Bulletin of the American Physical Society
74th Annual Meeting of the APS Division of Fluid Dynamics
Volume 66, Number 17
Sunday–Tuesday, November 21–23, 2021; Phoenix Convention Center, Phoenix, Arizona
Session E24: Vortex Dynamics and Vortex Flows: Instability |
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Chair: John McHugh, University of New Hampshire Room: North 224 B |
Sunday, November 21, 2021 2:45PM - 2:58PM |
E24.00001: Linear instability analysis of wake vortices by a spectral method using mapped Legendre functions Sangjoon Lee, Philip S Marcus A spectral-Galerkin method using mapped Legendre functions with a poloidal-toroidal decomposition is presented to find eigenmodes of q-vortices in an unbounded domain with correct boundary conditions. In the inviscid limit, the method can resolve a continuous spectrum of neutral modes despite the presence of critical-layer singularities. Spurious instabilities are removed as numerical parameters, including a map parameter, are adjusted to improve spatial resolution. When viscosity is given, a novel set of numerically converging modes is found, forming two contiguous curves in the spectrum. By fine-tuning the map parameter, their associated eigenvalues densely fill up the curves unlike the discrete ones. Each of the modes commonly exhibits a dominant wave structure localized in the vicinity of the critical layer due to viscous regularization and a minor structure comparable with its inviscid counterpart. The results strongly imply that these curved spectra are true viscous remnants of the inviscid continuous spectrum, which are known to contribute to destabilization via transient growth. The bifurcation of the spectrum is thought to be related to two-fold degeneracies due to the critical-layer singularities in the inviscid singular modes. |
Sunday, November 21, 2021 2:58PM - 3:11PM |
E24.00002: The stability of a horizontal stratified vortex John P McHugh A trailing vortex behind a wing moving through a stratified fluid will act to twist the density field into a pattern where the density profile continuously overturns along the axis of the vortex. This configuration is approximated here with a density field that is overturning periodically along the axis of the vortex. The matching velocity field is found approximately assuming weak stratification and constant axial vorticity at leading order, and confining the flow to a fixed radius. This base flow is shown to be unstable to a wave triad consisting of two disturbance waves and a component of the base flow as the third `wave'. Three components of this base flow lead to instability: 1) the twirling component, 2) the streaming component, and 3) the rolling component. All three instabilities depend strongly on the axial length for the density field to overturn (the pitch). The twirling and rolling instabilities are important when the pitch is small, and they also depend on the Froude number. The streaming instability is dominant when the pitch is large, and is independent of the Froude number. |
Sunday, November 21, 2021 3:11PM - 3:24PM |
E24.00003: Destabilizing Neutrally Stable Wake Vortices Using Degenerate Eigenmodes Jinge Wang, Sangjoon Lee, Philip S Marcus We demonstrate a method to de-stabilize linearly, neutrally stable q-vortices and other columnar vortices in a manner that has the potential to mitigate hazards of aircraft trailing wake vortices. Due to the symmetries of the vortices, in general, it is impossible to destabilize a neutral eigenmode by linearly perturbing the flow. Rather, it is necessary to simultaneously perturb a pair of degenerate eigenmodes such that one grows while the other decays. To quickly "tune" the flow to create degenerate eigenmodes from non-degenerate eigenmodes, non-degenerate perturbation theory is used. Then, to determine the required linear resonant perturbation to cause one of the eigenmodes of the degenerate pair to go unstable with a fast growth rate, degenerate perturbation theory is used. The resulting perturbation is then used in an initial-value calculation to determine the nonlinear evolution and growth of the instability. The special role of eigenmodes with critical layers is examined. |
Sunday, November 21, 2021 3:24PM - 3:37PM |
E24.00004: Vortex Line Pair Instabilities in a Stable, Density Stratified Fluid Jabari Lawrence We present an experimental study of the flow instabilities developed by a pair of counter-rotating vortices descending in a stable, density-stratified environment. The vortex line pair is generated by flapping two sharp-edged long foils in a way that both the vortex line Reynolds number and vortex line gap can be controlled. The instabilities developed can be captured by the shadowgraph imaging and refractive index matching methods. The results can shed new light on how the vortex wake in a stratified environment is affected by the Reynolds number and Froude number. |
