# gst: vortex formation around islands in random waves.

<< ️Wave vortices are fundamental topological features of interference fields, occurring at nodal points where the wave amplitude vanishes. A distinct class of vortices can instead form around it islands or `holes' in two-dimensional wavefields, where the wave intensity remains finite and may even peak at the boundary. >> 

<< ️Here (AA) develop a statistical theory of vortices around islands in random two-dimensional wavefields, with and without the Coriolis effect, and test it experimentally. (They) determine the probabilities of vortices with different topological charges as functions of island size and Coriolis parameter.  ️(They) find that island-bound vortices emerge with unexpectedly high probability, approaching 50% in non-rotating systems and nearly 100% in rotating systems. Moreover, for a broad range of parameters, the presence of a subwavelength island dramatically enhances vortex formation compared with homogeneous random wavefields. >>

<< ️(AA) results explain the formation of tidal vortices around ocean islands of particular sizes (~0.1 of the characteristic wavelength) and establish a general mechanism for generating localized high-intensity vortices around defects in diverse wave systems, from water waves to nanophotonic structures. >>

Alex J. Vernon, Junyi Ye, Wenzhe Liu, et al. Vortex formation around islands in random waves. arXiv: 2607.15938v1 [physics.flu-dyn]. Jul 17, 2026.

https://arxiv.org/abs/2607.15938

Also: waves, vortex, random, defect, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, waves, vortex, randomness, defects, wave vortices, tidal vortices, interference fields, homogeneous random wavefields, random two-dimensional wavefields, rotating non-rotating systems.

# gst: stability of vortex lattices in rotating flows.

<< Vortex lattices—highly ordered arrays of vortices—are known to arise in quantum systems such as type II superconductors and Bose-Einstein condensates. More recently, similar arrangements have been reported in classical rotating fluids. However, the mechanisms governing their formation, stability, and eventual breakdown remain poorly understood. >>

<< (AA) explore the dynamical stability of vortex lattices in three-dimensional rotating flows. To that end (They) construct controlled initial conditions consisting of vortex lattices superimposed on turbulent backgrounds. (They) then characterize their evolution across different Rossby numbers and domain geometries. >>

<< By introducing an Ekman drag (AA)  are able to reach a steady state where vortex lattices persist with near constant amplitude up until spontaneous breakup of the lattice, or an equivalent of “melting,” occurs. (They) examine an ensemble of runs in order to determine the mean lifetime of the lattice as a function of the system parameters. >>

<< (AA) results reveal that the stability of the lattices is a memory-less random process whose mean lifetime depends sensitively on the system parameters that if finely tuned can lead to very long-lived lattice states. These metastable states exhibit statistical properties reminiscent of critical systems and can offer insight into long-lived vortex patterns observed in planetary atmospheres. >>

Julián Amette Estrada, Alexandros Alexakis, Marc E. Brachet, et al. Stability of vortex lattices in rotating flows. Phys. Rev. Fluids 11, 074401. Jul 10, 2026. 

https://journals.aps.org/prfluids/abstract/10.1103/k8zw-s6kj

arXiv: 2510.06374v1 [physics.flu-dyn]. Oct 7, 2025.

https://arxiv.org/abs/2510.06374

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

Keywords: gst, vortex, turbulence, randomness, vortex lattices, rotating flows, mean lifetime, spontaneous breakups, memory-less random process, metastable states, criticality.

