# gst: apropos of smallest amplitude perturbations that trigger transition to turbulence, the minimal seeds in the Stokes boundary layer.

<< ️Minimal seeds, the smallest amplitude perturbations that trigger transition to turbulence, are presented in the Stokes boundary layer, the oscillating flow of a viscous fluid above a flat plate. The minimal seed trajectories are dominated by the Stokes boundary layer's large linear transient growth at early times, but only 73% of the initial energy is formed from the linearly optimal growing mode; the remainder ensures that nonlinear interaction transfers energy from spanwise- to streamwise- independent structures, and makes up for a timing mismatch between the end of linear transient growth and the production phase of the edge state (the saddle point separating laminar and turbulent basins of attraction). >>

Tom Eaves. Minimal seeds in the Stokes boundary layer. arXiv: 2604.23213v1 [physics.flu-dyn]. Apr 25, 2026.

https://arxiv.org/abs/2604.23213

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

Keywords: gst, turbulence, transitions, minimal seeds, laminar and turbulent basins of attraction.

# gst: turbulent pair dispersion with stochastic generative diffusion models.

<< ️Recent advances in data-driven modeling have shown that diffusion models can successfully generate synthetic Lagrangian trajectories in turbulent flows. Building on this progress, (AA) extend the method to the joint generation of pairs of Lagrangian velocity trajectories, enabling a fully data-driven representation of turbulent pair dispersion, a long-standing fundamental problem with broad relevance in fluid dynamics. >>

<< ️(They) demonstrate that diffusion models accurately reproduce the evolution of particle-pair separation, including deviations from Richardson's classical scaling law, while simultaneously preserving all key single-particle statistical properties reported in previous studies. These findings underscore the potential of diffusion-based generative models to emulate high-dimensional, multi-scale turbulent dynamics, further establishing them as a powerful tool for scientific modeling and for future geophysical and astrophysical applications. >>

Pantera A., Biferale L., Buzzicotti M., et al. Turbulent pair dispersion with Stochastic Generative Diffusion Models. arXiv: 2604.12932v1 [physics.flu-dyn]. Apr 14, 2026.

https://arxiv.org/abs/2604.12932

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

Keywords: gst, turbulence, waves, diffusion models, turbulent flows, turbulent pair dispersion, stochastic generative diffusion models (DM), direct numerical simulation (DNS).

# gst: early warning signals for primary and secondary bifurcation to oscillatory instabilities.

<< ️In several natural and engineering systems, changes in control parameters can trigger bifurcations that lead to sustained or growing periodic oscillations, indicating the onset of oscillatory instabilities. Such emergent behaviour often results from positive feedback between interacting subsystems, resulting in large-amplitude oscillations that can be detrimental. >>

<< ️Several precursors are available to provide early warning of an impending oscillatory instability. In reality, practical systems may exhibit different sequences of bifurcations, including a primary bifurcation to an oscillatory state that may be either continuous or abrupt, followed by an abrupt secondary bifurcation, and further transitions beyond the secondary bifurcation. Existing precursors for oscillatory instabilities typically forewarn the onset of the primary bifurcation to an oscillatory state and tend to saturate once the system enters the oscillatory regime. Notably, primary bifurcations often involve lower amplitudes compared to the more severe states after secondary bifurcation. >>

<< ️In this study, (AA) propose a methodology based on spectral visibility graphs to get forewarning for both primary and secondary bifurcations. The method inherently captures the evolution of the harmonic content of the signal relative to other frequency components. The approach employs tuning of a single sensitivity parameter to detect different sequences of bifurcation. (They) demonstrate the usefulness of (Their) method for thermo-acoustic and aero-acoustic instabilities in multiple engineering systems involving turbulent flow and reactions. (Their) methodology can help systems prepare in advance or even avoid undesirable transitions. Tuning the sensitivity parameter allows adaptive, risk-based warnings, ensuring high performance without tipping into undesirable regimes. >>

Rohit Radhakrishnan, Prasana Kumar, Induja Pavithran, et al. Early warning signals for primary and secondary bifurcation to oscillatory instabilities. arXiv: 2603.24068v1 [physics.flu-dyn]. Mar 25, 2026.

https://arxiv.org/abs/2603.24068

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

Keywords: gst, instability, turbulence, transitions, bifurcation, feedback.

# gst: apropos of different degrees of decimation, reduction of triadic interactions suppresses intermittency and anomalous dissipation in turbulence.

