# gst: alignment-induced self-organization of autonomously steering microswimmers: turbulence, clusters, vortices, and jets.

<< Microorganisms can sense their environment and adapt their movement accordingly, which gives rise to a multitude of collective phenomena, including active turbulence and bioconvection. In fluid environments, collective self-organization is governed by hydrodynamic interactions. >>

<< By large-scale mesoscale hydrodynamics simulations, (AA) study the collective motion of polar microswimmers, which align their propulsion direction by hydrodynamic steering with that of their neighbors. The simulations of the employed squirmer model reveal a distinct dependence on the type of microswimmer—puller or pusher—flow field. No global polar alignment emerges in both cases. Instead, the collective motion of pushers is characterized by active turbulence, with nearly homogeneous density and a Gaussian velocity distribution; strong self-steering enhances the local coherent movement of microswimmers and leads to local fluid-flow speeds much larger than the individual swim speed. >>

<< Pullers exhibit a strong tendency for clustering and display velocity and vorticity distributions with fat exponential tails; their dynamics is chaotic, with a temporal appearance of vortex rings and fluid jets. >>

AA << results show that the collective behavior of autonomously steering microswimmers displays a rich variety of dynamic self-organized structures. >>

Segun Goh, Elmar Westphal, et al. Alignment-induced self-organization of autonomously steering microswimmers: Turbulence, clusters, vortices, and jets. Phys. Rev. Research 7, 013142. Feb 7, 2025. 

https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.7.013142 

Also: swim, microswimmer, particle, turbulence, chaos, noise, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, swim, swimmer, microswimmers, particle, turbulence, chaos, noise

# gst: criticality and multistability in quasi-2D turbulence

       Fig. 1(a) Helmholtz resonators

<< Two-dimensional (2D) turbulence, despite being an idealization of real flows, is of fundamental interest as a model of the spontaneous emergence of order from chaotic flows. The emergence of order often displays critical behavior, whose study is hindered by the long spatial and temporal scales involved. >>

Here AA << experimentally study turbulence in periodically driven nanofluidic channels with a high aspect ratio using superfluid helium. (They) find a multistable transition behavior resulting from cascading bifurcations of large-scale vorticity and critical behavior at the transition to quasi-2D turbulence consistent with phase transitions in periodically driven many-body systems. >>

AA << demonstrate that quasi-2D turbulent systems can undergo an abrupt change in response to a small change in a control parameter, consistent with predictions for large-scale atmospheric or oceanic flows. >>️

Filip Novotny, Marek Talir, et al. Critical behavior and multistability in quasi-two-dimensional turbulence. arXiv: 2406.08566v1 [physics.flu-dyn]. Jun 12, 2024.

https://arxiv.org/abs/2406.08566

Also: order, disorder, disorder & fluctuations, turbulence, transition, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, order, disorder, disorder & fluctuations, criticality, turbulence, transition 

# gst: discontinuous transitions to active nematic turbulence.

<< Active fluids exhibit chaotic flows at low Reynolds number known as active turbulence. Whereas the statistical properties of the chaotic flows are increasingly well understood, the nature of the transition from laminar to turbulent flows as activity increases remains unclear. Here, through simulations of a minimal model of unbounded active nematics, (AA) find that the transition to active turbulence is discontinuous. (They) show that the transition features a jump in the mean-squared velocity, as well as bistability and hysteresis between laminar and chaotic flows. >>

<< From distributions of finite-time Lyapunov exponents, (AA) identify the transition at a value A∗≈4900 of the dimensionless activity number. Below the transition to chaos, (They) find subcritical bifurcations that feature bistability of different laminar patterns. These bifurcations give rise to oscillations and to chaotic transients, which become very long close to the transition to turbulence. Overall, (Their) findings contrast with the continuous transition to turbulence in channel confinement, where turbulent puffs emerge within a laminar background. >>

AA << propose that, without confinement, the long-range hydrodynamic interactions of Stokes flow suppress the spatial coexistence of different flow states, and thus render the transition discontinuous. >>️

Malcolm Hillebrand, Ricard Alert. Discontinuous Transition to Active Nematic Turbulence. arXiv: 2501.06085v1 [cond-mat.soft]. Jan 10, 2025.

