Session P18: Vortex Dynamics and Vortex Flows: General (3:10pm - 3:55pm CST)

Universal separation scaling for vortex reconnection in classical and quantum fluids

Reconnection plays a significant role in the dynamics of plasmas, polymers and macromolecules, as well as in numerous laminar and turbulent flow phenomena in both classical and quantum fluids. Extensive studies in quantum vortex reconnection show that the minimum separation distance between interacting vortices follows a $\delta (t) \sim t^{1/2}$ scaling. Due to the complex nature of the dynamics (e.g. the formation of bridges and threads as well as successive reconnections and avalanche), such scaling has never been reported for (classical) viscous vortex reconnection. Using direct numerical simulation of the Navier--Stokes equations, we study viscous reconnection of slender vortices, such as colliding vortex rings, orthogonal vortex tubes, and trefoil knotted vortex. For separations that are large compared to the vortex core size, we discover that $\delta (t) $between the two interacting viscous vortices surprisingly also follows the 1/2-power scaling for both pre- and postreconnection phases. The prefactors in this 1/2-power law depend not only on the initial configuration but also on the vortex Reynolds number (or viscosity). Our finding in viscous reconnection, complementing numerous works on quantum vortex reconnection, suggests that there is indeed a universal route for reconnection -- an essential result for understanding the various facets of the vortex reconnection phenomena and their potential modelling, as well as possibly explaining turbulence cascade physics.   

Chaotic Advection by Two Helical Vortices

We studied numerically the fluid motion induced by two equal helical vortices immersed in an inviscid, incompressible, and unbounded fluid. The vortices, being thin tubes of uniform vorticity on their circular cross section, move steadily when they are symmetric, i.e., when they occupy diametrically opposite points of the imaginary cylinder where they are coiled. If the initial configuration is slightly asymmetric, the vortices move with varying linear and angular velocities, performing a periodic motion analogous to the leapfrogging of ring vortices. We analyzed the vortex motion, as well as the associated fluid advection, as a function of the initial asymmetry and the vortices' pitch and core radius. We focused on two of the four regimes previously identified for the symmetric, steady case (Velasco Fuentes, J.F.M. 842, R2, 2018), namely, large-pitch and small-pitch vortices of relatively large core (within the thin-tube approximation). We found that the initial asymmetry slightly reduces the amount of fluid carried by large-pitch vortices, as regions of intense stirring gradually appear. In contrast, even the smallest asymmetry greatly reduces the amount of fluid carried by small-pitch vortices and produces large regions of intense stirring.   

Influence of strip thickness and roughness on flow induced motion of circular cylinders

Experiments were conducted to develop a thorough understanding of the mechanisms involved in enhancing flow induced motion (FIM) of circular cylinders with surface protrusions. Two types of strips -- smooth and rough were attached to the surface of a circular cylinder in order to decouple the effects of thickness from roughness in FIM response and the energy transfer process. Vibration amplitudes and frequencies were analyzed as a function of strip roughness ratio (height of roughness element/strip thickness, varied from 0{\%} to 100{\%}) and strip thickness ratio (strip thickness/ cylinder diameter, varied from 0.8{\%} to 8.2{\%}). An increase in strip thickness increased FIM vibration amplitudes. In comparison to smooth strips, the rough strips were found to result in an identifiable suppression of FIM amplitudes over the strip thickness ratio range of 2.4{\%} to 4.9{\%}. Both strip types were ineffective in inciting galloping oscillations at a strip thickness of 0.8{\%} and displayed negligible differences in FIM response beyond a strip thickness ratio of 8.2{\%}. System characteristics such as mechanical power and energy transfer efficiencies were also evaluated and will be discussed.   

Vortex droplet co-axial interaction: insights into the vortex dynamics

This experimental work is focused on the vortex dynamics observed during the co-axial interaction of a vortex ring with an incoming droplet. The complete progression of collision is sub-divided into three regimes which include deformation (regime-I), stretching and engulfment (regime-II) and break-up (regime-III) of the droplet. A slug of fluid is injected into a stagnant fluid stored in a chamber for generating vortex rings. The injection pressure of the fluid is varied to obtain different values of circulation ($\Gamma )$ strength (45- 161 cm$^{\mathrm{2}}$/sec). We have investigated the effect of the interaction on different characteristics of vortex rings, which includes pressure distribution, vorticity distribution, circulation strength, total energy, and total enstrophy. It was noticed that collision leads to a significant reduction in these parameters. The reduction in these characteristics is more (\textasciitilde 30{\%}) at lower vortex ring strengths.   

