Bulletin of the American Physical Society
73rd Annual Meeting of the APS Division of Fluid Dynamics
Sunday–Tuesday, November 22–24, 2020; Virtual, CT (Chicago time)
Session P19: Vortex Dynamics and Vortex Flows: Instability (3:10pm  3:55pm CST)Interactive On Demand

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P19.00001: Evolution in the outer domains of NavierStokes could allow finitetime dissipation to form without singularities. Robert Kerr Could the enstrophy $Z$ scaling regime $\sqrt{\nu}Z$ originally identified during trefoil vortex knot reconnection (JFM 839, R2, 2018), be universal? And can it lead to finite energy dissipation $\Delta E_\epsilon=\int_0^{t_\epsilon} \epsilon\,dt$ as $\nu\to0$? This reconnection regime is characterized by linear $B_\nu(t)=(\sqrt{\nu}Z(t))^{1/2}$ up to a time $t_x$ with fixed $B_\nu(t_x)$. Its enstrophy growth for $T_c(\nu)>t_x$ is $Z_{\nu}(t) \sim \nu^{1/2}(T_c(\nu)t)^{2}$, giving an energy dissipation rate $\epsilon(t_x)=\nu Z(t_x)\to0$ as $\nu\to0$. Nested coiled rings also have this scaling as they reconnect. Recently, two antiparallel vortex calculations have gotten $B_\nu(t)$ scaling during reconnection, identified by finite circulation exchange $\Delta\Gamma$. For trefoils, finite $\epsilon$ appears at $t_\epsilon\approx 2t_x$, with similar results for very long antiparallel vortices. By taking advantage of the antiparallel symmetries, the new highresolution data can identify a front perpendicular to the line of reconnection that would be blocked if the domains were fixed, perhaps explaining why the $B_\nu(t)$ scaling requires growing domains. These finitetime events are consistent Sobolev regularity inequalities, forming finite $\Delta E$ without singularities. [Preview Abstract] 

P19.00002: Threedimensional instabilities of vortices shed from a plunging wing: Experiments Onur Son, Zhijin Wang, Ismet Gursul The experiments are performed in a water tunnel to investigate the instabilities of vortices on a plunging wing. Parameters for periodic plunging motion are selected as k$=$0.25 to k$=$3 for reduced frequency, A/c$=$0.1 and A/c$=$0.5 for peaktopeak amplitude ratio at a Reynolds number of 10,000. Vortical structures are revealed via threedimensional velocimetry system. It is found that the instabilities on the leadingedge vortex are starting from the tip region. The leg of the leadingedge vortex remains attached to the wing surface until it sheds while instabilities are forming a helical shape similar to mode m$=$1. The wavelength of the instabilities on the leadingedge vortex are growing both in time and space. Both plunging frequency and plunging amplitude have an impact on instability wavelengths. Tip vortex has spiraling instabilities and the wavelength is found to be roughly constant for all cases in the measurement region. Trailingedge vortex has similar instability characteristics with the tip vortex when they interact. [Preview Abstract] 

P19.00003: Curvature instability of a vortex ring with density differences and surface tension Ching Chang, Stefan Llewellyn Smith Curvature instability is a parametric instability of vortex rings that was first reported by Hattori and Fukumoto (2003) in the shortwavelength limit and then investigated using normal modes in Fukumoto and Hattori (2005). The basic state consists of a Rankine vortex tube perturbed by small curvature of $O(\epsilon)$. This leads to resonance between two neutrally stable Kelvin waves whose azimuthal wavenumbers are separated by 1, leading to instability. We calculate the curvature instability using normal modes for a thin vortex ring whose density differs from that of the ambient fluid, with surface tension acting at the boundary of the ring. The growth rate and the instability bandwidth are calculated for the principal modes, defined appropriately, and some of the nonprincipal modes. Results show that density increases with growth rate of the instability for long waves, while surface tension has a marginal effect. [Preview Abstract] 

P19.00004: Flow Instabilities in Flutelike Instruments Rodolfo Ostilla Monico, Ahmed Janjua Flutelike instruments have a common working mechanism that consists of blowing across one end of a resonating tube to produce a jet of air that is directed at a sharp edge producing sound. Analysis of operation of flutes involves numerous research fields including fluid dynamics, physics, and aeroacoustics. In this study, an effort has been made to investigate more about the flow of air in flutes using 2D Direct Numerical Simulation. An analysis of the response of the jet of air by varying the jet width, profile, offset, and Reynolds number, and the flute labium angle in a 2D domain is the main focus of this study. We find that oscillations are sustained in the Reynolds number range 10002000, with lower Reynolds numbers producing no oscillations, and large Reynolds numbers developing a chaotic flow. These ranges also slightly differ for different parameters. We quantify the oscillation period and find heavy dependence on all parameters. These results lay out a framework to continue investigating instabilities in flutelike instruments. [Preview Abstract] 