https://arxiv.org/abs/2501.06085

Also: chaos, transition, turbulence, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, chaos, transition, turbulence, jumps, active nematics

# gst: apropos of viscoelastic flow instabilities, uncertainty in elastic turbulence.

<< Elastic turbulence can lead to increased flow resistance, mixing and heat transfer. Its control - either suppression or promotion - has significant potential, and there is a concerted ongoing effort by the community to improve our understanding. >>

AA << identify four regimes of uncertainty evolution, characterised by I) rapid transfer to large scales, with large scale growth rates of τ6 (where τ represents time), II) a dissipative reduction of uncertainty, III) exponential growth at all scales, and IV) saturation. These regimes are governed by the interplay between advective and polymeric contributions (which tend to amplify uncertainty), viscous, relaxation and dissipation effects (which reduce uncertainty), and inertial contributions. >>

<< In elastic turbulence, reducing Reynolds number increases uncertainty at short times, but does not significantly influence the growth of uncertainty at later times. At late times, the growth of uncertainty increases with Weissenberg number, with decreasing polymeric diffusivity, and with the logarithm of the maximum length scale, as large flow features adjust the balance of advective and relaxation effects. >>

Jack R. C. King, Robert J. Poole, et al. Uncertainty in Elastic Turbulence. arXiv: 2501.09421v1 [physics.flu-dyn]. Jan 16, 2025. 

https://arxiv.org/abs/2501.09421

Also: uncertainty, elastic, turbulence, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, uncertainty, elastic, elasticity, turbulence 

# gst: turbulence in viscous binary fluid mixtures induced by interfacial fluctuations.

AA << demonstrate the existence of interface-induced turbulence, an emergent nonequilibrium statistically steady state with spatiotemporal chaos, which is induced by interfacial fluctuations in low-Reynolds-number binary-fluid mixtures. >>️

<< Furthermore (they) demonstrate diffusive behavior at long times, a hallmark of strong mixing in turbulent flows. >>️

Nadia Bihari Padhan, Dario Vincenzi, Rahul Pandit. Interface-induced turbulence in viscous binary fluid mixtures. Phys. Rev. Fluids 9, L122401. Dec 3, 2024. 

https://journals.aps.org/prfluids/abstract/10.1103/PhysRevFluids.9.L122401

Also: fluctuations, turbulence, transition,  in https://www.inkgmr.net/kwrds.html 

Keywords: gst, fluctuations, turbulence, transition 

# gst: intermittency of bubble deformation in turbulence.

<< The deformation of finite-sized bubbles in intense turbulence exhibits complex geometries beyond simple spheroids as the bubbles exchange energy with the surrounding eddies across a wide range of scales. (AA)  study investigates deformation via the velocity of the most stretched tip of the deformed bubble in three dimensions, as the tip extension results from the compression of the rest of the interface by surrounding eddies. >>

<< The results show that the power spectrum based on the tip velocity exhibits a scaling akin to that of the Lagrangian statistics of fluid elements, but decays with a distinct timescale and magnitude modulated by the Weber number based on the bubble size. This indicates that the interfacial energy is primarily siphoned from eddies of similar sizes as the bubble. >>

<< Moreover, the tip velocity appears much more intermittent than the velocity increment, and its distribution near the extreme tails can be explained by the proposed model that accounts for the fact that small eddies with sufficient energy can contribute to extreme deformation. >>

<< These findings provide a framework for understanding the energy transfer between deformable objects and multiscale eddies in intense turbulence. >>

Xu Xu, Yinghe Qi, et al. Intermittency of Bubble Deformation in Turbulence. Phys. Rev. Lett. 133, 214001. Nov 19, 2024.