<< ️(AA) investigate how the defining statistical features of three-dimensional turbulence respond to systematic reductions of the Fourier-space triadic interaction network. Using direct numerical simulations of both fractally and homogeneously decimated Navier-Stokes dynamics, (They) show that progressive thinning of the set of active modes leads to a systematic suppression of intermittency and, most strikingly, to the vanishing of the mean dissipation rate in the large-Reynolds-number limit. >>

<< ️Structure-function exponents collapse onto their dimensional values, the multifractal singularity spectrum contracts, and the analyticity width extracted from the exponential spectral tail increases monotonically with decimation-each indicating a substantial regularization of the velocity field. >>

<< ️Together, these results provide direct evidence that anomalous dissipation in incompressible turbulence is not a generic property of the Navier-Stokes equations, but instead requires the full combinatorial richness of their triadic nonlinear interactions. >>

Anikat Kankaria, Ritwik Mukherjee, Sugan Durai Murugan, et al. Reduction of triadic interactions suppresses intermittency and anomalous dissipation in turbulence. arXiv: 2603.19180v1 [physics.flu-dyn]. Mar 19, 2026.

https://arxiv.org/abs/2603.19180

Also: turbulence, intermittency, dissipation, singularity, collapse, transition, network, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, turbulence, three-dimensional turbulence, incompressible turbulence, intermittency, dissipation, anomalous dissipation, singularity, multifractal singularity spectrum contracts, collapse, transitions, networks, triadic interactions, progressive thinning, decimation.

# gst: geometric dynamics of turbulence; a minimal oscillator structure from non-local closure

<< ️Turbulence remains one of the central open problems in classical physics, largely due to the absence of a closed dynamical description of the Reynolds stress. Existing approaches typically rely either on local constitutive assumptions or on high-dimensional statistical representations, without identifying a minimal set of dynamical variables governing the cascade response. >>

<< ️Here (AA) show that the non-local stress response implied by the Navier-Stokes equations admits a systematic reduction onto a low-dimensional anisotropic sector of the turbulent cascade. This reduction leads to a minimal dynamical system with the structure of a damped oscillator, arising from the coupling between the leading angular mode and its nonlinear transfer to higher-order sectors. >>

<< ️Within this framework, classical turbulent behaviors -- including inertial-range scaling, shear-driven transport, and wall-bounded logarithmic profiles -- emerge as different realizations of the same underlying dynamical structure. Universal quantities such as the Kolmogorov constant and the von Kármán constant appear as leading-order consequences of internal consistency conditions applied across homogeneous and shear-driven regimes. >>

<< ️These results suggest that turbulence admits a minimal dynamical backbone governed by non-local cascade response, providing a unified perspective that connects spectral transfer, anisotropy, and mean-flow interaction within a single reduced framework. >>

Alejandro Sevilla. Geometric Dynamics of Turbulence: A Minimal Oscillator Structure from Non-local Closure. arXiv: 2603.18913v3 [physics.flu-dyn]. Mar 24, 2026. 

https://arxiv.org/abs/2603.18913

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

Keywords: gst, turbulence, cascade response, non-local stress response, damped oscillators, inertial-range scaling, shear-driven transport, wall-bounded log profiles, spectral transfer, anisotropy, mean-flow interaction.

# gst: dynamics of small bubbles in turbulence in non-dilute conditions.

<< Turbulent flows laden with small bubbles are ubiquitous in many natural and industrial environments. From the point of view of numerical modeling, to be able to handle a very large number of small bubbles in direct numerical simulations, one traditionally relies on the one-way coupling paradigm. There, bubbles are passively advected and are noninteracting, implicitly assuming dilute conditions. >>

<< Here, (AA) study bubbles that are four-way coupled, where both the feedback on the fluid and excluded-volume interactions between bubbles are taken into account. (They) find that, while the back reaction from the bubble phase onto the fluid phase remains energetically small under most circumstances, the excluded-volume interactions between bubbles can have a significant influence on the Lagrangian statistics of the bubble dynamics. (They) show that as the volume fraction of bubbles increases, the preferential concentration of bubbles in filamentary high-vorticity regions decreases as these strong vortical structures get filled up; this happens at a volume fraction of around one percent for Re𝜆=𝒪⁡(10^2). >>

<< (AA) furthermore study the influence on the Lagrangian velocity-structure function as well as pair dispersion, and find that, while the mean dispersive behavior remains close to that obtained from one-way coupling simulations, some evident signatures of bubble collisions can be retrieved from the structure functions and the distribution of the dispersion, even at very small volume fractions. >>

