# 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: uncertainty growth in stably stratified turbulence.

<< ️(AA) investigate uncertainty growth and chaotic dynamics in statistically steady, stably stratified three-dimensional turbulence. Using direct numerical simulations of the Boussinesq equations, (They) quantify the divergence of initially infinitesimal perturbations via twin simulations and decorrelator diagnostics. >>

<< ️At short times, perturbations exhibit exponential growth, allowing us to define a (largest) Lyapunov exponent. (AA) systematically examine how this exponent depends on stratification strength, quantified by the Brunt-Väisälä frequency and the Froude number, in a parameter regime relevant to oceanic flows. >>

<< (They) find that increasing stratification leads to a monotonic reduction of the Lyapunov exponent, indicating suppressed chaoticity. Despite this reduction, uncertainty growth retains the universal temporal sequence observed in homogeneous isotropic turbulence—initial decay, exponential growth, and saturation. The growth phase is characterized by self-similar decorrelator spectra, but exhibits strong anisotropy: uncertainty spreads much more slowly along the stratification direction than horizontally, with the disparity increasing with stratification strength. >>

<< ️An analysis of the decorrelator evolution equation reveals that the suppression of chaos arises primarily from strain-mediated alignment dynamics rather than direct buoyancy coupling. (AA) results provide a quantitative characterization of predictability and uncertainty growth in stratified turbulence and highlight the utility of decorrelator-based methods for anisotropic geophysical flows. >>

Mrinal Jyoti Powdel, Samriddhi Sankar Ray. Uncertainty growth in stably stratified turbulence. Phys. Rev. Fluids 11, 064615. Jun 23, 2026. 

https://journals.aps.org/prfluids/abstract/10.1103/xblr-vpl3

arXiv: 2512.05656v1 [physics.flu-dyn].

https://arxiv.org/abs/2512.05656

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

Keywords: gst, chaos, turbulence, transitions, uncertainty growth, three-dimensional turbulence, stratified turbulence, infinitesimal perturbations, stratification strength, anisotropy. 

# 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: free-surface deformations induced by three-dimensional turbulence.

<< ️(AA) report the experimental characterization of free-surface deformations generated by three-dimensional homogeneous and isotropic turbulence. Using Fourier transform profilometry in a jet-forced turbulent tank, (They) perform spatiotemporal measurements of the surface elevation field over a wide range of turbulence intensities. >>

<< ️The standard deviation of surface deformations scales linearly with subsurface velocity fluctuations. The spectra of surface deformations highlight the coexistence of two mechanisms: transient coherent structures (e.g., upwelling) contributing to the low-frequency, large-scale spectral components, and a passive response to subsurface turbulent pressure fluctuations responsible for the power-law spectral scaling. The wavenumber and frequency spectra of surface deformations exhibit similar power-law exponents (−2.5), suggesting the advection of turbulent structures at the free surface. >> 

<< ️(They) develop a linear response model based on the transfer function from the free surface to turbulent pressure fluctuations, incorporating wave-turbulent damping. The model successfully predicts the main features of the turbulent surface: spatiotemporal spectrum shape, similar spectrum power-law exponents (−7/3), and dominance of passive response over wave generation. These findings provide new insights into free-surface turbulence in regimes where turbulent velocities remain below the surface-breaking threshold. >>

Michaël Berhanu, Eric Falcon. Free-surface deformations induced by three-dimensional turbulence. arXiv: 2605.13654v1 [physics.flu-dyn]. May 13, 2026.

https://arxiv.org/abs/2605.13654

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

Keywords: gst, free-surface turbulence, free-surface deformations, subsurface velocity fluctuations, wave-turbulent damping, surface-breaking threshold.

# gst: apropos of dissipation of fast tides, turbulent damping of fast tidal oscillations by three-dimensional Rayleigh-Bénard convection with a radiating free surface.

<< ️(AA) present three-dimensional Dedalus simulations of Rayleigh–Benard convection with a blackbody-radiating free upper surface, subject to a low-amplitude oscillatory forcing that mimics tidal perturbations in convective envelopes of stars and planets. The forcing period is 10–100 times shorter than the convective timescale, tconv. Using a Reynolds decomposition of the velocity field averaged over one oscillation period, in which the tidal oscillations naturally constitute the fluctuating field and xconvection the mean flow, (They) elucidate the kinetic energy exchange between the two. >>

<< ️Provided the oscillatory Reynolds number exceeds a modest threshold, (They) find that the oscillations systematically transfer kinetic energy to the mean flow at a volume-averaged rate D_R∼u′^(2)t^−1_conv, where u′ is the rms fluctuation velocity. This reflects strong, order-unity correlations between the fluctuation velocities and the mean flow. These arise because the oscillatory forcing displaces fluid elements that are then redirected by buoyancy and incompressibility in the same manner as the mean flow. >>

<< The transfer is dominated by correlations involving vertical velocity fluctuations and vertical gradients of the mean flow. The resulting energy transfer rate is consistent, within the equilibrium-tide framework, with the observed tidal circularisation of solar-type binaries and with the orbital evolution of moons of Jupiter and Saturn. This validates the formalism proposed by Terquem (2021) for the dissipation of fast tides, a longstanding problem. Replacing the free surface with a rigid upper boundary significantly and artificially modifies the correlations. >>

Caroline Terquem, Alexander Boone, Enrico Martinez. Turbulent damping of fast tidal oscillations by three-dimensional Rayleigh-Bénard convection with a radiating free surface. arXiv: 2605.05108v1 [astro-ph.SR]. May 6, 2026.

https://arxiv.org/abs/2605.05108

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

Keywords: gst, turbulence, fluctuations, dissipation, turbulent damping, tidal oscillations, tidal perturbations, Rayleigh-Bénard convection, dissipation of fast tides.

# 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: dynamics and frictional dissipation for treading slowly in a puddle.

<< ️The process of producing a liquid column is common in daily life and industrial applications, such as walking through a puddle and roller printing. While governed by the Navier-Stokes equation, its dynamics are often studied by numerical means, which hinders a full understanding of the rich mixture of physics behind, for instance, the competition of surface and potential energies, and how the pinch off is affected by the kinetic energy and water jet when a large cylinder is used. For pedestrians rushing out of the rain, the water column inevitably involves turbulence and defies simple theoretical analyses.  >>

<< ️As a result, this (AA) work will focus only on cases with a low Reynolds number to enable laminar flow and the existence of reversible and quasistatic stages. Combined with simple models, (They) elucidate the mechanism that drives the change of morphology and derive analytic expressions for the critical height and upper radius for the liquid column when transiting between three stages. >>

<< ️Stage I is characterized by a static and reversible profile for the column whose upper radius 𝑟𝑡 equals that of the cylinder. The column becomes irreversible and 𝑟𝑡 starts shrinking upon entering stage II. It is not until 𝑟𝑡 stops shrinking that the column neck accelerates its contraction and descends toward the pool, the quantitative behavior of which is among the successful predictions of our theory. Pinch off dominates the second half of stage III without its usual signature of self-similarity. This is discussed and explained with an interesting incident involving a water jet similar to that made by a dropping stone. >>

Chung-Hao Chen, Zong-Rou Jiang, Tzay-Ming Hong. Dynamics and frictional dissipation for treading slowly in a puddle. Phys. Rev. E 112, 025105. Aug 25, 2025.

https://journals.aps.org/pre/abstract/10.1103/7t1g-f3fz

arXiv: 2310.09737v2 [physics.flu-dyn]. May 18, 2024.

https://arxiv.org/abs/2310.09737

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

Keywords: walk, walking.

# 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).