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.133.214001

Also: bubble, turbulence, intermittency, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, bubble, turbulence, intermittency

# gst: phase transitions in anisotropic turbulence.

<<  

Turbulence is a widely observed state of fluid flows, characterized by complex, nonlinear interactions between motions across a broad spectrum of length and time scales. While turbulence is ubiquitous, from teacups to planetary atmospheres, oceans and stars, its manifestations can vary considerably between different physical systems. For instance, three-dimensional (3D) turbulent flows display a forward energy cascade from large to small scales, while in two-dimensional (2D) turbulence, energy cascades from small to large scales. In a given physical system, a transition between such disparate regimes of turbulence can occur when a control parameter reaches a critical value. The behavior of flows close to such transition points, which separate qualitatively distinct phases of turbulence, has been found to be unexpectedly rich. Here, (AA) survey recent findings on such transitions in highly anisotropic turbulent fluid flows, including turbulence in thin layers and under the influence of rapid rotation. (They) also review recent work on transitions induced by turbulent fluctuations, such as random reversals and transitions between large-scale vortices and jets, among others. The relevance of these results and their ramifications for future investigations are discussed.

>>️

Adrian van Kan. Phase Transitions in Anisotropic Turbulence. arXiv: 2408.02844v1 [physics.flu-dyn]. Aug 5, 2024. 

https://arxiv.org/abs/2408.02844

Also:  turbulence, vortex, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, turbulence, vortex

# gst: apropos of inertial particles, they dispersion in turbulent canopy flows with buoyant and nonbuoyant plumes.

<< In an idealized “wind-driven” model system, (AA) consider the impact of plume buoyancy, plume momentum, and canopy turbulence on the downstream transport of particles in the wake of a canopy, and in particular the mean and standard deviation of the distribution of landing sites. >>

<< In a first set of experiments, particles were released with a fixed starting elevation above the plumes' upper boundaries, such that the particles were not lofted by the plume. In these cases, observations suggest that plumes have a role in extending particles' streamwise transport by delaying their downward transport. The plumes also have a strong role in increasing absolute dispersion of the particles, although less so when dispersion is normalized by distance traveled. While canopy turbulence alone significantly increases particle dispersion, in the presence of the plume its impact is more limited. Canopy turbulence was also found to cause shorter mean landing positions. >>

<< In a second set of experiments, particles were released at the plume source/outlet such that their initial vertical momentum was provided by the plume's momentum and buoyancy. In these cases, the impact of canopy turbulence on particle transport is observed more distinctly. The canopy coherent structures introduce a mechanical instability to the plume, which manifests as vertical oscillatory motions that lead to variability in the particles' initial conditions and, therefore, trajectories. This leads to particles settling at both shorter and longer downstream distances. >>

Hayoon Chung, Laura K. C. Sunberg, et al. Dispersion of inertial particles in turbulent canopy flows with buoyant and nonbuoyant plumes. Phys. Rev. Fluids 9, 093801. Sept 25, 2024.

https://journals.aps.org/prfluids/abstract/10.1103/PhysRevFluids.9.093801  

Also: particle, turbulence, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, particle, turbulence

# gst: apropos of intermittent switchings, presence of chaotic saddles in fluid turbulence.

<< Intermittent switchings between weakly chaotic (laminar) and strongly chaotic (bursty) states are often observed in systems with high-dimensional chaotic attractors, such as fluid turbulence. They differ from the intermittency of a low-dimensional system accompanied by the stability change of a fixed point or a periodic orbit in that the intermittency of a high-dimensional system tends to appear in a wide range of parameters. >>️

Here AA << demonstrate the presence of chaotic saddles underlying intermittency in fluid turbulence and phase synchronization. Furthermore, (they) confirm that chaotic saddles persist for a wide range of parameters. Also, a kind of phase synchronization turns out to occur in the turbulent model. >>️

Hibiki Kato, Miki U Kobayashi, et al. A laminar chaotic saddle within a turbulent attractor. arXiv: 2409.08870v1 [nlin.CD]. Sep 13, 2024. 

https://arxiv.org/abs/2409.08870

Also: transition, turbulence, intermittency, chaos, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, transition, turbulence, intermittency, chaos

# gst: vortex structures under dimples and scars in turbulent free-surface flows

<< Turbulence beneath a free surface leaves characteristic long-lived signatures on the surface, such as upwelling 'boils', near-circular 'dimples' and elongated 'scars', easily identifiable by eye, e.g., in riverine flows. >>️

