Vortex Reconnection Research Articles

Sound generation mechanism of compressible vortex reconnection

We study the sound generation mechanism of initially subsonic viscous vortex reconnection at vortex Reynolds number $Re~(\equiv \text {circulation}/\text {kinematic viscosity})=1500$ through decomposition of Lighthill's acoustic source term. The Laplacian of the kinetic energy, flexion product, enstrophy and deviation from the isentropic condition provide the dominant contributions to the acoustic source term. The overall (all time) extrema of the total source term and its dominant hydrodynamic components scale linearly with the reference Mach number $M_o$ ; the deviation from the isentropic condition shows a quadratic scaling. The significant sound arising from the flexion product occurs due to the coiling and uncoiling of the twisted vortex filaments wrapping around the bridges, when a rapid strain is induced on the filaments by the repulsion of the bridges. The spatial distributions of the various acoustic source terms reveal the importance of mutual cancellations among most of the terms; this also highlights the importance of symmetry breaking in the sound generation during reconnection. Compressibility acts to delay the start of the sequence of reconnection events, as long as shocklets, if formed, are sufficiently weak to not affect the reconnection. The delayed onset has direct ramifications for the sound generation by enhancing the velocity of the entrained jet between the vortices and increasing the spatial gradients of the acoustic source terms. Consistent with the near-field pressure, the overall maximum instantaneous sound pressure level in the far field has a quadratic dependence on $M_o$ . Thus, reconnection becomes an even more dominant sound-generating event at higher $M_o$ .

Flow field and vortex interactions in the near wake of two counter-rotating propellers

The wake hydrodynamics of counter-rotating propellers (CRP) is studied via phase-locked particle image velocimetry for three operating conditions featuring distinct flow dynamics. We focus our work on the flow field and the associated vortex dynamics that take place in the near wake, using a special on-line/off-line phase-locking technique that allows the velocity measurements to be phase-averaged based on both forward and aft propeller angular positions. The effect of propellers relative position on the flow features is investigated with support from high-speed visualizations of the vortex system, which is observed by inducing cavitation in the cores of the vortices. We report the relevant interactions that take place between the forward and aft propellers’ tip vorticity, in particular the regular patterns of vortex reconnection and break-up that depend on the advance coefficient, as well as the unique formation of isolated vortex rings and a highly coherent vortex wake.

Numerical study of the vortex breakdown and vortex reconnection in the flow path of high-pressure water turbine

The paper presents a study of the instability of the precessing vortex core in the model of the draft tube of a hydraulic turbine. The study was carried out using numerical modeling using various approaches: URANS, RSM, LES. The best agreement with the experimental data was shown by the RSM and LES methods with the modelling of the runner rotation by the sliding mesh method. In the regime under consideration, the precessing vortex rope is subject to instability, which leads to reconnection of its turns and the formation of an isolated vortex ring. Reconnection of the vortex core leads to aperiodic and intense pressure fluctuations recorded on the diffuser wall.

Topology and transport in generalized helical flows

Pure helical or screw flow presents a unique combination of zero net advection, alignment of vorticity dissipation with vorticity field, and maximal helicity. Helicity is a measure of knottedness in a flow structure as manifested in terms of a net imbalance between right and left handed helical motion. Topology, which is intrinsic to helicity, provides a geometric perspective to vortex reconnection in helical flow. However, the topological evolution and the resulting transport in helical flows remain unclear. Here, we investigate the evolution of isosurfaces associated with the Galilean invariant Q-criterion in generalized models of helical flow. While we categorize the stagnation points with Δ-criterion, the Gaussian curvature shows that the creation and annihilation of these points occur in pairs for specific instances of helical flow. The contours of finite-time Lyapunov exponent reveal the fluidic mixing due to the strain and shear transport barriers. These findings have far-reaching implications in diverse fields, ranging from classical turbulence in superfluid helium to dynamos in growing magnetic field. The present article sheds insights into these applications.

