scholarly journals Spatial scaling of optical fluctuations during substorm-time aurora

2007 ◽  
Vol 25 (4) ◽  
pp. 915-927 ◽  
Author(s):  
B. V. Kozelov ◽  
K. Rypdal
Keyword(s):  
Turbulent Flows ◽  
Spatial Scales ◽  
Turbulence Models ◽  
Scaling Properties ◽  
Ionosphere Plasma ◽  
Self Organized ◽  
Self Organized Criticality ◽  
Substorm Activity ◽  
Heavy Tailed ◽  
Non Gaussian

Abstract. A study of statistical features of auroras during substorm activity is presented, emphasizing characteristics which are commonly applied to turbulent flows. Data from all-sky television (TV) observations from the Barentsburg observatory (Svalbard) have been used. Features of the probability density function (PDF) of auroral fluctuations have been examined at different spatial scales. We find that the observed PDFs generally have a non-Gaussian, heavy-tailed shape. The generalized structure function (GSF) for the auroral luminosity fluctuations has been analyzed to determine the scaling properties of the higher (up to 6) order moments, and the evolution of the scaling indices during the actual substorm event has been determined. The scaling features obtained can be interpreted as signatures of turbulent motion of the magnetosphere-ionosphere plasma. Relations to previously obtained results of avalanche analysis of the same event, as well as possible implications for the validity of self-organized criticality models and turbulence models of the substorm activity, are discussed.

FRACTALS, SCALING AND THE QUESTION OF SELF-ORGANIZED CRITICALITY IN MAGNETIZATION PROCESSES

Fractals ◽  
1995 ◽  
Vol 03 (02) ◽  
pp. 351-370 ◽  
Author(s):  
GIANFRANCO DURIN ◽  
GIORGIO BERTOTTI ◽  
ALESSANDRO MAGNI
Keyword(s):  
Fractal Dimension ◽  
Domain Wall ◽  
Power Spectra ◽  
Domain Wall Motion ◽  
Soft Magnetic Materials ◽  
Barkhausen Effect ◽  
Scaling Properties ◽  
Domain Wall Dynamics ◽  
Self Organized ◽  
Self Organized Criticality

The main physical aspects and the theoretical description of stochastic domain wall dynamics in soft magnetic materials are reviewed. The intrinsically random nature of domain wall motion results in the Barkhausen effect, which exibits scaling properties at low magnetization rates and 1/f power spectra. It is shown that the Barkhausen signal ν, as well as the size Δx and the duration Δu of jumps follow distributions of the form ν−α, Δx−β, Δu−γ, with α=1−c, β=3/2−c/2, γ=2–c, where c is a dimensionless parameter proportional to the applied field rate. These results are analytically calculated by means of a stochastic differential equation for the domain wall dynamics in a random perturbed medium with brownian properties and then compared to experiments. The Barkhausen signal is found to be related to a random Cantor dust with fractal dimension D=1−c, from which the scaling exponents are calculated using simple properties of fractal geometry. Fractal dimension Δ of the signal v is also studied using four different methods of calculation, giving Δ≈1.5, independent of the method used and of the parameter c. The stochastic model is analyzed in detail in order to clarify if the shown properties can be interpreted as manifestations of self-organized criticality in magnetic systems.

scholarly journals Elastically driven Kelvin–Helmholtz-like instability in straight channel flow

2021 ◽  
Vol 118 (34) ◽  
pp. e2105211118
Author(s):  
Narsing K. Jha ◽  
Victor Steinberg
Keyword(s):  
Turbulent Flows ◽  
Channel Flow ◽  
Elastic Waves ◽  
Hoop Stress ◽  
Spatial Scales ◽  
Shear Layers ◽  
Velocity Difference ◽  
Self Organized ◽  
Free Shear Layers ◽  
Elastic Wave Energy