AA << explore the connection between these surface signatures and the underlying vortical structures. We investigate dimples, known to be imprints of surface-attached vortices, and scars, which have yet to be extensively studied, by analysing the conditional probabilities that a point beneath a signature is within a vortex core as well as the inclination angles of sub-signature vorticity. >>️

<< The analysis shows that the likelihood of vortex presence beneath a dimple decreases from the surface down through the viscous and blockage layers in a near-Gaussian manner, influenced by the dimple's size and the bulk turbulence. When expressed as a function of depth over the Taylor microscale λT, this probability is independent of Reynolds and Weber number. >>️

<< Conversely, the probability of finding a vortex beneath a scar increases sharply from the surface to a peak at the edge of the viscous layer, at a depth of approximately λT/4. Distributions of vortical orientation also show a clear pattern: a strong preference for vertical alignment below dimples and an equally strong preference for horizontal alignment below scars. >>️

AA << findings suggest that scars can be defined as imprints of horizontal vortices approximately a quarter of the Taylor microscale beneath the surface, analogous to how dimples can be defined as imprints of surface-attached vertical vortex tubes. >>

Jørgen R. Aarnes, Omer Babiker, et al. Vortex structures under dimples and scars in turbulent free-surface flows. arXiv: 2409.05409v1 [physics.flu-dyn]. 

9 Sep 2024.

https://arxiv.org/abs/2409.05409

Also: vortex, turbulence, waves, bubble, drop, transition, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, vortex, turbulence, waves, bubble, drop, transition

# gst: dynamics of small droplets in turbulent multiphase flows

AA << show unambiguously that the formation of small droplets is governed by the internal dynamics which occurs during the breakup of large drops and that the high vorticity and the extreme dissipation associated to these events are the consequence and not the cause of the breakup. >>️

M. Crialesi-Esposito, G. Boffetta, L. Brandt, et al. How small droplets form in turbulent multiphase flows. Phys. Rev. Fluids 9, L072301. Jul 29, 2024. 

https://journals.aps.org/prfluids/abstract/10.1103/PhysRevFluids.9.L072301

Also: drop, bubble, transition, turbulence, intermittency, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, drop, droplet, droploid,  bubble, transition, turbulence, intermittency

# gst: evolution of turbulence using a random jet array

AA << perform a series of laboratory experiments in which (They) alter the parameters of the randomized algorithm, along with the jet spacing and outlet velocity of the jets. (They) first determine the location where turbulence transitions to a fully developed state and show that it is a function of jet penetration length, ℒ𝒥, and effective jet spacing, 𝑆𝑒. (AA)  identify three distinct regions for the spatial decay of turbulence in RJA (Random Jet Array) facilities and notably, (They) find different decay rates, unlike previous studies that report only one spatial decay rate using similar facilities. These regions are shown to depend on the variations of input parameters yet independent of the strength of the mean flow. (AA) also find the strength of the mean flow does not affect the homogeneity, nor the production, transport, or advection terms of the turbulent kinetic energy budget equation. >>

Finally, AA << address a longstanding question toward estimating turbulence metrics with an RJA based on the input parameters. >>

️

Arefe Ghazi Nezami, Blair Anne Johnson. Evolution of turbulence using a random jet array. Phys. Rev. Fluids 9, 074610. Jul 26, 2024.

https://journals.aps.org/prfluids/abstract/10.1103/PhysRevFluids.9.074610

Also: turbulence, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, turbulence

# gst: tracking four-way coupled particles in turbulence

<< In many natural and industrial applications, turbulent flows encompass some form of dispersed particles. Although this type of multiphase turbulent flow is omnipresent, its numerical modeling has proven to be a remarkably challenging problem. >>

AA << present an efficient method for point-based simulation of particles in turbulence that are four-way coupled. In contrast with traditional one-way coupled simulations, where only the effect of the fluid phase on the particle phase is modeled, this method additionally captures the back-reaction of the particle phase on the fluid phase, as well as the interactions between particles themselves. >>

AA << focus on the most challenging case of very light particles or bubbles, which show strong clustering in the high-vorticity regions of the fluid. >>

️

Xander M. de Wit, Rudie P. J. Kunnen, et al. Efficient point-based simulation of four-way coupled particles in turbulence at high number density. Phys. Rev. E 110, 015301. Jul 1, 2024. 