# gst: spatially heterogeneous noise restructures flocking into geometry-locked and vortex states.

<< ️Spatially heterogeneous environments continually challenge the ability of active matter to sustain coherent collective motion. Understanding how collective motion remains robust under changing environments is central to both the functioning of biological systems and the design of smart active matter. >>

<< ️Here, (AA) extend the Vicsek model to include a circular non-noisy region surrounded by a noisy environment - a configuration in which the noise difference sets up a contrast in local directional order between the two regions. (They) find that, as the surrounding noise is increased, the system passes through three distinct dynamical regimes: (i) conventional global flocking at low noise; (ii) geometry-locked motion, aligned with simulation boundaries, at intermediate noise; and (iii) vortical motion within the non-noisy region at high noise. >>

<< Extending the environment to multiple non-noisy regions, (AA) find that the geometry-locked regime can develop a directional coupling, while the vortex mode leads to antiferromagnetic order between the regions. Taken together, (Their) results demonstrate that the spatial modulation of order and disorder offers a powerful and generic strategy for steering active matter, aligning with recent experimental observations of active particles in patterned landscapes. >>

Ankush Semwal, Mahak Poonia, Pintu Patra. Spatially heterogeneous noise restructures flocking into geometry-locked and vortex states. arXiv: 2607.05870v1 [cond-mat.soft]. Jul 7, 2026.

https://arxiv.org/abs/2607.05870

Also: particle, noise, vortex, order, disorder, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, particle, noise, vortex, order, disorder, active matter, steering active matter, coherent collective motion, noisy environment, vortical motion, geometry-locked regime. 

# gst: quadruple decomposition of boundary vorticity flux.

<< ️First introduced by Lighthill in 1963 for two-dimensional flows and later generalized by Jie-Zhi Wu to three-dimensional scenarios since 1986, the boundary vorticity flux (BVF) is the cornerstone of boundary vorticity dynamics, which quantifies the vorticity source strength on a solid boundary. Recent advances in vorticity and vortex dynamics have revealed both the rigid-rotation and spin modes of vorticity from multiple perspectives. >>

<< ️In the present study, (AA) propose a novel quadruple decomposition of the BVF on a stationary solid wall, which essentially uncovers the boundary creation rates of the elementary vorticity modes for both the tangential and wall-normal BVF components, respectively. >>

<< The proposed framework is illustrated through skin-friction and surface-pressure measurements for flow over a hill model in a low-speed wind tunnel, revealing a set of intriguing BVF patterns for the first time. These theoretical results are expected to be valuable for global surface flow diagnostics when combined with experiments, as well as for understanding the formation mechanisms of near-wall coherent structures and flow-induced noise. >>

Tao Chen, Tianshu Liu. Quadruple decomposition of boundary vorticity 

flux. arXiv: 2606.28761v1 [physics.flu-dyn]. Jun 27, 2026. 

https://arxiv.org/abs/2606.28761

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

Keywords: gst, vortex, noise, transitions, boundary vorticity dynamics, boundary vorticity flux (BVF), skin-friction, 

surface-pressure, near-wall coherent structures, flow-induced noise. 

# gst: superflows around corners.

<< ️(AA) investigate analytically and numerically the dynamics of a two-dimensional superflow governed by the Gross-Pitaevskii equation passing over finite-size rectangular obstacles: an impenetrable wall and an impenetrable rectangular well. >>

<< ️Extending classical studies of vortex nucleation around smooth obstacles, (They) focus on the role of sharp corners in determining the onset of vortex nucleation. Using a combination of analytical techniques based on the Schwarz-Christoffel methods for potential flow and on numerical simulations, (They) show that local velocity amplification near sharp corners crucially controls the critical flow velocity for vortex nucleation. For both wall and well configurations, (They) identify analytically and theoretically the critical velocities as a function of the obstacle width and its height or depth, finding excellent agreement between the theory and numerical simulations. >>

<< ️(Their) results provide a simple  framework for understanding superflow stability past finite-size obstacles with sharp features, and they are directly relevant to experimentally realizable configurations in atomic Bose-Einstein condensates and related superfluid systems. >>

Thomas Frisch, Christophe Josserand, Sergio Rica. Superflows around corners. Phys. Rev. Fluids 11, 054703. May 20, 2026.

https://journals.aps.org/prfluids/abstract/10.1103/77hn-2hqf

arXiv:2602.18876v1 [cond-mat.quant-gas]. Feb 21, 2026.

https://arxiv.org/abs/2602.18876

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

Keywords: gst, vortex, vortex nucleation, two-dimensional superflow. 