Originally, Kelvin–Helmholtz instability (KHI) describes the growth of perturbations at the interface separating counterpropagating streams of Newtonian fluids of different densities with heavier fluid at the bottom. Generalized KHI is also used to describe instability of free shear layers with continuous variations of velocity and density. KHI is one of the most studied shear flow instabilities. It is widespread in nature in laminar as well as turbulent flows and acts on different spatial scales from galactic down to Saturn’s bands, oceanographic and meteorological flows, and down to laboratory and industrial scales. Here, we report the observation of elastically driven KH-like instability in straight viscoelastic channel flow, observed in elastic turbulence (ET). The present findings contradict the established opinion that interface perturbations are stable at negligible inertia. The flow reveals weakly unstable coherent structures (CSs) of velocity fluctuations, namely, streaks self-organized into a self-sustained cycling process of CSs, which is synchronized by accompanied elastic waves. During each cycle in ET, counter propagating streaks are destroyed by the elastic KH-like instability. Its dynamics remarkably recall Newtonian KHI, but despite the similarity, the instability mechanism is distinctly different. Velocity difference across the perturbed streak interface destabilizes the flow, and curvature at interface perturbation generates stabilizing hoop stress. The latter is the main stabilizing factor overcoming the destabilization by velocity difference. The suggested destabilizing mechanism is the interaction of elastic waves with wall-normal vorticity leading to interface perturbation amplification. Elastic wave energy is drawn from the main flow and pumped into wall-normal vorticity growth, which destroys the streaks.

scholarly journals 1/ f Noise and multifractality from bristlecone pine growth explained by the statistical convergence of random data

2017 ◽  
Vol 473 (2198) ◽  
pp. 20160586 ◽  
Author(s):  
Wayne S. Kendal
Keyword(s):  
Power Law ◽  
Random Systems ◽  
Mean Power ◽  
Random Data ◽  
Pine Tree ◽  
Self Organized ◽  
Bristlecone Pine ◽  
Tweedie Distribution ◽  
Self Organized Criticality ◽  
Non Gaussian

Tree-ring growth records from bristlecone pines reveal an irregular pattern of fluctuations that have been linked to climatic change but otherwise have remained poorly understood. We find within these records evidence for a temporally related variance to mean power law, 1/ f noise and multifractality that empirically resembles a fractal stochastic process and could be attributed to self-organized criticality. These growth records, however, also conformed to a non-Gaussian statistical distribution (the Tweedie compound Poisson distribution) characterized by an inherent variance to mean power law, that by itself implies 1/ f noise. This distribution has a fundamental role in statistical theory as a focus of convergence for many types of random data, much like the Gaussian distribution has with the central limit theorem. The growth records were also multifractal, with the dimensional exponent of the Tweedie distribution critically balanced near the transition point between fractal stochastic processes and gamma distributed data, possibly consequent to a related convergence effect. Non-Gaussian random systems, like those related to bristlecone pine tree growth, may express 1/ f noise and multifractality through mathematical convergence effects alone, without the dynamical assumptions of self-organized criticality.

scholarly journals Self-organized criticality of turbulence in strongly stratified mixing layers

2018 ◽  
Vol 856 ◽  
pp. 228-256 ◽  
Author(s):  
Hesam Salehipour ◽  
W. R. Peltier ◽  
C. P. Caulfield
Keyword(s):  
Turbulent Flows ◽  
Initial Conditions ◽  
Self Regulation ◽  
Extended Period ◽  
Quasi Equilibrium ◽  
Mean Flow ◽  
Wave Instability ◽  
Scale Invariant ◽  
Self Organized ◽  
Self Organized Criticality

Motivated by the importance of stratified shear flows in geophysical and environmental circumstances, we characterize their energetics, mixing and spectral behaviour through a series of direct numerical simulations of turbulence generated by Holmboe wave instability (HWI) under various initial conditions. We focus on circumstances where the stratification is sufficiently ‘strong’ so that HWI is the dominant primary instability of the flow. Our numerical findings demonstrate the emergence of self-organized criticality (SOC) that is manifest as an adjustment of an appropriately defined gradient Richardson number, $Ri_{g}$, associated with the horizontally averaged mean flow, in such a way that it is continuously attracted towards a critical value of $Ri_{g}\sim 1/4$. This self-organization occurs through a continuously reinforced localization of the ‘scouring’ motions (i.e. ‘avalanches’) that are characteristic of the turbulence induced by the breakdown of Holmboe wave instabilities and are developed on the upper and lower flanks of the sharply localized density interface, embedded within a much more diffuse shear layer. These localized ‘avalanches’ are also found to exhibit the expected scale-invariant characteristics. From an energetics perspective, the emergence of SOC is expressed in the form of a long-lived turbulent flow that remains in a ‘quasi-equilibrium’ state for an extended period of time. Most importantly, the irreversible mixing that results from such self-organized behaviour appears to be characterized generically by a universal cumulative turbulent flux coefficient of $\unicode[STIX]{x1D6E4}_{c}\sim 0.2$ only for turbulent flows engendered by Holmboe wave instability. The existence of this self-organized critical state corroborates the original physical arguments associated with self-regulation of stratified turbulent flows as involving a ‘kind of equilibrium’ as described by Turner (1973, Buoyancy Effects in Fluids, Cambridge University Press).