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.110.015301  

Also: particle, bubble, turbulence, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, particles, bubbles, turbulence

# gst: elasticity of fibres prefers the chaos of turbulence.

FIG. 4. Maximal Lyapunov exponents λ1 associated with the flow regions sampled by the fibre centre of masses in a 3D turbulent flow. 

<< Turbulent flows are ubiquitous in nature and are responsible for numerous transport phenomena that help sustain life on earth. >>️

AA << have shown that the stretching of fibres is due only to elasticity and their inertia playing a minimal role as they are advected by a turbulent carrier flow. A highly elastic fibre is much more likely to be stretched out and as a result prefers a “straighter” configuration rather than a coiled one. >>️

<< These inertial, elastic fibres then exhibit non-trivial preferential sampling of a 3D turbulent flow in a manner qualitatively similar to 2D turbulence (..). Inertia leads fibres away from vortical regions while their elasticity pulls them inside the vortices. Upto a moderate inertia (St ∼ O(1)), fibres increasingly prefer the straining regions of the flow, while at much larger inertia (St ≫ 1) they decorrelate from the flow and preference for straining regions begins to diminish again. >>️

<< However, owing to a large elasticity, fibres get trapped in vortical regions (at small St), as well as are unable able to exit the straining regions quickly. A more elastic and extensible fibre is, thus, more likely to spend longer times in both vortical and the straining regions of the flow. >>️

<< This picture of preferential sampling of a 3D turbulent flow by elastic, inertial fibres is also confirmed by alternately studying the chaoticity of the sampled flow regions via Lyapunov Exponents. Less elastic fibres prefer less chaotic (vortical) regions of the flow while more chaotic (straining) regions are preferred at large Wi. LEs also confirm that preferential sampling has a non-monotonic dependence on St for small elasticity but which is lost when Wi becomes very large.  >>

<< It would (..) be even more interesting to see how chaotic the fibre trajectories themselves are and what that has to say about fibre dynamics in turbulent flows. >>️

️

Rahul K. Singh. Elasticity of fibres prefers the chaos of turbulence. arXiv: 2406.06033v1. Jun 10, 2024.

https://doi.org/10.48550/arXiv.2406.06033

Also: elastic, chaos, turbulence, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, elastic, chaos, turbulence

# gst: helical instabilities from mixed mode transitions in boundary layers

<< Recent (..) direct numerical simulations (DNS) of adverse- and zero-pressure-gradient boundary layers beneath moderate levels of free stream turbulence (𝑇⁢𝑢≤2%) revealed a mixed mode transition regime, intermediate between orderly and bypass routes. >>️

<< In this regime, the amplitudes of the Klebanoff streaks and instability waves are similar, and both can contribute significantly as these interact. Three-dimensional visualizations of transitional eddies revealed a helical pattern, quite distinct from the sinuous and varicose forms seen in pure bypass transition. This raises the fundamental question of whether the helical pattern could be attributed to a previously unknown instability mode. >>️

In AA work << based on stability analyses, (they) show that it is indeed the case. Two-dimensional stability analyses are performed herein for base flows extracted from DNS flow fields. >>️

Rikhi Bose, Paul A. Durbin. Mixed mode transition in boundary layers: Helical instability. Phys. Rev. Fluids 9, 063905. Jun 12, 2024. 

https://journals.aps.org/prfluids/abstract/10.1103/PhysRevFluids.9.063905

Also: instability, transition, turbulence, waves, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, instability, transition, turbulence, waves

# gst: defects around obstacles, active nematic ratchet in asymmetric arrays

AA << numerically investigate the effect of an asymmetric periodic obstacle array in a two-dimensional active nematic. (They) find that activity in conjunction with the asymmetry leads to a ratchet effect or unidirectional flow of the fluid along the asymmetry direction. The directional flow is still present even in the active turbulent phase when the gap between obstacles is sufficiently small. >>️

AA << demonstrate that the dynamics of the topological defects transition from flow mirroring to smectic-like as the gap between obstacles is made smaller, and explain this transition in terms of the pinning of negative winding number defects between obstacles. >>

️

Cody D. Schimming, C. J. O. Reichhardt, C. Reichhardt. Active nematic ratchet in asymmetric obstacle arrays. Phys. Rev. E 109, 064602. Jun 3, 2024. 