P19.00005: Threedimensional instabilities of vortices shed from a plunging wing: Computations AnKang Gao, Spencer J. Sherwin, Chris D. Cantwell The threedimensional (3D) instability of leadingedge vortex (LEV) in the flow past a plunging wing is studied numerically using the open source spectral element code, Nektar$++$. The plunging motion has a reduced frequency of k$=$2, and a peaktopeak amplitude of A/c$=$0.5. The effect of Reynolds number based on the chord length c and incoming flow velocity is explored in the range from 200 to 10000. BiGlobal linear stability analysis shows an unstable mode with a spanwise wavelength longer than 1.5c exits for Re \textgreater $=$ 400. This wavelength increases with Reynolds number. In this unstable mode, the LEV forms a bending mode; the back and forth flow around the leading edge is the main cause of instability. 3D direct numerical simulation of infinite wing shows the disturbed LEV has a saturate peaktopeak bending amplitude of 0.06c during the upward stroke and that it breaks down in the downward stroke. Numerical simulation of finite wing is also conducted. Excellent agreement is found between the current numerical result and experimental result (see the Experiments part). Unlike the infinite span case, LEV of the finite wing forms a helical mode and its wavelength is around 1c. [Preview Abstract] 

P19.00006: Koopman analysis of vortex dynamics KeChu Lee, Sam KaufmanMartin, Samaneh Sadri, Poorva Shukla, Igor MeziÄ‡, Paolo LuzzattoFegiz Vortex dynamics plays an important role in transitional and turbulent flows, where instabilities play a fundamental role. Instabilities are usually understood through the lens of linear stability analysis (LSA), which is centered around equilibria. However, one often needs to understand dynamics starting from an unsteady flow field, found from simulation or experiment. Here we explore the ability of Koopman mode decomposition (KMD) to provide such an analysis. We examine the dynamics of likesigned vortex pairs with different initial area ratios. We find that KMD reliably detects the distinctive phases of vortex merger. We quantify the eigenvalues as a function of flow geometry, and compare eigenvalues and eigenmodes from KMD to those from LSA. These results suggest a path forward towards using KMD for datadriven modeling of vortex flows. [Preview Abstract] 

P19.00007: Characteristics of vortices associated with a nonbuoyant elevated jet in crossflow. Jyoti Gupta, Arun K. Saha Jet emission from elevated stack draws attention towards environmental field and its industrial applications which include smoke exhausting from stack into atmosphere and sewage water disposal in deepocean. In the present work, the dynamics of elevated jet issuing into crossflow are studied using the streak image of dye visualization and the mean velocity measured using Laser Doppler Velocimetry (LDV). The crossflow environment is generated in a water tunnel where the jet discharge same fluid as that of crossflow making it nonbuoyant. The experiments have been performed for axisymmetric round jet of aspect ratio of 9.0 with the velocity ratio varying from 0.161.5 to unveil the physics of vortex formation at a Reynolds number (calculated based on free stream crossflow velocity and jet external diameter) of 2000. Result shows the formation of KH instability at the upstream jet shear layer along with other vortices found to vary on velocity ratio: (i) clockwise vortices (for velocity ratio ranging from 0.160.4), (ii) backward rolling vortices (for velocity ratio having range 0.50.67), (iii) swing induced mushroom vortices (for velocity ratio of 0.741.0) and (iv) jet like vortices (for velocity ratio ranging from 1.11.5). [Preview Abstract] 

P19.00008: Elliptical Instability in Asymmetric Vortex Pairs Doris Stumps, Keiko Nomura The elliptical instability in two unequal counter rotating vortices is studied with numerical simulations for Re$_{\mathrm{\Gamma \thinspace }}=$ 3100. The initially Gaussian vortices with nearly equal circulation but unequal peak vorticity and core size are subjected to random perturbations, and their time evolution in the linear and weakly nonlinear phases are examined. Asymmetry is achieved by simultaneously increasing core radius and lowering peak vorticity on one vortex while keeping the properties on the other vortex fixed between simulations. The effects of this asymmetry on the interaction between the two vortices are then studied, and it is found that deformation is more prominent on the larger vortex, which wraps around the smaller one; the most unstable wavenumber increases for increasingly asymmetrical cases; the global growth rate of the most unstable mode is higher in the weakly asymmetrical pair than the symmetrical pair, but the growth rate begins to decrease as the disparity in core size and peak vorticity becomes larger than a critical threshold. Details including vortex separation, relative inclination angle, and strain rate are presented. [Preview Abstract] 
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