Kraichnan–Leith–Batchelor similarity theory and two-dimensional inverse cascades

2015 ◽  
Vol 767 ◽  
pp. 467-496 ◽  
Author(s):  
B. H. Burgess ◽  
R. K. Scott ◽  
T. G. Shepherd
Keyword(s):  
Large Scale ◽  
Similarity Theory ◽  
Vortex Formation ◽  
Turbulence Models ◽  
Two Dimensional ◽  
Scaling Properties ◽  
Inverse Cascade ◽  
Coherent Vortices ◽  
Coherent Vortex ◽  
Non Gaussian

AbstractWe study the scaling properties and Kraichnan–Leith–Batchelor (KLB) theory of forced inverse cascades in generalized two-dimensional (2D) fluids (${\it\alpha}$-turbulence models) simulated at resolution $8192^{2}$. We consider ${\it\alpha}=1$ (surface quasigeostrophic flow), ${\it\alpha}=2$ (2D Euler flow) and ${\it\alpha}=3$. The forcing scale is well resolved, a direct cascade is present and there is no large-scale dissipation. Coherent vortices spanning a range of sizes, most larger than the forcing scale, are present for both ${\it\alpha}=1$ and ${\it\alpha}=2$. The active scalar field for ${\it\alpha}=3$ contains comparatively few and small vortices. The energy spectral slopes in the inverse cascade are steeper than the KLB prediction $-(7-{\it\alpha})/3$ in all three systems. Since we stop the simulations well before the cascades have reached the domain scale, vortex formation and spectral steepening are not due to condensation effects; nor are they caused by large-scale dissipation, which is absent. One- and two-point p.d.f.s, hyperflatness factors and structure functions indicate that the inverse cascades are intermittent and non-Gaussian over much of the inertial range for ${\it\alpha}=1$ and ${\it\alpha}=2$, while the ${\it\alpha}=3$ inverse cascade is much closer to Gaussian and non-intermittent. For ${\it\alpha}=3$ the steep spectrum is close to that associated with enstrophy equipartition. Continuous wavelet analysis shows approximate KLB scaling $\mathscr{E}(k)\propto k^{-2}~({\it\alpha}=1)$ and $\mathscr{E}(k)\propto k^{-5/3}~({\it\alpha}=2)$ in the interstitial regions between the coherent vortices. Our results demonstrate that coherent vortex formation (${\it\alpha}=1$ and ${\it\alpha}=2$) and non-realizability (${\it\alpha}=3$) cause 2D inverse cascades to deviate from the KLB predictions, but that the flow between the vortices exhibits KLB scaling and non-intermittent statistics for ${\it\alpha}=1$ and ${\it\alpha}=2$.

scholarly journals Exposing the plural nature of molecular clouds

2019 ◽  
Vol 628 ◽  
pp. A33 ◽  
Author(s):  
J.-F. Robitaille ◽  
F. Motte ◽  
N. Schneider ◽  
D. Elia ◽  
S. Bontemps
Keyword(s):  
Power Spectrum ◽  
Turbulent Flows ◽  
Spectrum Analysis ◽  
Spatial Scales ◽  
Inertial Range ◽  
Power Spectrum Analysis ◽  
Characteristic Scale ◽  
Data Set ◽  
Analysis Technique ◽  
Non Gaussian