Vortex Reconnection and Turbulence Cascade

As a fundamental topology-transforming event, reconnection plays a significant role in the dynamics of plasmas, polymers, DNA, and fluids—both (classical) viscous and quantum. Since the 1994 review by Kida & Takaoka, substantial advances have been made on this topic. We review recent studies of vortex reconnection in (classical) viscous flows, including the physical mechanism, its relationship to turbulence cascade, the formation of a finite-time singularity, helicity dynamics, and aeroacoustic noise generation.

Targeted particle delivery via vortex ring reconnection

A conceptual model for targeted particle delivery is proposed using controlled vortex ring reconnection. Entrained particles can be efficiently transported within the core of vortex rings which advect via self-induction. A pair of these particle-transporting vortex rings traveling in the streamwise direction along parallel trajectories will mutually interact, resulting in a pair of vortex reconnection events. The reconnection causes a topological change to the vortex ring which is accompanied by a rapid repulsion in a perpendicular plane to the direction of travel, effectively transporting the particles toward the desired location on the sidewalls of a ducted flow. In addition to proposing this conceptual model, we show the dominant physics of the process and the considerations for targeted delivery.

The influence of collision angle for viscous vortex reconnection

We revisit the mechanism of viscous vortex reconnection by considering the collision of vortex rings over a range of initial collision angles and Reynolds numbers. While the overall reconnection process is similar to anti-parallel vortex reconnection, we find that collision angle exerts significant influence over the process, altering the evolution of various global and local quantities. The collision angle primarily manipulates the “pyramid” process, a recently identified stretching mechanism proposed by Moffatt and Kimura [“Towards a finite-time singularity of the Navier-Stokes equations Part 1. Derivation and analysis of dynamical system,” J. Fluid Mech., 861, 930–967 (2019)] to be a potential pathway for finite-time singularity of Euler’s equations, during the approach stage of the rings. However, the “pyramid” process is short-lived for viscous vortices. The present work shows that the “pyramid” process is arrested by parallelization of the colliding vortices, wherein contact of the colliding vortices halts their motion toward each other at the pyramid apex, allowing the rest of the vortex tube to “catch up,” breaking the pyramid structure. Parallelization marks the transition to a second phase of stretching, where the colliding vortices remain parallel. Vorticity amplification from pyramid stretching is significantly stronger than for its parallel counterpart, and is thus the dominant factor determining reconnection properties. Based upon the findings in this study, we conjecture that the parallelization process is the primary mechanism that prevents the finite-time singularity through the pyramid process. Critically, the Reynolds number scaling for the reconnection rate differs depending on the collision angle, which challenges the conjecture of universal Reynolds number scaling in the literature.

Effects of the secondary baroclinic vorticity on the energy cascade in the Richtmyer–Meshkov instability

We investigate the effect of the secondary baroclinic vorticity (SBV) on the energy cascade in the mixing induced by the multi-mode Richtmyer–Meshkov instability (RMI). With the aid of vorticity-based simplified models and the vortex-surface field, we find that the effect of the SBV peaks at a critical time when the vortex reconnection widely occurs in the mixing zone. Before the critical time, spikes and bubbles evolve almost independently, and we demonstrate that the variation of the kinetic energy spectrum induced by the SBV has the $-1$ scaling law at intermediate wavenumbers using the model of vortex rings. This SBV effect causes the slope of the total energy spectrum at intermediate wavenumbers to evolve towards $-3/2$ at the critical time. Subsequently, the SBV effect diminishes and the energy spectrum decays to the $-5/3$ law. Inspired by the vortex dynamics, we develop a model for estimating the mixing width and validate the model using numerical simulations of the multi-mode RMI with various modes of initial perturbations. This model captures the nonlinear growth of the mixing width before the self-similar growth stage.