# gst: orbital instability and spanwise vortex structure of unstable periodic orbits in large-eddy simulations of plane Couette flow.

<< ️(AA) perform an unstable periodic orbit (UPO) analysis of moderately developed Couette turbulence with large-eddy simulations (LES) using a static eddy viscosity model. >>

<< ️(They) find that spanwise vortices, stretched between streamwise rolls, approach the walls, over which new spanwise vortices are generated. The stretching of these vortices is driven by strong shear layers induced by the streamwise rolls. This vortex-generation mechanism, as revealed by the LES UPOs, is a significant dynamical process in LES turbulence at high Reynolds numbers. >>

<< ️By computing local Lyapunov exponents, which quantify the least stable perturbation growth rates along the UPOs, (They) show that the stretching process amplifies their growth. The corresponding Lyapunov vectors highlight the instability of prominent shear layers through which the stretched spanwise vortices emerge between the rolls. >>

<< ️(Their) results suggest that high-strain-rate structures in developed turbulence play a central role in shaping the geometrical structure of turbulent orbits in phase space. >>

Eiichi Sasaki, Javier Jiménez, Genta Kawahara. Orbital instability and spanwise vortex structure of unstable periodic orbits in large-eddy simulations of plane Couette flow. Phys. Rev. Fluids 11, 054603. May 14, 2026.

https://journals.aps.org/prfluids/abstract/10.1103/mtw2-29r3

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

Keywords: gst, instability, turbulence, vortex, spanwise vortices, eddy viscosity model, unstable periodic orbit (UPO), streamwise rolls, stretching process.

# gst: rigorous ultimate scaling in rapidly rotating steady convection.

<< ️Rapidly rotating Rayleigh-Bénard convection admits a class of exact steady single-mode solutions describing high-amplitude convection cells. Using a matched asymptotic analysis in the high-Rayleigh-number limit, (AA) obtain a rigorous characterization of their bulk and boundary-layer structure, yielding explicit scaling laws for the Nusselt and Reynolds numbers, including their dependence on the horizontal wavenumber. >>

<< (They) show that, for suitable wavenumbers, these solutions attain the diffusivity-free ultimate scalings frequently assumed for geophysical and astrophysical convection, with additional enhancing logarithmic corrections. This reveals a specific mechanism through which rapidly rotating convection can approach ultimate heat transport via coherent columnar structures with well-defined horizontal scales. >>

Gabriel Hadjerci, Shingo Motoki, Genta Kawahara. Rigorous ultimate scaling in rapidly rotating steady convection. arXiv: 2605.05574v1 [physics.flu-dyn]. May 7, 2026.

https://arxiv.org/abs/2605.05574

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

Keywords: gst, waves, vortex, convection, convection cells, Rayleigh-Bénard convection, bulk and boundary-layer structure, rotation, rotating convection.

# gst: apropos of unsteady two-dimensional flows, the Lagrangian rotating contracting structures.

<< ️(AA) identify materially defined regions in unsteady two-dimensional flows that combine finite-time contraction with elevated accumulated intrinsic rotation along trajectories, which (They) term Lagrangian rotating contracting structures (LRCS). These regions are detected using existing objective diagnostics—the Lagrangian-averaged vorticity deviation (LAVD) together with direct tests of material contraction—without relying on the geometry of LAVD level sets. >>

<< ️In strongly deforming flows, LAVD maxima need not correspond to vortical regions or be enclosed by regular level sets, rendering geometry-based identification unreliable. Nevertheless, regions exhibiting inward spiraling motion and contraction can be extracted by combining LAVD with a contraction criterion. >>

<< ️Applications to atmospheric and oceanic flows show that such behavior arises both in twisted LAVD fields generated at submesoscales and in mesoscale flows where it is enhanced by inertial effects, with finite-time contraction providing the dynamical constraint that isolates materially organized regions with elevated intrinsic rotation. >>

F.J. Beron-Vera. Lagrangian Rotating Contracting Structures. arXiv: 2604.25036v1 [nlin.CD]. Apr 27, 2026.

https://arxiv.org/abs/2604.25036

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

Keywords: gst, vortex, instability, finite-time contraction, accumulated intrinsic rotation, Lagrangian rotating contracting 

structures, inward spiraling motion.