Xander M. de Wit, Hessel J. Adelerhof, André Freitas, et al. Dynamics of small bubbles in turbulence in non-dilute conditions. Phys. Rev. Fluids 11, 024602. Feb 5, 2026.

https://journals.aps.org/prfluids/abstract/10.1103/ny7h-wlxl

arXiv: 2510.03968v2 [physics.flu-dyn]. Jan 29, 2026.

https://arxiv.org/abs/2510.03968

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

Keywords: gst, bubble, bubble dynamics, bubble collisions, turbulence, one-way coupling, four-way coupling.

# gst: time-delayed dynamics in regular Kuramoto networks with inertia: multistability, traveling waves, chimera states, and transitions to seizure-like activity.

<< ️This (AA) study examines the complex interplay between inertia and time delay in regular rotor networks within the framework of the second-order Kuramoto model. By combining analytical and numerical methods, (AA) demonstrate that intrinsic time delays -- arising from finite information transmission speeds - induce multistability among fully synchronized phase-locked states. >>

<< ️Unlike systems without inertia, the presence of inertia destabilizes these phase-locked states, reduces their basin of attraction, and gives rise to nonlinear phase-locked dynamics over specific inertia ranges. >>

<< ️In addition, (They) show that time delays promote the emergence of turbulent chimera states, while inertia enhances their spatial extent. Notably, the combined influence of inertia and time delay produces dynamic patterns reminiscent of partial epileptic seizures. >>

Esmaeil Mahdavi, Mina Zarei, Philipp Hövel, Farhad Shahbazi. Time-Delayed Dynamics in Regular Kuramoto Networks with Inertia: Multistability, Traveling Waves, Chimera States, and Transitions to Seizure-Like Activity.  arXiv: 2512.16640v1 [nlin.AO]. Dec 18, 2025.

https://arxiv.org/abs/2512.16640

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

Keywords: gst, networks, transitions, waves, chimera, turbulence, inertia, time delay, multistability, epileptic seizures.

# gst: degrees of universality in wave turbulence

<< ️Turbulence of weakly interacting waves displays a great deal of universality: independence of the details of the interaction and of the pumping and dissipation scales. Here (AA) study how inverse turbulent cascades (from small to large scales) transition from weak to strong. (They) find that while one-loop corrections can be dependent on excitation and dissipation scales, new types of universality appear in strong turbulence. (They) contrast turbulence of spin waves in ferromagnets with turbulent cascades in the Nonlinear Schrödinger Equation (NSE) and in an MMT-like (Majda-McLaughlin-Tabak) model in higher dimensions having a multiplicative interaction vertex: vertex renormalization gives rise to dependence on the pumping (UV scale) in the former but not in the latter. >>

<< ️As a result of this spectral nonlocality, spin-wave turbulence stops being weak if one is sufficiently far from the pumping scale, even when the interaction of waves with comparable wavenumbers is weak. (AA) paraphrase this as: nonlocality enhances nonlinearity. >>

<< ️(AA) then describe strong turbulence in a multi-component version of these models with a large number of components. (They) argue that strong spin-wave turbulence is similar to turbulence of the focusing NSE, as it realizes a critical-balance state. However, UV nonlocality causes the level of spin-wave turbulence at large scales to decrease with increasing pumping level, culminating in a state that is independent of the level of pumping. >>

Jiasheng Liu, Vladimir Rosenhaus, Gregory Falkovich. Degrees of universality in wave turbulence. arXiv: 2512.04866v1 [cond-mat.stat-mech]. Dec 4, 2025.

https://arxiv.org/abs/2512.04866

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

Keywords: gst, waves, turbulence, transitions.