Local vortex line topology and geometry in turbulence

The local streamline topology classification method of Chong et al. (Phys. Fluids A: Fluid Dyn., vol. 2, no. 5, 1990, pp. 765–777) is adapted and extended to describe the geometry of infinitesimal vortex lines. Direct numerical simulation (DNS) data of forced isotropic turbulence reveals that the joint probability density function (p.d.f.) of the second ( $q_\omega$ ) and third ( $r_\omega$ ) normalized invariants of the vorticity gradient tensor asymptotes to a self-similar bell shape for $Re_\lambda > 200$ . The same p.d.f. shape is also seen at the late stages of breakdown of a Taylor–Green vortex suggesting the universality of the bell-shaped p.d.f. form in turbulent flows. Additionally, vortex reconnection from different initial configurations is examined. The local topology and geometry of the reconnection bridge is shown to be nearly identical in all cases considered in this work. Overall, topological characterization of the vorticity field provides a useful analytical basis for examining vorticity dynamics in turbulence and other fluid flows.

Approximation Theorems for the Schr\xf6dinger Equation and Quantum Vortex Reconnection

We prove the existence of smooth solutions to the Gross–Pitaevskii equation on mathbb {R}^3 that feature arbitrarily complex quantum vortex reconnections. We can track the evolution of the vortices during the whole process. This permits to describe the reconnection events in detail and verify that this scenario exhibits the properties observed in experiments and numerics, such as the t^{1/2} and change of parity laws. We are mostly interested in solutions tending to 1 at infinity, which have finite Ginzburg–Landau energy and physically correspond to the presence of a background chemical potential, but we also consider the cases of Schwartz initial data and of the Gross–Pitaevskii equation on the torus. In the proof, the Gross–Pitaevskii equation operates in a nearly linear regime, so the result applies to a wide range of nonlinear Schrödinger equations. Indeed, an essential ingredient in the proofs is the development of novel global approximation theorems for the Schrödinger equation on mathbb {R}^n. Specifically, we prove a qualitative approximation result that applies for solutions defined on very general spacetime sets and also a quantitative result for solutions on product sets in spacetime Dtimes mathbb {R}. This hinges on frequency-dependent estimates for the Helmholtz–Yukawa equation that are of independent interest.

Construction and evolution of knotted vortex tubes in incompressible Schrödinger flow

We propose a theoretical method for constructing an initial two-component wave function that can be transformed into a knotted velocity field with finite kinetic energy and enstrophy. The wave function is constructed using two complex-valued polynomials, with one determining the desired shape of the knotted central axis and the other encoding the twisting nature of vortex lines, which facilitates the study of helicity conversions. We construct six knotted vortex fields with various centerline and twist helicity as initial conditions for direct numerical simulation of incompressible Schrödinger flow (ISF) in a periodic box. Although the evolution of morphological structure is similar for ISF and classical viscous flow, with all the knots becoming untied after a short time to form one or more separate vortex rings, their statistics are quite different. During the critical period of vortex reconnection, the increase in enstrophy is much more moderate in ISF than in viscous flow, indicating that the Landau–Lifshitz term in ISF inhibits the energy cascade from large to small scales. We also find that the centerline helicity changes dramatically during reconnection, which is consistent with the evolution of the geometrical shape of vortex lines.

Universal aspects of vortex reconnections across the BCS-BEC crossover

Reconnecting vortices in a superfluid allows for the energy transfer between different length scales and its subsequent dissipation. The present picture assumes that the dynamics of a reconnection is driven mostly by the phase of the order parameter, and this statement can be justified in the case of Bose-Einstein Condensates (BECs), where vortices have a simple internal structure. Therefore, it is natural to postulate that the reconnection dynamics in the vicinity of the reconnection moment is universal. This expectation has been confirmed in numerical simulations for BECs and experimentally for the superfluid $^{4}\mathrm{He}$. Not much has been said about this relation in the context of Fermi superfluids. In this Letter, we aim to bridge this gap, and we report our findings, which reveal that the reconnection dynamics conforms with the predicted universal behavior across the entire BCS-BEC crossover. The universal scaling also survives for spin-imbalanced systems, where unpaired fermions induce a complex structure of the colliding vortices.

