is 4 and Reynolds number $Re=2500$ based on the rotation of the endwall is conducted. A base axisymmetric flow is first established through the DNS by enforcing flow axisymmetry. Then, linear stability analysis of the base flow shows stability to axisymmetric disturbances but instability to spiral disturbances. The fastest linearly growing mode is with an azimuthal wave number $m=3$, which is in an excellent agreement with the DNS results. The physical mechanism of the instability of the $m=3$ mode is revealed through the use of the ReynoldsOrr equation. It pinpoints the exact location of perturbation's kinetic energy production/loss inside of the flow domain. It is also found that the nonaxial homogeneity of the base axisymmetric flow plays a major role in the onset of the instability. A similar mechanism was recently identified for the unstable spiral modes found in the solidbody rotation flow in a finitelength, straight, open rotating pipe. The current model has a theoretical advantage since the boundary condition is well defined and used in this study. 
Tuesday, November 20, 2018 1:55PM  2:08PM 
Q18.00006: Amplitude effects of initial perturbations on nonlinear transient growth dynamics for a vortex column Christopher Bryson, Eric Nicholas Stout, Fazle Hussain Nonlinear dynamics present in the evolution of finite amplitude perturbations to a vortex column are discussed, where the initial perturbations are designed to optimize transient energy gain for a linearized NavierStokes system. Previous studies of linear transient growth speculated that nonlinear saturation played an important role in the limitation of perturbation energy growth and in causing substantial distortion to the base vortex. New results show that there is no set saturation amplitude, suggesting that the nonlinear dynamics responsible for the distortion of the column change depending on the initial perturbation amplitude. A range of amplitudes and linear transient growth optimals are explored, ranging from nearly linear dynamics for all times to strongly nonlinear at early times, and the resulting differences in the evolution are discussed with a focus on understanding vortex breakup. Additionally, superposition of multiple linear transient growth modes are explored to assess the potential in computing nonlinear optimal perturbations. 
Tuesday, November 20, 2018 2:08PM  2:21PM 
Q18.00007: Simulations of inviscid swirling flows in pipes with various geometries Yuxin Zhang, Zvi Rusak, Shixiao Wang Numerical simulations of the dynamics of highRe swirling flows in pipes with varying geometries is a challenging computational problem, specifically when vortexbreakdown or wallseparation regions naturally evolve in the flows. The paper describes a simulation scheme of the evolution of inviscidlimit, axisymmetric and incompressible swirling flows in expanding or converging pipes. Integration in time of the circulation and azimuthal vorticity uses an explicit, firstorder accurate finitedifference scheme with a secondorder accurate upwind difference formulation in the axial and radial directions. A Poisson solver for the spatial distribution of the stream function uses a secondorder accurate overrelaxation difference scheme. The solver provides the natural evolution of flows including the dynamics to states with slowspeed recirculation zones along the pipe centerline or attached to the wall. The simulations show convergence of results with mesh refinement for various swirl levels and pipe geometry variations. Results of timeasymptotic states also present agreement with available theoretical predictions of steady vortex flows in diverging or contracting pipes. Results support theoretical predictions and clarify the nature of highRe flow evolution. 
Tuesday, November 20, 2018 2:21PM  2:34PM 
Q18.00008: Linear Stability of Inviscid Vortex Rings to Axisymmetric Perturbations Bartosz Protas We consider the linear stability to axisymmetric perturbations of the family of inviscid vortex rings discovered by Norbury (1973). Since these vortex rings are obtained as solutions to a freeboundary problem, their stability analysis is performed using recentlydeveloped methods of shape differentiation applied to the contourdynamics formulation of the problem in a 3D axisymmetric geometry. This approach allows us to systematically account for the effect of boundary deformations on the linearized evolution of the vortex ring. Stability properties are then determined by the spectrum of a singular integrodifferential operator defined on the vortex boundary in the meridional plane. The resulting generalized eigenvalue problem is solved numerically with a spectrallyaccurate discretization. Our results reveal that while thin vortex rings remain neutrally stable, they become linearly unstable when they are sufficiently "fat". Analysis of the structure of the eigenmodes demonstrates that they approach the corresponding eigenmodes of Rankine's vortex when the vortex ring is thin and the eigenmodes of Hill's vortex when the vortex ring is fat. This study is a stepping stone leading to a complete stability analysis of inviscid vortex rings with respect to general perturbations. 