Sunday, November 21, 2021 3:37PM - 3:50PM |
E24.00005: Why are Knotted Vortices Unstable? Dustin P Kleckner, Stefan Faaland, Diego Tapia Silva Concentrated filaments of vorticity are a ubiquitous feature of flow at high Reynolds number. While many models of vortex behavior focus on simple geometries like rings or lines, vortices in real flows (e.g. turbulence) have a complex structure of links and tangles. This should significantly affect their behavior: simulations and experiments have shown that even elementary knotted vortices are unstable, unlike rings or lines. Crucially, this instability appears to be independent of the small scale details of the fluid, and the same general behavior is seen in classical fluid experiments, superfluid simulations, and even reduced order vortex filament models. This suggests the instability is driven by the large-scale advection of the vortex lines. In particular, I will show that self-stretching produced by the knotted vortices leads directly to instability and reconnections. |
Sunday, November 21, 2021 3:50PM - 4:03PM |
E24.00006: Why do Knotted Vortices Stretch? Stefan Faaland, Dustin Kleckner, Diego Silva
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Sunday, November 21, 2021 4:03PM - 4:16PM |
E24.00007: Linear stability and optimal perturbations of a trailing vortex pair in ground effect Mark A Herndon, Justin W Jaworski The stability characteristics of a trailing vortex pair interacting with its image in the ground plane is formulated analytically and studied numerically. The theoretical framework models the inviscid interaction between a counter-rotating pair of perturbed finite-core vortices near a planar surface. The stability equations are derived by matching the Biot-Savart integrals of the vortices with their temporally-varying position vectors, which are subject to constraints that represent a ground-image system. The stability problem is then cast into an optimal perturbation analysis to deduce the maximum growth rate for a prescribed disturbance as a function of time and the induced vortex trajectories. |
Sunday, November 21, 2021 4:16PM - 4:29PM |
E24.00008: Vortex bursting on a vortex tube with initial core-size perturbations Lingbo Ji, Wim M Van Rees When a straight vortex tube is endowed with core-size perturbations, the differential rotation along the tube leads to the tilting of vortex lines and the generation of twist waves. The waves propagate and collide, resulting in a drastic expansion of the vortex core and the formation of an annular structure with high azimuthal vorticity, a phenomenon known as vortex bursting. Such phenomenon is relevant for understanding the behavior of aircraft trailing wakes, as well as the dynamics of vortical structures in turbulent flows. In this talk we examine vortex bursting using numerical simulations on straight vortex tubes with initial perturbations and focus on the effects of different perturbation amplitudes. We investigate quantitatively each stage of evolution, including early-time twist wave propagation, bursting (time scale and intensity) and the late-time flow evolution along the tube. |
Sunday, November 21, 2021 4:29PM - 4:42PM |
E24.00009: Dynamic triade interactions by dual vortex shedding in a laminar jet Mengjia Ren, Preben Buchhave, Clara M Velte Interactions between Fourier modes, so-called triad interactions, are widely seen as fundamental components in the physical process of turbulence. In this experiment, we study the triad interactions initiated by a single or a pair of near-sinusoidal eddies generated by vortex shedding from rods inserted into the core of a laminar jet in air. We measure the interactions as they develop downstream and plot the spectral components as they are created by the nonlinear effect of the convection. We analyze the combinations of frequency components and their cascading into higher frequency components and compare to the results of a simulation of Navier Stokes equation operating on the velocity signal measured close to the rods. |
Sunday, November 21, 2021 4:42PM - 4:55PM |
E24.00010: Computer simulation of the dynamic development of triad interactions created by dual vortex shedding Preben Buchhave, Mengjia Ren, Clara M Velte Interactions between modes in a turbulent flow, so-called triad interactions, are essential to the process of turbulence development. We present results of a computer simulation of an experiment with vortex shedding from two rectangular rods mounted in the core of a laminar jet [1]. The purpose is to follow the cascade process initiated by two clean oscillatory modes created by vortex shedding from two slightly different rectangular rods mounted parallel to and near each other. |
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