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.109.064602 

Also: transition, turbulence, defect, error,  in https://www.inkgmr.net/kwrds.html 

Keywords: gst, nematic ratchet,  transition, turbulence, defect, error

# gst: periodic defect braiding in active nematics confined to a cardioid.

AA' paper << examines self-mixing in active nematics, a class of fluids in which mobile topological defects drive chaotic flows in a system comprised of biological filaments and molecular motors. (They) present experiments that demonstrate how geometrical confinement can influence the braiding dynamics of the defects. >>️

<< Notably, (AA) show that confinement in cardioid-shaped wells leads to realization of the golden braid, a maximally efficient mixing state of exactly three defects with no defect creation or annihilation. >>

<< Increasing the size of the confining cardioid produces a transition from the golden braid, to the fully chaotic active turbulent state. >>️️

Fereshteh L. Memarian, Derek Hammar, et al. Controlling Chaos: Periodic Defect Braiding in Active Nematics Confined to a Cardioid. Phys. Rev. Lett. 132, 228301. May 28, 2024. 

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.132.228301

https://x.com/PhysRevLett/status/1796622457303876000

Also: chaos, turbulence, particle, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, chaos, turbulence, active nematics, cardioid

# gst: random walk model for dual cascades in wave turbulence.

<< Dual cascades in turbulent systems with two conserved quadratic quantities famously arise in both two-dimensional hydrodynamic turbulence and also in wave turbulence based on four-wave interactions. >>

<< in wave turbulence the systematic spectral fluxes observed in a dual cascade do not require an irreversible dynamical mechanism, rather, they arise as the inevitable outcome of blind chance. >>️️

Oliver Bühler. Random walk model for dual cascades in wave turbulence. Phys. Rev. E 109, 055102. May 1, 2024. 

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.109.055102

Also: waves, turbulence, random, weak, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, waves, turbulence, weak turbulence, random, random walks

# gst: pulsating active matter.

<< the mechanical pulsation of locally synchronized particles is a generic route to propagate deformation waves. >>

️

AA << consider a model of dense repulsive particles whose activity drives periodic change in size of each individual. >>️

They << show that the competition between repulsion and synchronization triggers an instability which promotes a wealth of dynamical patterns, ranging from spiral waves to defect turbulence. >>️

Yiwei Zhang, Etienne Fodor. Pulsating Active Matter. Phys. Rev. Lett. 131, 238302. Dec 8, 2023. 

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.131.238302

Also: waves, particle, transition, instability, turbulence, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, waves, particle, transition, instability, turbulence

# gst: when a turbulence can be confined

<< Turbulence is hard to control. Its ephemeral nature prevents us from treating it as an ordinary state of matter. Here (AA) create a stationary and isolated blob of turbulence using only elemental building blocks: vortex rings.  The turbulence is confined in a spherical region, surrounded by a quiescent environment, initiated and sustained by vortex rings. Crucially, vortex rings can be endowed with conserved quantities such as energy and helicity, which can be transferred to the turbulent state. Using 2D particle image velocimetry and 3D particle tracking velocimetry, (AA) demonstrate how confinement of turbulence occurs when vortex rings repeatedly collide, in contrast to coherent vortex reconnections. The pathlines depict the difference between these states of flow. >>️

Takumi Matsuzawa, Noah P. Mitchell, Stéphane Perrard, William T. M. Irvine. Turbulence through sustained vortex ring collisions. Phys. Rev. Fluids 8, 110507. Nov 16, 2023.

https://journals.aps.org/prfluids/abstract/10.1103/PhysRevFluids.8.110507

75TH ANNUAL MEETING OF THE APS DIVISION OF FLUID DYNAMICS (NOVEMBER 20, 2022 — NOV 22, 2022). V0008: Turbulence through sustained vortex ring collisions. 

https://doi.org/10.1103/APS.DFD.2022.GFM.V0008

Also: turbulence, vortex, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, turbulence, vortex, vortex ring collisions