# gst: comparative analysis of detonation and shock waves interacting with droplets.

<< ️The interaction mechanisms among detonation waves, shock waves, and liquid droplets play a critical role in advancing propulsion technologies such as rotating detonation engines. This (AA) study conducts a detailed comparison of wave dynamics, cavitation phenomena, and droplet deformation during the detonation wave and the shock-wave interactions with a water droplet, employing a high-resolution numerical model that integrates multicomponent compressible fluid dynamics, chemical reactions, and phase transition effects. >>

<< ️Numerical simulations reveal distinct characteristics between detonation and shock-induced phenomena. Unlike the shock wave, detonation-induced reflected shock waves exhibit significantly higher propagation velocities while maintaining nearly identical wave configurations, a phenomenon this (AA) study mechanistically explains by the unique postwave conditions. >> 

<< ️A fundamental distinction arises in cavitation dynamics between the detonation wave and the shock wave, with the detonation-wave triggering cavitation zone collapse at significantly higher rates compared with the shock wave. This difference is attributed to the shorter persistence of low-pressure regions behind the detonation front, where rapid attenuation of postwave pressure and flow velocity occurs. >>

<< ️Moreover, detonation-induced flow interactions create unique droplet fragmentation patterns. The rapid postwave velocity reduction prevents Rayleigh-Taylor instability-driven forward jet formation, instead causing leeward-side flattening of the droplet through the vortex in the recirculation zone. >>

Hanbing Zou, Xin Jin, Haotian Chen, et al. Comparative analysis of detonation  and shock waves interacting with droplets: Characteristics and mechanisms. Phys. Rev. Fluids 11, 034303. Mar 18, 2026.

https://journals.aps.org/prfluids/abstract/10.1103/mp9z-tlk3  

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

Keywords: gst, waves, shock-waves, drop, droplet, droploid, bubble, collapse, vortex, transitions, phase transition, cavitation, detonation wave, detonation front, droplet fragmentation patterns. 

# gst: apropos of flows of hyperpycnal river plumes

<< ️The flow of a hyperpycnal river plume into a lake with a sloping bed and without any lateral confinement is a common occurrence in nature. A characteristic example of such geophysical fluid flow system is the inflow of river Rhone in Llake Geneva. >>

<< ️In this work, (AA) study the near-field plunging dynamics of an unconfined hyperpycnal plume at laboratory scale, over an idealized bed, with a slope that is similar to the one of the natural system. The study is based on large-eddy simulation of the Navier-Stokes equations in the Boussinesq approximation. (They) focus on the effect of varying the inflow conditions and in particular the densimetric Froude number, Fr_𝑑, which is the nondimensional parameter describing the ratio between inertial and buoyancy forces acting on the plume. >>

<< ️Three simulations were performed at different values of Fr_𝑑, within the range encountered in the natural system. Similarly to previous works, (They) are able to identify lateral slumping as the main mechanism that leads to plunging of the dense river water and the formation of the characteristic triangular pattern at the lake surface. (They) are able to further identify the formation of a wake downstream of the vertex plunge point, due to the transport of mixed river-ambient water from the converging mixing layers across the plunge curve on both sides of the plume. >>

<< ️The extent of both the wake and the overall plunge region increases significantly with increase of Fr_𝑑. This mechanism can be associated to the changes of the surface patterns of the plume observed in the field. In addition, (AA) compute the total entrainment, 𝐸, of ambient lake water as the streamwise increase of volumetric flow rate downstream of the river mouth. 𝐸 is found to increase with distance from the mouth, as the plume continuously entrains ambient lake water. >> 