Experimental Investigation of a Vortex Ring Impinging on a Concave Cavity

The fundamental physical interaction of a vortex ring impinging on a concave hemispherical cavity is investigated, which is a flow scenario that finds wide application in nature and engineering flows. A vortex ring of formation number $F =$ 2.67, and Reynolds number \textit{Re }$=$ 1450 is generated using a piston-cylinder arrangement in a water tank. The interaction is investigated for six different hemispherical diameters, where the ratio of vortex ring radius to hemisphere radius ($\gamma )$ varies as $\gamma = $0 (flat plate), 1/4, 1/3, 2/5, 1/2, and 2/3. For \quad $\gamma \quad =$ 1/4, 1/3, and 2/5, a secondary vortex ring forms and rotates around the primary vortex ring, analogous to flat plate interactions. However, a Widnall-like instability occurs in the secondary ring with the upper ends of the loops subsequently experiencing a head on collision, while the lower ends rotate around the core of the primary ring. This results in ejection of the secondary vorticity away from the hemispherical surface. The escape velocity of the secondary vortex increases with increasing values of $\gamma $. For $\gamma \quad =$ 1/2, the induction of the primary ring with the lip of the hemisphere prior to impact induces edge vorticity on the lip that interacts with, and weakens, the secondary vorticity. The lower ends of the secondary ring subsequently experience head on collision instead of the upper ends. For $\gamma =$ 2/3, the primary ring directly impacts on the edge of the hemispherical surface.   

Helicity Dynamics in Unknotting and Unlinking Events of Topologically Complex Vortex Flows

In this study, we address the question of whether helicity is conserved through viscous reconnection events in vortical flows. To answer this question, we performed direct-numerical-simulations (DNS) focused on two topologically complex vortex flow cases: (1) a trefoil knot, and (2) a two-ring linkage, for various vortex core radii. The adopted DNS framework relies on a block-structured Adaptive Mesh Refinement (AMR) technique. A third, a companion simulation of the collision of two unlinked vortex rings is also performed to serve as a baseline case for trivial helicity dynamics. The results show that a well-defined helicity jump occurs during the unknotting/unlinking events of cases (1) and (2), and is initiated after the complete annihilation of the local helicity density magnitude in certain flow regions. Similar helicity dynamics are observed for various core radii explored for cases (1) and (2), while they are not present for the third topologically trivial colliding-ring case. Further analysis of the simulation results suggests that the integral of helicity density in a volume surrounding the reconnection region can be used as an estimator for the magnitude of the helicity rise during the reconnection event. Finally, a mechanistic model is provided to explain the local helicity annihilation, which relates the helicity annihilation rate to circulation transfer rate and local helicity content.   

Helicity and its Geometric Evolution in Viscous Vortex Loops

The helicity of a laminar vortex ring is prescribed by its geometry in the forms of writhe and twist. In viscous fluids, helicity is not conserved, but nonetheless its evolution is naturally characterized by the geometry and topology of the vorticity field. By generating helical vortices using hydrofoils, we are able to measure their helicity and its evolution over a range of Reynolds numbers. Fully resolved DNS simulations with adaptive mesh refinement provide complementary insight. We present an analytic model for helicity evolution in vortex tubes with a natural geometric interpretation and compare its predictions to experiments and simulations.   

Vortices by design in pipe flow by a mechanism of Langmuir circulation

Using DNS we study a mechanism for creating secondary flow by design in the form of longitudinal vortices in pipe flow. By furnishing the pipe wall with a pattern of crossing waves, vorticity already present in the wall boundary layer is rotated into the streamwise direction by a resonant kinematic mechanism known in oceanography as `CL1' (Craik & Leibovich's 1st mechanism), one of the drivers of Langmuir circulation. CL1 is strongest when the wall waves cross at an acute angle of $\varphi \sim 10^\circ$ to $20^\circ$ (a `contracted egg carton' pattern), vanishes in the vicinity of $45^\circ$ and is weak and oppositely directed for larger angles (`protracted egg carton'). The results are compared to a simple theory in the vein of Craik (1970).\\ \\ CL1 co-exists with a dynamic mechanism of secondary motion due to the asimuthally varying wall rougness caused by the pattern. For the `contracted' pattern the two effects oppose each other with CL1 prevailing, whereas the dynamic effect dominates at $45^\circ$ and above, causing a reversal of circulation. Flow reversal also results with increasing amplitude due to flow separation.\\ \\ We presently report only laminar simulations; the effect on turbulent pipe flow is a potentially important question for the future.   