Tuesday, November 20, 2018 2:34PM  2:47PM 
Q18.00009: Transient growth mechanisms in a highspeed rapidlyswirling jet with vortex breakdown Arnab Samanta We consider an experimentallymeasured, high Reynolds and swirl number jet that has undergone an axisymmetric vortex breakdown, known to be dominated by a selfexcited, lowestorder, absolutely unstable helical mode. We have shown this jet to also possess significant shorttime transient growths in the wake region at even helical orders and moderate streamwise wavenumbers, easily exceeding the corresponding exponential growths at these times. We investigate transient growth mechanisms via analyzing the input and output optimal perturbation structures which resemble patterns similar to Kelvin waves of LambOseen and Batchelor vortices. The input perturbations appear as azimuthal velocity streaks in the streamwise planes, which once located exclusively inside the core region, uncoil via the classical Orr mechanism. If the output state resembles a compact spiral structure at the core, we show these situations to yield the strongest transient growths in the swirling jet. In contrast, initial perturbations that are spread out near the quasipotential region rolls up to yield thin spirals outside the core region while a second compact region appears at the center via core contamination. Unlike in the LambOseen vortex, such waves yield only moderate transient amplifications. 
Tuesday, November 20, 2018 2:47PM  3:00PM 
Q18.00010: Magnetohyperbolic instability: a new instability due to hyperbolic instability and phase shift by Alfven waves Yuji Hattori, Makoto Hirota, Masaru Furukawa The linear stability of vortices which possess hyperbolic stagnation points and are subjected to weak magnetic field is studied by local and modal stability analysis. The base flow is the twodimensional TaylorGreen vortices. The local stability analysis shows that strong instability emerges near the heteroclinic streamlines connecting the hyperbolic stagnation points. Unstable regions form bands in a parameter space. These features are similar to those of stratohyperbolic instability discovered recently (Suzuki et al., 2018). The modal stability analysis is performed numerically using the Krylov method. In addition to the magnetorotational instability, asymmetric instability which is closely related to the local instability is observed. The corresponding eigenmodes have large amplitude near the heteroclinic streamlines and are again similar to those of stratohyperbolic instability. This new instability is due to the hyperbolic instability and phase shift by the Alfven waves, the latter being replaced by the internal gravity waves in the stratohyperbolic instability. Thus it is named as magnetohyperbolic instability. 
Tuesday, November 20, 2018 3:00PM  3:13PM 
Q18.00011: On the transition between Kelvin’s equilibria Mira Kim, Hamid Ait Abderrahmane, Mohamed Fayed, Georgios H. Vatistas, Hoi Dick Ng In earlier studies we have showed experimentally that the polygonal patterns observed in a rotating shallow water layer in confined cylinder are Kelvin’s equilibria [PRL 100, 174503 (2008)]. We have also reported that the transition of m into (m + 1) equilibria involves a beatwave resonance that mediates energy transfer between the background flow and the vortex core [PRE 83, 056319 (2011)]. Here, we revisit this transition between relative equilibria involving two and three satellite vortices. This transition is investigated forward and backward, using particle image velocimetry (PIV). The evolution of the satellite vortices is depicted and analyzed. 
Tuesday, November 20, 2018 3:13PM  3:26PM 
Q18.00012: Exotic vortex streets created behind triangular objects Ildoo Kim We discuss two distinct spatial structures of von Karman vortex streets. The ‘conventional mushroom’ structure is commonly discussed in many experimental studies, but the exotic ‘separated rows’ structure is characterized by a thin irrotational fluid between two rows of vortices. In our experimental studies in twodimensional soap films, we show that these spatial structures are determined by the ratio between the boundary layers and their separation distance. The spatial structures then determines the physical mechanism for the decay of vortex streets. We find that the conventional mushroom structure decays due to the mixing, and the separated rows structure decays because its arrangement is hydrodynamically unstable. 
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