# gst: turbulence at low Reynolds numbers.

<< ️Turbulence -- ubiquitous in nature and engineering alike  -- is traditionally viewed as an intrinsically inertial phenomenon, emerging only when the Reynolds number (Re), which quantifies the ratio of inertial to dissipative forces, far exceeds unity. >>

<< ️Here, (AA) demonstrate that strong energy flux between different length scales of motion -- a defining hallmark of turbulence -- can persist even at Re ~ 1, thereby extending the known regime of turbulent flows beyond the classical high-Re paradigm. (They) show that scale-to-scale energy transfer can be recast as a mechanical process between turbulent stress and large-scale flow deformation. >>

<< ️In quasi-two-dimensional (quasi-2D) flows driven by electromagnetic forcing, (They) introduce directionally biased perturbations that enhance this interaction, amplifying the spectral energy flux by more than two orders of magnitude, even in the absence of dominant inertial forces. >>

<< ️This (AA) study establishes a new regime of 2D Navier-Stokes (N-S) turbulence, challenging long-standing assumptions about the high Re conditions required for turbulent flows. Beyond revising classical belief, (Their) results offer a generalizable strategy for engineering multiscale transport in flows that lack inertial dominance, such as those found in microfluidic and low-Re biological systems. >>

Ziyue Yu, Xinyu Si, Lei Fang. Turbulence at Low Reynolds Numbers. arXiv: 2511.05800v1 [physics.flu-dyn]. Nov 8, 2025.

https://arxiv.org/abs/2511.05800

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

Keywords: gst, turbulence, chaos,  transitions.

# gst: geometric intermittency in turbulence.

<< ️Equal-time scaling exponents in fully developed turbulence typically exhibit non anomalous scaling in the inverse cascade of two-dimensional (2D) turbulence and anomalous scaling in three dimensions. >>

<< ️(AA) have shown that intermittency in turbulence is not exhausted by longitudinal and transverse velocity increments: geometric increments of the velocity field display equally strong, and in some regimes stronger, multiscaling. This reveals a previously hidden intermittency in the 2D inverse cascade and identifies a universal class of geometric scaling exponents. >>

<< ️This, of course, leads to questions of whether long-lived vortical structures play a more significant role in making flows intermittent, especially in 2D, than appreciated hitherto. >>

<< ️(AA) results also suggest that the geometry of turbulent velocity fields plays a fundamental role in cascade dynamics and opens a route to probing intermittency, blind to conventional structure functions, in other flows. >>

Ritwik Mukherjee, Siddhartha Mukherjee, I. V. Kolokolov, et al. Geometric Intermittency in Turbulence. arXiv: 2511.06439v1 [physics.flu-dyn]. Nov 9, 2025.

https://arxiv.org/abs/2511.06439

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

Keywords: gst, turbulence, intermittency, cascade dynamics, multiscaling, multiscaling 2D inverse cascade, 

# gst: effect of stochasticity on initial transients and chaotic itinerancy for a natural circulation loop.

<< ️The introduction of stochastic forcing to dynamical systems has been shown to induce qualitatively different behaviors, such as attractor hopping, to otherwise stable systems as they approach bifurcation. In this (AA) study, the effect of stochastic forcing on systems that have already undergone bifurcation and evolve on a chaotic attractor is explored. Markov and state-independent models of turbulence-induced stochasticity are developed, and their effects on a natural circulation loop operating in the chaotic regime are compared. >>

<< ️Stochasticity introduces considerable uncertainty into the duration of the initial chaotic transient but tends to accelerate it on average. An Ornstein-Uhlenbeck model of turbulent fluctuations is shown to produce results equivalent to a bootstrapped raw direct numerical simulation signal. >>

<< Similar, though less pronounced, effects are found for systems operating in the chaotic itinerant regime. The Markov model of chaotic itinerancy which is typically applied to this class of problems is shown to be invalid for this system and the Lorenz system, to which it has been applied in the past. >>

<< ️Off-discrete transitions and an upper limit on the time between flow reversals are explained by near misses of the attractor ruins caused by lingering excitation of high-order modes during chaotic itinerancy. >>

John Matulis, Hitesh Bindra. Effect of stochasticity on initial transients and chaotic itinerancy for a natural circulation loop. Phys. Rev. E 112, 044223. Oct 23, 2025

https://journals.aps.org/pre/abstract/10.1103/42pn-wttx

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

Keywords: gst, disorder, fluctuations, turbulence, attractor, chaos, transition, uncertainty, stochasticity, flow instability, chaotic itinerancy, noise-induced transitions.