We present the Multiscale non-Gaussian Segmentation (MnGSeg) analysis technique. This wavelet-based method combines the analysis of the probability distribution function (PDF) of map fluctuations as a function of spatial scales and the power spectrum analysis of a map. This technique allows us to extract the non-Gaussianities identified in the multiscaled PDFs usually associated with turbulence intermittency and to spatially reconstruct the Gaussian and the non-Gaussian components of the map. This new technique can be applied on any data set. In the present paper, it is applied on a Herschel column density map of the Polaris flare cloud. The first component has by construction a self-similar fractal geometry similar to that produced by fractional Brownian motion (fBm) simulations. The second component is called the coherent component, as opposed to fractal, and includes a network of filamentary structures that demonstrates a spatial hierarchical scaling (i.e. filaments inside filaments). The power spectrum analysis of the two components proves that the Fourier power spectrum of the initial map is dominated by the power of the coherent filamentary structures across almost all spatial scales. The coherent structures contribute increasingly from larger to smaller scales, without producing any break in the inertial range. We suggest that this behaviour is induced, at least partly, by inertial-range intermittency, a well-known phenomenon for turbulent flows. We also demonstrate that the MnGSeg technique is itself a very sensitive signal analysis technique that allows the extraction of the cosmic infrared background (CIB) signal present in the Polaris flare submillimetre observations and the detection of a characteristic scale for 0.1 ≲ l ≲ 0.3 pc. The origin of this characteristic scale could partly be the transition of regimes dominated by incompressible turbulence versus compressible modes and other physical processes, such as gravity.

Self-Organized Critical Dynamics and Phase Transition Behavior During Avalanche Breakdown in p-Germanium

1991 ◽  
Vol 46 (12) ◽  
pp. 1009-1011
Author(s):  
M. Knoop ◽  
J. Parisi ◽  
W. Clauß ◽  
U. Rau ◽  
J. Peinke
Keyword(s):  
Phase Transition ◽  
Low Temperature ◽  
Experimental Evidence ◽  
Avalanche Breakdown ◽  
Critical Dynamics ◽  
Phase Transition Behavior ◽  
Scaling Properties ◽  
Self Organized ◽  
Self Organized Criticality ◽  
Parameter Ranges

Abstract We give experimental evidence that self-organized criticality takes place during the formation of low-temperature semiconductor breakdown. Quantitative evaluation of the characteristic scaling properties together with the appropriate parameter ranges of validity further support the applicability of the model conjectured

scholarly journals Synchronization and desynchronization in the Olami-Feder-Christensen earthquake model and potential implications for real seismicity

2011 ◽  
Vol 18 (5) ◽  
pp. 635-642 ◽  
Author(s):  
S. Hergarten ◽  
R. Krenn
Keyword(s):  
Power Law ◽  
Statistical Properties ◽  
Scaling Exponent ◽  
Power Law Distribution ◽  
Scaling Properties ◽  
Temporal Clustering ◽  
Self Organized ◽  
Earthquake Model ◽  
Self Organized Criticality ◽  
Large Earthquakes

Abstract. The Olami-Feder-Christensen model is probably the most studied model in the context of self-organized criticality and reproduces several statistical properties of real earthquakes. We investigate and explain synchronization and desynchronization of earthquakes in this model in the nonconservative regime and its relevance for the power-law distribution of the event sizes (Gutenberg-Richter law) and for temporal clustering of earthquakes. The power-law distribution emerges from synchronization, and its scaling exponent can be derived as τ = 1.775 from the scaling properties of the rupture areas' perimeter. In contrast, the occurrence of foreshocks and aftershocks according to Omori's law is closely related to desynchronization. This mechanism of foreshock and aftershock generation differs strongly from the widespread idea of spontaneous triggering and gives an idea why some even large earthquakes are not preceded by any foreshocks in nature.

scholarly journals Cellular automaton for realistic modelling of landslides

1995 ◽  
Vol 2 (1) ◽  
pp. 1-15 ◽  
Author(s):  
E. Segre ◽  
C. Deangeli
Keyword(s):  
Numerical Model ◽  
Debris Flow ◽  
Cellular Automaton ◽  
Field Data ◽  
Three Dimensional ◽  
Scaling Properties ◽  
Self Organized ◽  
Self Organized Criticality

Abstract. A numerical model is developed for the simulation of debris flow in landslides over a complex three dimensional topography. The model is then validated by comparing a simulation with reported field data. Our model is in fact a realistic elaboration of simpler "sandpile automata", which have in recent years been studied as supposedly paradigmatic of "self-organized criticality". Statistics and scaling properties of the simulation are examined, and show that the model has an intermittent behaviour.

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