<< (They) find that for the same distance from the river mouth, 𝐸 is larger for lower Fr_𝑑. This increase of 𝐸 with decreasing Fr_𝑑 is attributed to two mechanisms. First, in the plunge region, lower Fr_𝑑 leads to greater lateral spread and therefore increased interface area between plume and ambient water. Second, in the underflow region, lower Fr_𝑑 results in higher mean streamwise plume velocity, enhancing entrainment intensity. >>

Georgios Giamagas, Cyrille Bonamy, Koen Blanckaert, et al. Plunging and entrainment dynamics of an unconfined hyperpycnal plume over a sloping bed. Phys. Rev. Fluids 11, 033801. Mar 5, 2026.

https://journals.aps.org/prfluids/abstract/10.1103/41p1-sn3p

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

Keywords: gst, vortex, vortices, transitions, unconfined hyperpycnal plume, lateral confinements, near-field plunging dynamics, inertial and buoyancy forces, lateral slumping, wake downstream of the vertex plunge point, lateral spread, streamwise plume velocity.

# gst: multi-ring necklace vortex solitons in Kerr nonlinear media with azimuthally modulated Bessel potentials.

<< ️(AA) address the existence, stability, and dynamics of single-ring and multi-ring vorticity-carrying necklace solitons under the action of the Kerr nonlinearity and a Bessel-lattice potential modulated in the azimuthal direction. The model may be realized in the spatial domain for bulk optical waveguides, the spatiotemporal domain for optical cavities, and for effectively two-dimensional Bose-Einstein condensates. The setup supports single- and multi-ring necklace vortex patterns, including monopoles, dipoles, tripoles, quadrupoles, pentapoles, sextupoles, octupoles, and 12-poles. >>

<< ️In contrast with the inherent instability of conventional vortex beams with high topological charges (winding numbers), vortex necklace-shaped solitons with large winding numbers are found to be stable in the present setup. In particular, octupoles exhibit stable breathing dynamics, and 12-pole necklaces with high winding numbers may be stable. >>

<< ️These (AA) findings provide a new way for generating stable vortex necklaces, offering a vast potential for manipulations of complex spatiotemporal light fields. >>

Ruolan Zhao, Jing Chen, Boris A. Malomed, et al. Multi-ring necklace vortex solitons in Kerr nonlinear media with azimuthally modulated Bessel potentials. arXiv: 2602.18703v1 [physics.optics]. Feb 21, 2026.

https://arxiv.org/abs/2602.18703

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

Keywords: gst, vortex, solitons, vortex necklace-shaped solitons, single-ring vorticity, multi-ring vorticity, stable vortex necklace, transitions.

# gst: superflows around corners.

<< ️(AA) investigate analytically and numerically the dynamics of a two-dimensional superflow governed by the Gross-Pitaevskii equation passing over finite-size rectangular obstacles: an impenetrable wall and an impenetrable rectangular well. Extending classical studies of vortex nucleation around smooth obstacles, (They) focus on the role of sharp corners in determining the onset of vortex nucleation. Using a combination of analytical techniques based on the Schwarz-Christoffel methods for potential flow and on numerical simulations, (They) show that local velocity amplification near sharp corners crucially controls the critical flow velocity for vortex nucleation. >>

<< ️For both wall and well configurations, (They) identify analytically and theoretically the critical velocities as a function of the obstacle width and its height or depth, finding an excellent agreement between the theory and (Their) numerical simulations. (Their) results provide a simple framework for understanding superflow stability past finite-size obstacles with sharp features and are directly relevant to experimentally realizable configurations in atomic Bose-Einstein condensates and related superfluid systems. >>

Thomas Frisch, Christophe Josserand, Sergio Rica. Superflows around corners. arXiv: 2602.18876v1 [cond-mat.quant-gas]. Feb 21, 2026.

https://arxiv.org/abs/2602.18876

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

Keywords: gst, vorticity, vortex nucleation, two-dimensional superflow, superflow stability, smooth obstacles, sharp corners. 