Chiral Edge Modes in Helmholtz-Onsager Vortex Systems

Vortices play a fundamental role in the physics of 2 dimensional (2d) fluids across a range of length scales, from quantum superfluids to geophysical flows. Despite a history dating back to Helmholtz, the study of point vortices in a classical 2d fluid continues to present challenges, owing to its unusual statistical mechanics. Here we show that these Helmholtz-Onsager systems contain edge modes at subcritical temperatures, extending a previously identified analogy between vortex matter and quantum hall systems. Through numerical simulations and mean field models, we demonstrate that angular momentum conservation in a disk leads to a symmetry protected edge mode. These edge modes are robust, persisting in nonconvex domains. Furthermore, using analytics and numerical simulations, we exhibit a subcritical phase separation associated with edge modes in neutral Helmholtz-Onsager systems.   

The role of core flattening during vortex reconnection

Vortex reconnection is the only fundamental vortex dynamics interaction capable of alternating the topology of vortex tubes. The process is so extreme that Moffatt and Kimura (2019) have considered it to be a viable path towards a finite-time singularity of the Navier-Stokes equations. To date, researchers have mainly focused on the effects of Reynolds number, leaving the roles of initial geometry relatively undocumented in the literature. Herein, we explore the contribution of initial collision angle to the reconnection process through simulations of vortex ring collisions. In particular, we investigate the influence of approach angle on the core flattening phenomenon during impact, which alters the reconnection process. The simulations elucidate the stages of core flattening and its physical underpinnings. A simplified inviscid finite area vortex model based on contour dynamics is introduced to complement the simulations and demonstrate that the primary core flattening mechanism is actually the result of the ejection of excess vorticity in the reconnection threads. Last, the relationship between core flattening and the end of the reconnection process will be discussed.   

Analysis of vortex reconnection sound via decomposition of Lighthill's source term

Vortex reconnection is a dominant source of sound produced in vortical flows (Daryan \textit{et. al.}, Phys. Rev. Fluids, 5, 062702(R) (2020)). We study the noise generation mechanisms in the reconnection of two antiparallel vortices at the vortex Reynolds number of 1500 via high-order direct numerical simulations of the compressible Navier-Stokes equation. A decomposition of the Lighthill's source term is provided; the evolution of each term is investigated for three subsonic Mach numbers of 0.3, 0.5, and 0.7. More specifically, the role of the tilting of the vorticity vector and deviation from the isentropic condition in sound generation is explored. Finally, scaling relations based on Mach number are considered for the dominant source terms and far-field sound. The current study provides a detailed analysis of the sound generation mechanism in a three-dimensional canonical viscous flow.   

Dynamics and deformation of interacting vortices in background shear

Although the dynamics of a vortex under the influence of a background strain field and under that of another nearby vortex are often studied separately, in complex flows such as turbulence, both influences may be present simultaneously. This combined influence is here investigated by considering the fundamental case of a two-dimensional co-rotating vortex pair, having circulation ratio $Λ = Γ_1/Γ_2 = (a_1/a_2)^2(ω_1/ω_2)$, interacting in the presence of linear background shear, having vorticity $ω_S$ and relative strength $ζ = ω_S/ω_2$. Numerical simulations are performed for viscous flow, and the main flow regimes, pairing and separation, are identified. This work focuses on vortex-dominated pairings: in this subregime, the vortices revolve with varying peak-peak distance b, causing the strain rate induced by each vortex on the other to vary in time, while the orientation of this vortex-induced strain rate relative to that of the fixed background shear also varies. This results in a periodic phenomenon in which the deformation of each vortex varies with the relative orientation of the vortices and the shear. This phenomenon and its effect on the subsequent interaction outcomes are examined and discussed.   