Topological constraints in the reconnection of vortex braids

We study the relaxation of a topologically nontrivial vortex braid with zero net helicity in a barotropic fluid. The aim is to investigate the extent to which the topology of the vorticity field—characterized by braided vorticity field lines—determines the dynamics, particularly the asymptotic behavior under vortex reconnection in evolution at high Reynolds numbers (25 000). Analogous to the evolution of braided magnetic fields in plasma, we find that the relaxation of our vortex braid leads to a simplification of the topology into large-scale regions of opposite swirl, consistent with an inverse cascade of the helicity. The change of topology is facilitated by a cascade of vortex reconnection events. During this process, the existence of regions of positive and negative kinetic helicities imposes a lower bound for the kinetic energy. For the enstrophy, we derive analytically a lower bound given by the presence of unsigned kinetic helicity, which we confirm in our numerical experiments.

The generation and diffusion of vorticity in three-dimensional flows: Lyman's flux

Abstract

Some topological aspects of fluid dynamics

Abstract

Control Possibility of Explosive Vortex Stretching in Vortex Reconnection

Control Possibility of Explosive Vortex Stretching in Vortex Reconnection

Investigation of Localized Induction Approximation in Vortex Reconnection

Investigation of Localized Induction Approximation in Vortex Reconnection

Influence of a variable thermal diffusion coefficient on convection of a binary mixture in rectangular cavities

This paper presents the results of numerical simulation of nonlinear convection regimes of a NaCl aqueous solution in square and horizontally elongated rectangular cavities with hard and impermeable boundaries. The vertical boundaries of the cavities are thermally insulated, and the horizontal ones are maintained at different constant temperatures, which corresponds to heating from below. Calculations are carried out within the non-stationary approach using of Boussinesq approximation and taking into account the polynomial temperature dependence of the thermal diffusion coefficient. According to this approximation, at T*≈285.4 K, the thermal diffusion coefficient changes sign, and thus the direction of the concentration gradient also changes. The temperature gradients on the horizontal boundaries are chosen so that the thermal diffusion coefficient changes sign inside the cavity. Other transport coefficients are considered to be constant. Simulations were performed under Earth-gravity and reduced-gravity conditions. Based on the results of simulations, the local and integral characteristics of non-linear regimes were obtained, and the structure of the emerging flow and the distribution of NaCl concentration were determined. It is shown that the temperature dependence of the thermal diffusion coefficient only slightly affect the structure and intensity of the emerging flow but significantly reduces the degree of separation of mixture components. Under the influence of the Earth’s gravitational field, an oscillatory four-vortex flow with reconnection of vortices occurs in the square cavity, and a multi-vortex flow - in the rectangular cavity. The characteristics of the multi-vortex flow vary irregularly. At reduced gravity, a stationary flow is observed in both square and rectangular cavities. Under microgravity conditions, the concentration isolines are “frozen” into the stream function field, i.e., the similarity between the fields is pronounced.

On the flow field induced by two counter-rotating propellers at varying load conditions

The hydrodynamics of the flow between and in the wake of contra-rotating propellers is investigated experimentally via Particle Image Velocimetry (PIV) at different advanced coefficients. Results show that the flow dynamics is deeply influenced by the interplay between the two systems of helical vorticity that develop in the wake. The forward and aft propellers’ slipstream structure is analyzed in terms of blade loading and relative phase angle. The onset of tip vortex break-up, reconnection and pairing processes occurring within the wake is discussed with a focus on instability mechanisms. Flow field measurements between propellers highlight that the distribution of the tangential component is balanced more effectively by the aft propeller at specific loading conditions.

Characterizing most irregular small-scale structures in turbulence using local Hölder exponents.

Two scalar fields characterizing respectively pseudo-Hölder exponents and local energy transfers are used to capture the topology and the dynamics of the velocity fields in areas of lesser regularity. The present analysis is conducted using velocity fields from two direct numerical simulations of the Navier-Stokes equations in a triply periodic domain. A typical irregular structure is obtained by averaging over the 213 most irregular events. Such structure is similar to a Burgers vortex, with nonaxisymmetric corrections. A possible explanation for such asymmetry is provided by a detailed time-resolved analysis of birth and death of the irregular structures, which shows that they are connected to vortex interactions, possibly vortex reconnection.