# gst: vorticity-induced surfing and trapping in porous media

<< Microorganisms often encounter strong confinement and complex hydrodynamic flows while navigating their habitats. Combining finite-element methods and stochastic simulations, (AA) study the interplay of active transport and heterogeneous flows in dense porous channels. (They) find that swimming always slows down the traversal of agents across the channel, giving rise to robust power-law tails of their exit-time distributions. These exit-time distributions collapse onto a universal master curve with a scaling exponent of ≈ 3/2 across a wide range of packing fractions and motility parameters, which can be rationalized by a scaling relation. >> 

<< ️(AA) further identify a new motility pattern where agents alternate between surfing along fast streams and extended trapping phases, the latter determining the power-law exponent. Unexpectedly, trapping occurs in the flow backbone itself -- not only at obstacle boundaries -- due to vorticity-induced reorientation in the highly-heterogeneous fluid environment. >>

Pallabi Das, Mirko Residori, Axel Voigt, et al. Vorticity-induced surfing and trapping in porous media. arXiv: 2511.02471v1 [cond-mat.soft]. Nov 4, 2025.

https://arxiv.org/abs/2511.02471

Also: swim, microswimmers, intermittency, disorder, vortex, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, swim, microswimmers, intermittency, disorder, vortex, self-propel, run-and-tumble dynamics, hop-and-trap pattern, surf-and-trap motility pattern.

# gst: effect of varying degrees of freedom on self-propelled undulatory swimmers.

<< ️This (AA) study investigates the influence of varying degrees of freedom (DOFs) on the swimming performance of self-propelled undulatory swimmers navigating a straight path in three flow configurations: an unbounded fluid, near a solid wall, and in a side-by-side arrangement. >>

<< ️Vertical and rotational DOFs are frozen or actively controlled, resulting in four trajectory control scenarios. In unbounded flow, freezing motion DOFs generally underestimate the cost of transport while overestimating time-averaged amplitudes and Strouhal numbers, discrepancies that grow with increasing Reynolds number. Additionally, swimmers with two frozen DOFs exhibit phase shifts in lateral force and torque oscillations. Near solid boundaries, constrained swimmers experience more pronounced wall effects, whereas in side-by-side configurations, frozen-DOF swimmers display intensified channel effects. >>

<< ️Analysis of the pressure distribution and wake topology reveals marked differences in pressure concentration and vortex street structures depending on DOFs. >>

<< ️These (AA) findings underscore the critical role of motion DOFs in shaping swimming dynamics and emphasize the importance of appropriate trajectory control strategies for accurate modeling of fish locomotion. >>

Zhiqian Xin, Jiadong Wang, et al. Effect of varying degrees of freedom on self-propelled undulatory swimmers. Phys. Rev. E 112, 035103. Sep 19, 2025

https://journals.aps.org/pre/abstract/10.1103/gy7m-4ysj

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

Keywords: gst, swim, microswimmers, vortex, vortex interactions.

# gst: spiral defect chaos with intermittency increases mean termination time

<< ️Cardiac models are examples of excitable systems and can support stable spiral waves. For certain parameter values, however, these spiral waves can become unstable, resulting in spiral defect chaos (SDC), characterized by the continuous creation and annihilation of spiral waves and thought to underlie atrial fibrillation. During SDC, the number of spiral waves fluctuates and drops to zero at termination. >>

<< ️In this work, (AA) demonstrate that varying a single parameter allows the system to transition from SDC to a single spiral wave, passing through an intermediate regime of intermittency. In such intermittent dynamics, intervals of SDC are sandwiched between non-SDC intervals during which the number of spiral waves remains small and constant. (They) quantify this intermittency and show that the mean termination time increases significantly as the control parameter approaches values for which a single spiral wave is stable. >>

<<  In addition, (AA) observe that quasistable spiral waves may intermittently persist in part of the computational domain, while the rest of the domain exhibits SDC. >> 

Mahesh Kumar Mulimani, Wouter-Jan Rappel. Spiral defect chaos with intermittency increases mean termination time. Phys. Rev. E 112, 034203. Sep 3, 2025.

https://journals.aps.org/pre/abstract/10.1103/bwpl-qqyl

arXiv: 2505.06427v1 [nlin.CD]. May 9,  2025

https://arxiv.org/abs/2505.06427

Also: waves, intermittency, vortex, chaos, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, waves, spiral & scroll waves, intermittency, vortex, chaos, spiral defect chaos.