Persistent Homology of FTLE Patterns Generated by Point Vortex Motion

The method of Persistent Homology (PH) was used to investigate the structure and evolution of a set of point vortices moving and interacting under their own induced velocities. PH is a multiscale approach to quantifying topological features, such as connected components, topological circles, and trapped volumes in point clouds and in level sets of scalar fields. PH was applied to the point cloud of vortices, to the finite-time Lyapunov exponent (FTLE) scalar field, and to the point cloud of points on ridges of FTLE. The goal was to evaluate to what degree their topological features can be quantitatively correlated to each other, for the purpose of robust classification of regimes of fluid motion. In particular, the talk will explore how vortex circulation and FTLE magnitude can be incorporated into the classical distance-based PH framework by comparing generated persistence diagrams and evaluating their interpretation in the context of fluid physics. Results indicate that joining PH and FTLE methods may lead to a way of robust pattern detection in vortex-dominated fluid flows.   

Reynolds Number Effects on Vortex Merging Criterion

Asymmetric vortex pair interactions are effectively characterized by a mutuality parameter, $MP=S_1/S_2$, which compares the relative straining, $S_i=s_i/w_i$, experienced by each vortex (Folz and Nomura, JFM 2017). When $S_1$ and $S_2$ are comparable, $MP\approx 1$, a two-way interaction ensues: both vortices undergo core detrainment ($S_i>S_c_r$), which enables a mutual entrainment process to form a compound vortex. As relative straining becomes more disparate, mutuality is diminished until $MP>MP_c_r$, and the interaction is one-way: one vortex detrains and is destroyed by the other, which remains unaffected. The value of the merging criterion, $MP_c_r$, differed for the values of Re = 1000 and 5000 considered. In this study, a range of $Re=250$ to 50000 is investigated using numerical simulations. Three flow regimes are identified: when $Re<500$, diffusion dominates, and in the absence of convection, $MP_c_r$ is not observed; when $5005000$, convection dominates and $MP_c_r$ is independent of $Re$. These results provide insight to more complicated flows, such a 2D turbulence, which are driven by asymmetric vortex interactions occurring over a range of $Re$.   

Experimental study on flow-induced vibration of a flexible cylinder with high-mass ratio in tandem arrangement

Flow-induced vibration of a flexible cylinder placed in the wake of a stationary cylinder is studied, experimentally. The flexible cylinder with an aspect ratio of 47 and a mass ratio of 120 was held fixed at both ends and placed horizontally in the wake of the upstream rigid cylinder in the test-section of a subsonic wind tunnel. The dynamic response of the cylinder is studied in both the streamwise (inline) and transverse (crossflow) directions for center-to-center spacing range from 3 to 9 times the diameter of the cylinder. Amplitudes and frequencies of oscillation, as well as flow forces on the cylinder are studied in the reduced velocity range of $U^*=3.3-50.3$ and the Reynolds number range of $Re=3,057-46,536$. Despite the high-mass ratio of the flexible cylinder, higher modes of vibrations up to the fifth mode are excited in both the crossflow and inline directions, owing to the high-flexibility of the cylinder. Both odd and even modes are excited in the crossflow and inline directions. As the separation distance between the cylinders increases, the amplitudes of oscillation increase over a wider range of reduced velocities. Spanwise trajectories of motion are studied and regions along the length of the cylinder that are excited or damped by the flow, are identified.   

Scaled Experimental Investigation of Downburst Physics in a Crossflow

The behavior of downbursts in a crossflow and their interaction with the ground is investigated in order to better understand their complex behavior and derive appropriate scaling relations. Downbursts are extremely powerful and relatively under-examined atmospheric phenomena that cause extensive damage to both ground structures and aircraft within the vicinity. Most damage is generally caused by an outburst of descending air upon impact with the ground. Tests are performed in a water tunnel using an elevated cylinder of dense fluid to simulate the high-density air seen within the downburst. The fluid is released and its interaction with the ground is observed using qualitative and quantitative flow visualization techniques, including particle image velocimetry. Observations quantified to develop scaling laws to apply to full-scale downbursts. Conditions analyzed include a range of quiescent and crossflow conditions as well as a variety of densities and varying sizes and volumes of the downburst as previous tests showed correlation between these factors and the resulting outburst strength. Results are compared against other experimental simulations, theoretical scaling, and atmospheric observations.   