# gst: a probability space at inception of stochastic process.

<< ️Recently, progress has been made in the theory of turbulence, which provides a framework on how a deterministic process changes to a stochastic one owing to the change in thermodynamic states. It is well known that, in the framework of Newtonian mechanics, motions are dissipative; however, when subjected to periodic motion, a system can produce nondissipative motions intermittently and subject to resonance. It is in resonance that turbulence occurs in fluid flow, solid vibration, thermal transport, etc. In this, the findings from these physical systems are analyzed in the framework of statistics with their own probability space to establish their compliance to the stochastic process. >>

<< ️In particular, a systematic alignment of the inception of the stochastic process with the signed measure theory, signed probability space, and stochastic process was investigated. It was found that the oscillatory load from the dissipative state excited the system and resulted in a quasi-periodic probability density function with the negative probability regimes. In addition, the vectorial nature of the random velocity splits the probability density function along both the positive and negative axes with slight asymmetricity. By assuming that a deterministic process has a probability of 1, (AA) can express the inception of a stochastic process, and the subsequent benefit is that a dynamic fractal falls on the probability density function. Moreover, (They) leave some questions of inconsistency between the physical system and the measurement theory for future investigation. >>

Liteng Yang, Yuliang Liu, et al. A Probability Space at Inception of Stochastic Process. arXiv: 2510.20824v1 [nlin.CD]. Oct 8, 2025.

https://arxiv.org/abs/2510.20824

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

Keywords: gst, turbulence, dissipation, intermittency, randomness, transitions.

# gst: extreme vertical drafts as drivers of Lagrangian dispersion in stably stratified turbulent flows.

<< ️The dispersion of Lagrangian particle pairs is a fundamental process in turbulence, with implications for mixing, transport, and the statistical properties of particles in geophysical and environmental flows. While classical theories describe pair dispersion through scaling laws related to energy cascades, extreme events in turbulent flows can significantly alter these dynamics. This is especially important in stratified flows, where intermittency manifests itself also as strong updrafts and downdrafts. >>

<< ️In this study, (AA) investigate the influence of extreme events on the relative dispersion of particle pairs in stably stratified turbulence. Using numerical simulations (They) analyze the statistical properties of pair separation across different regimes, and quantify deviations from classical Richardson scaling. (Their) results highlight the role of extreme drafts in accelerating dispersion. >>

Christian Reartes, Pablo D. Mininni, Raffaele Marino. Extreme vertical drafts as drivers of Lagrangian dispersion in stably stratified turbulent flows. arXiv: 2509.12962v1 [physics.flu-dyn]. Sep 16, 2025.

https://arxiv.org/abs/2509.12962

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

Keywords: gst, turbulence, stratified turbulence,  intermittency, chaos, transitions, particles, extreme events, stratified flows, accelerating dispersion.

# gst: extreme event precursor prediction in turbulence.

<< ️(AA) present a general framework to predict precursors to extreme events in turbulent dynamical systems. The approach combines phase-space reconstruction techniques with recurrence matrices and convolutional neural networks (CNN) to identify precursors to extreme events. >>

<< ️(They) evaluate the framework across three distinct testbed systems: a triad turbulent interaction model, a prototype stochastic anisotropic turbulent flow, and the Kolmogorov flow. This method offers three key advantages: (1) a threshold-free classification strategy that eliminates subjective parameter tuning, (2) efficient training using only O (100) recurrence matrices, and (3) ability to generalize to unseen systems. >>

<< ️The results demonstrate robust predictive performance across all test systems: 96% detection rate for the triad model with a mean lead time of 1.8 time units, 96% for the anisotropic turbulent flow with a mean lead time of 6.1 time units, and 93% for the Kolmogorov flow with a mean lead time of 22.7 units. >> 

Rahul Agarwal, Mustafa A. Mohamad. Extreme Event Precursor Prediction in Turbulent Dynamical Systems via CNN-Augmented Recurrence Analysis. arXiv: 2508.04301v1 [cs.CE]. Aug 6, 2025.

https://arxiv.org/abs/2508.04301

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

Keywords: gst, turbulence, chaos, extreme events, convolutional neural networks (CNN).

# gst: fluctuations around turbulence

<< ️Numerical simulations of turbulent flows at realistic Reynolds numbers generally rely on filtering out small scales from the Navier Stokes equations and modeling their impact through the Reynolds stress tensor τ_ij. Traditional models approximate τ_ij solely as a function of the filtered velocity gradient, leading to deterministic subgrid scale closures. However, small scale fluctuations can locally exhibit instantaneous values whose deviation from the mean can have a significant influence on flow dynamics. >>

<< ️In this work, (AA) investigate these effects by employing direct numerical simulations combined with Gaussian filtering to quantify subgrid scale effects and evaluating the local energy flux in both space and time. The mean performance of the canonical Clark model is assessed by conditioning the energy flux distributions on the invariants of the filtered velocity gradient tensor, Q and R. The Clark model captures to a good degree the mean energy flux. However, the fluctuations around these mean values for given (Q, R) are of the order of the mean displaying fat tailed distributions. ️To become more precise, (AA) examine the joint distributions of true energy flux and the predictions from both the Clark and the Smagorinsky models. >>