# gst: apropos of drift surfaces, e.g., banana orbits, perturbed toroidal vortices display internal simply connected topology.

<< ️This (AA) work shows that the interiors of perturbed zero-helicity vortices display simply connected topology with a crescent-shaped boundary. Flux surfaces in fluid and magnetic vortices were explored analytically, while particle trajectories in the context of plasma confinement were examined numerically, demonstrating the existence of both toroidal and simply connected topologies. >>

<< ️Numerical simulations of particle trajectories were conducted in the context of fusion confinement to calculate particle trajectories in a perturbed Soloviev equilibrium where simply connected flux surfaces were observed. The orbits often displayed crescent shapes, yet showed several marked differences from the flux surfaces, e.g., gyro-radii of size comparable to the crescent diameter, asymmetric crescents, connections between well-separated crescent tips, and possibly toroidal shapes, with an inversion of the roles played by the major and minor axes. >>

<< ️This new topology appears for perturbations in a broad class, with amplitudes and spatial variance allowed to be arbitrarily small. A corollary of this work proves the closedness of field lines under odd-parity perturbations of zero-helicity vortices. >>

Taosif Ahsan, Samuel A. Cohen, Alan H. Glasser. Perturbed Toroidal Vortices Display Internal Simply Connected Topology. arXiv: 2507.04596v1 [math-ph]. Jul 7, 2025. 

https://arxiv.org/abs/2507.04596

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

Keywords: gst, vortex, particle, transition, foliated torus, toroidal vortices, banana orbits. 

# gst: the turbulence development at its initial stage, a scenario based on the idea of vortices decay.

<< ️In this paper, a model of the development of a quantum turbulence in its initial stage is proposed. The origin of the turbulence in the suggested model is the decay of vortex loops with an internal structure. >>

AA << ️consider the initial stage of this process, before an equilibrium state is established. As result of (Their) study, the density matrix of developing turbulent flow is calculated. The quantization scheme of the classical vortex rings system is based on the approach proposed by the author earlier. >>

S.V. Talalov. The turbulence development at its initial stage: a scenario based on the idea of vortices decay. arXiv: 2303.05908v3 [physics.flu-dyn]. Feb 16, 2024.

https://arxiv.org/abs/2303.05908

Also: << Lo "smoothing" e', nell' essenziale, un atteggiamento, un comportamento piu' o meno automatico, una tecnica, una prassi. (..) tutte le volte che uno "smoother" livella un vortice (piu' verosimilmente crede di aver circoscritto un vortice per livellarlo), se non e' accorto (non lo e' quasi mai) mentre cerca di spianare lo potenzia e, allo stesso tempo - questo e' il fatto curioso - puo' avere inconsapevolmente generato i presupposti per accenderne in prospettiva almeno un' altro. Oppure altri due. Oppure 'n'. >> In: Smoothers. Notes (quasi-stochastic poetry). Mar 27, 2006.

http://inkpi.blogspot.com/2006/03/1980-smoothers.html

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

Keywords: gst, turbulence, vortex.