Harnessing vortices for the energy-efficient jet propulsion

Jellyfish are among the most energy-efficient swimmers: their evolved physiology and propulsive motion offer them the advantage of being able to generate large amounts of thrust at low energy costs. These organisms optimally harness vortices and inspire designs for vehicles for underwater transport. Here, we present a robust vortex propulsor that generates thrust through pulsed jet propulsion. Vortex rings of varying strengths are produced by controlling a large range of input motion profiles. Using velocity fields from particle image velocimetry and force measurements, we relate vortex ring formation, pinch-off, and separation in the wake to the transient thrust output of the device. We validate and use a pressure-methodology for characterizing vortex ring pinch-off and its separation from the trailing jet. Features in the pressure field can provide a novel means of characterizing vortices. These findings contribute to our understanding of the role of vortices in jet propulsion and enable us to manipulate them for the design of energy-efficient bio-inspired vehicles.   

Fully nonlinear waves on quantized vortex rings

Vortex filaments are primitive geometric elements in a variety of physical theories, e.g., classical and quantum hydrodynamics, astrophysical plasmas, biological soft matter etc. Our work studies curvature driven binormal flows induced by isolated vortex filaments defining the skeleton upon which free superfluid turbulence must end. Here, the flow of an irrotational inviscid fluid can be mapped onto the evolution of the curvature and torsion of isolated vortices. Dimensional reductions of this type originated in the early 20th-century. The first of which, known as the local induction approximation, asserts that a vortex filament induces an ambient flow, aligned with the local binormal vector, whose speed is proportional to the curvature. This flow is integrable and, as we have found, represents the lowest-order approximation to a fully nonlinear arclength conserving Hamiltonian flow consistent with inviscid fluid dynamics. We briefly discuss how these higher-order corrections allow localized curvature profiles to transport bending along the vortex by leveraging nonlinear gain/loss and dispersion in the vortex medium. In particular, we review the simulations of fully nonlinear waves propagating along simple closed vortex filaments embedded in a three-dimensional superfluid.   

Vortex Axis-line Extraction with the VATIP Algorithm: Application in Newtonian and Viscoelastic Channel Flow

Vortex is a central concept in the understanding of turbulent dynamics. Objective algorithms for the detection and extraction of vortex structures can facilitate the physical understanding of turbulence regeneration dynamics by enabling automated and quantitative analysis of these structures. Despite the wide availability of vortex identification criteria, they only label spatial regions belonging to vortices, without any information on the identity, topology, and shape of individual vortices. This latter information is stored in the axis-lines lining the contours of vortex tubes. We propose a new tracking algorithm which propagates along the vortex axis-lines and iteratively search for new directions for growth. Vortex axis-lines in near-wall turbulence are automatically identified and extracted. Vortices are classified into different shapes, including quasi-streamwise vortices, hairpins, hooks, and branches, according to the axis-line topology. The VATIP (vortex axis tracking by iterative propagation) algorithm is applied to both Newtonian and viscoelastic turbulence to reveal vortex organization patterns and self-sustaining dynamics.   

Creation of an isolated turbulent blob sustained by vortex ring injection

We experimentally study a steady, localized blob of turbulence generated and sustained by the collision of multiple vortex rings. Through PIV and 3D PTV we examine the mass flux, distributions of kinetic energy and enstrophy, and turbulence statistics. Our measurements reveal that the blob consists of a turbulent core surrounded by comparatively quiescent fluid. The intensity and geometry of the turbulent blob can be controlled by altering properties of the injected coherent vortex loops. This system provides an ideal playground to investigate the generation and the decay of turbulence with controlled inputs of energy, enstrophy, and helicity.   

Automated Identification of Vortex properties from individual vector fields using Bayesian approach.

While we have architypes for a number of turbulent coherent structures, such as a prograde vortex paired with a saddle point in 2D velocity fields of wall-bounded flows, it remains difficult to identify these structures using an automated procedure due to the complexity of the flow field and the number of parameters required. Here, we propose a Bayesian approach for the local identification of turbulent coherent structures by matching a model structure to turbulent velocity fields. As an initial validation of this approach, we employ a Markov Chain Monte Carlo solver to automate the extraction of the prograde vortex properties from individual PIV velocity fields, including estimation of convective velocity, which cannot be achieved with traditional vortex localization methods. Gaussian mixture models are then used to isolate portions of the resulting probability distributions corresponding to individual vortices in close proximity. These results enable the automated clustering of hairpin candidates into packets moving at the same convective velocity and investigations of the relationship between prograde and retrograde vortices. We intend to extend the use of this approach to more complicated flow structures such as vortex/saddle-point pairs.