<< ️This approach mirrors the strategy adopted in early stochastic subgrid scale models. Clear non Gaussian characteristics emerge from the obtained distributions, particularly through the appearance of heavy tails. The mean, the variance, the skewness and flatness of these distributions are quantified. (Their) results emphasize that fluctuations are an integral component of the small scale feedback onto large scale dynamics and should be incorporated into subgrid scale modeling through an appropriate stochastic framework. >>

Flavio Tuteri, Alexandros Alexakis, Sergio Chibbaro. Fluctuations around Turbulence Models. arXiv: 2507.17575v1 [physics.flu-dyn]. Jul 23, 2025. 

https://arxiv.org/abs/2507.17575

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

Keywords: gst, disorder & fluctuations, turbulence.

# 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: wave-kinetic dynamics of forced-dissipated turbulent internal gravity waves

<< Internal gravity waves are an essential feature of stratified media, such as oceans and atmospheres. >>

<< To investigate their dynamics, (AA) perform simulations of the forced-dissipated kinetic equation describing the evolution of the energy spectrum of weakly nonlinear internal gravity waves. >>

<< During the early evolution, three well-known nonlocal interactions, the elastic scattering, the induced diffusion, and the parametric subharmonic instability, together with a superharmonic resonance play a prominent role. >>

<< In contrast, local interactions are responsible for anisotropic energy cascade on longer timescales. >>

AA << reveal emergence of a condensate at small horizontal wave vectors that can be interpreted as a pure wave-wave interaction-mediated layering process. >>

Vincent Labarre, Giorgio Krstulovic, Sergey Nazarenko. Wave-Kinetic Dynamics of Forced-Dissipated Turbulent Internal Gravity Waves. Phys. Rev. Lett. 135, 014101. Jul 1, 2025.

https://journals.aps.org/prl/abstract/10.1103/b82h-z21n

arXiv:2407.11469v3 [physics.flu-dyn]. Mar 28, 2025.

https://arxiv.org/abs/2407.11469

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

Keywords: gst, waves, weakness, turbulence, transitions, stratified turbulence, wave-turbulence interactions, weak turbulence.

# 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: turbulence spreading and anomalous diffusion on combs.

<< This (AA) paper presents a simple model for such processes as chaos spreading or turbulence spillover into stable regions. In this simple model the essential transport occurs via inelastic resonant interactions of waves on a lattice. The process is shown to result universally in a subdiffusive spreading of the wave field. The dispersion of this spreading process is found to depend exclusively on the type of the interaction process (three- or four-wave), but not on a particular underlying instability. The asymptotic transport equations for field spreading are derived with the aid of a specific geometric construction in the form of a comb. >>

<< The results can be summarized by stating that the asymptotic spreading proceeds as a continuous-time random walk (CTRW) and corresponds to a kinetic description in terms of fractional-derivative equations. The fractional indexes pertaining to these equations are obtained exactly using the comb model. >>

<< A special case of the above theory is a situation in which two waves with oppositely directed wave vectors couple together to form a bound state with zero momentum. This situation is considered separately and associated with the self-organization of wave-like turbulence into banded flows or staircases. >>

<< Overall, (AA) find that turbulence spreading and staircasing could be described based on the same mathematical formalism, using the Hamiltonian of inelastic wave-wave interactions and a mapping procedure into the comb space. Theoretically, the comb approach is regarded as a substitute for a more common description based on quasilinear theory. Some implications of the present theory for the fusion plasma studies are discussed and a comparison with the available observational and numerical evidence is given. >>

Alexander V. Milovanov, Alexander Iomin, Jens Juul Rasmussen. Turbulence spreading and anomalous diffusion on combs. Phys. Rev. E 111, 064217 – Published 24 June, 2025

https://journals.aps.org/pre/abstract/10.1103/cmf5-sf8x#d93038b1-6671-419d-be1e-219e5bf78523

Also: waves, turbulence, walk, self-assembly, instability, chaos, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, waves, turbulence, walk, self-assembly, instability, chaos, comb model, inelastic resonant interactions, inelastic wave-wave interactions, continuous-time random walk, self-organization of wave-like turbulence, Lévy flights, Lévy walks