# gst: irreversibility in scalar active turbulence, the role of topological defects.

<< ️In many active systems, swimmers collectively stir the surrounding fluid to stabilize some self-sustained vortices. The resulting nonequilibrium state is often referred to as active turbulence, by analogy with the turbulence of passive fluids under external stirring. Although active turbulence clearly operates far from equilibrium, it can be challenging to pinpoint which emergent features primarily control the deviation from an equilibrium reversible dynamics. >>

Here, AA << reveal that dynamical irreversibility essentially stems from singularities in the active stress. Specifically, considering the coupled dynamics of the swimmer density and the stream function, (AA) demonstrate that the symmetries of vortical flows around defects determine the overall irreversibility. (Their) detailed analysis leads to identifying specific configurations of defect pairs as the dominant contribution to irreversibility. >>

Byjesh N. Radhakrishnan, Francesco Serafin, et al. Irreversibility in scalar active turbulence: The role of topological defects. arXiv:2507.06073v1 [cond-mat.stat-mech]. Jul 8, 2025.

https://arxiv.org/abs/2507.06073

Also: swim, turbulence, vortex, self-assembly, chaos, clinamen, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, swim, swimmers, turbulence, active turbulence, vortex, self-assembly, chaos, defects, topological defects, deviation, clinamen.

# gst: energy spectra and fluxes of 2D turbulent quantum droplets.

AA << explore the energy spectra and associated fluxes of turbulent two-dimensional quantum droplets subjected to a rotating paddling potential which is removed after a few oscillation periods. A systematic analysis on the impact of the characteristics (height and velocity) of the rotating potential and the droplet atom number reveals the emergence of different dynamical response regimes. >>

<< ️Significant distortions are observed in the droplet periphery in the presence of a harmonic trap. A direct energy cascade (from large to small length scales) is mainly identified through the flux. >>

Their << ️findings offer insights into the turbulent response of exotic phases of matter, featuring quantum fluctuations, and may inspire investigations aiming to unravel self-similar nonequilibrium dynamics. >>

Shawan Kumar Jha, Mahendra K. Verma, et al. Energy spectra and fluxes of two-dimensional turbulent quantum droplets. Phys. Rev. Fluids 10, 064618. Jun 25, 2025.

https://journals.aps.org/prfluids/abstract/10.1103/pj6n-3w6p

arXiv:2501.01771v1 [cond-mat.quant-gas]. Jan 3, 2025.

https://arxiv.org/abs/2501.01771

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

Keywords: gst, drop, droplet, droploid, turbulence, vortex, harmonic trap, quantum fluctuations, exotic phases of matter, self-similar nonequilibrium dynamics

# gst: diffusion and decay of an expanding turbulent blob; the cascade can leave an indelible footprint far into the decay process

<< Turbulence, left unforced, decays and invades the surrounding quiescent fluid. Though ubiquitous, this simple phenomenon has proven hard to capture within a simple and general framework. >>

Here, AA << circumvent these issues by creating a spatially-localized blob of turbulent fluid using eight converging vortex generators focused towards the center of a tank of water, and observe its decay and spread over decades in time, using particle image velocimetry with a logarithmic sampling rate. >>

<< The blob initially expands and decays until it reaches the walls of the tank and eventually transitions to a second regime of approximately spatially uniform decay. (AA) interpret these dynamics within the framework of a nonlinear diffusion equation, which predicts that the ideal quiescent-turbulent fluid boundary is sharp and propagates non-diffusively, driven by turbulent eddies while decaying with characteristic scaling laws. >>

AA << find direct evidence for this model within the expansion phase of (their) turbulent blob and use it to account for the detailed behavior (they) observe, in contrast to earlier studies. (AA) work provides a detailed spatially-resolved narrative for the behavior of turbulence once the forcing is removed, and demonstrates unexpectedly that the turbulent cascade leaves an indelible footprint far into the decay process. >>

Takumi Matsuzawa, Minhui Zhu, et al. Nonlinear Diffusion and Decay of an Expanding Turbulent Blob. arXiv: 2505.22737v2 [physics.flu-dyn]. May 30, 2025

https://arxiv.org/abs/2505.22737

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

Keywords: gst, quiescence, quiescent fluids, blobs, turbulent blobs, turbulent eddies, turbulent cascade, expansion and decay.