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Special Issue "Intermittency and Self-Organisation in Turbulence and Statistical Mechanics"

A special issue of Entropy (ISSN 1099-4300).

Deadline for manuscript submissions: 28 February 2019

Special Issue Editor

Guest Editor
Dr. Eun-jin Kim

School of Mathematics and Statistics, University of Sheffield, Sheffield S3 7RH, UK
Website | E-Mail
Interests: fluid dynamics; magnetohydrodynamics (MHD); plasma physics; self-organisation; non-equilibrium statistical mechanics; turbulence; solar/stellar physics; magnetic fusion; information theory; homeostasis in biosystems; solar/stellar physics

Special Issue Information

Dear Colleagues,

There is overwhelming evidence, from laboratory experiments, observations, and computational studies, that coherent structures can cause intermittent transport, dramatically enhancing transport. A proper description of this intermittent phenomenon, however, is extremely difficult, requiring a new non-perturbative theory, such as statistical description. Furthermore, multi-scale interactions are responsible for inevitably complex dynamics in strongly non-equilibrium systems, a proper understanding of which remains a main challenge in classical physics. As a remarkable consequence of multi-scale interaction, a quasi-equilibrium state (the so-called self-organisation) can however be maintained.

This Special Issue aims to present different theories of statistical mechanics to understand this challenging multiscale problem in turbulence. Submissions addressing intermittency, coherent structures and self-organisation are especially welcome.

Dr. Eun-jin Kim
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Turbulence
  • Statistical Mechanics
  • Intermittency
  • Coherent Structure
  • Multi-scale Problem
  • Self-Organisation

Published Papers (8 papers)

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Research

Open AccessArticle Wall-Normal Variation of Spanwise Streak Spacing in Turbulent Boundary Layer With Low-to-Moderate Reynolds Number
Entropy 2019, 21(1), 24; https://doi.org/10.3390/e21010024
Received: 19 November 2018 / Revised: 18 December 2018 / Accepted: 27 December 2018 / Published: 31 December 2018
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Abstract
Low-speed streaks in wall-bounded turbulence are the dominant structures in the near-wall turbulent self-sustaining cycle. Existing studies have well characterized their spanwise spacing in the buffer layer and below. Recent studies suggested the existence of these small-scale structures in the higher layer where
[...] Read more.
Low-speed streaks in wall-bounded turbulence are the dominant structures in the near-wall turbulent self-sustaining cycle. Existing studies have well characterized their spanwise spacing in the buffer layer and below. Recent studies suggested the existence of these small-scale structures in the higher layer where large-scale structures usually receive more attention. The present study is thus devoted to extending the understanding of the streak spacing to the log layer. An analysis is taken on two-dimensional (2D) wall-parallel velocity fields in a smooth-wall turbulent boundary layer with R e τ = 440∼2400, obtained via either 2D Particle Image Velocimetry (PIV) measurement taken here or public Direct Numerical Simulation (DNS). Morphological-based streak identification analysis yields a R e -independent log-normal distribution of the streak spacing till the upper bound of the log layer, based on which an empirical model is proposed to account for its wall-normal growth. The small-scale part of the spanwise spectra of the streamwise fluctuating velocity below y + = 100 is reasonably restored by a synthetic simulation that distributes elementary streak units based on the proposed empirical streak spacing model, which highlights the physical significance of streaks in shaping the small-scale part of the velocity spectra beyond the buffer layer. Full article
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Open AccessArticle Alternation of Defects and Phase Turbulence Induces Extreme Events in an Extended Microcavity Laser
Entropy 2018, 20(10), 789; https://doi.org/10.3390/e20100789
Received: 10 August 2018 / Revised: 8 October 2018 / Accepted: 9 October 2018 / Published: 15 October 2018
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Abstract
Out-of-equilibrium systems exhibit complex spatiotemporal behaviors when they present a secondary bifurcation to an oscillatory instability. Here, we investigate the complex dynamics shown by a pulsing regime in an extended, one-dimensional semiconductor microcavity laser whose cavity is composed by integrated gain and saturable
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Out-of-equilibrium systems exhibit complex spatiotemporal behaviors when they present a secondary bifurcation to an oscillatory instability. Here, we investigate the complex dynamics shown by a pulsing regime in an extended, one-dimensional semiconductor microcavity laser whose cavity is composed by integrated gain and saturable absorber media. This system is known to give rise experimentally and theoretically to extreme events characterized by rare and high amplitude optical pulses following the onset of spatiotemporal chaos. Based on a theoretical model, we reveal a dynamical behavior characterized by the chaotic alternation of phase and amplitude turbulence. The highest amplitude pulses, i.e., the extreme events, are observed in the phase turbulence zones. This chaotic alternation behavior between different turbulent regimes is at contrast to what is usually observed in a generic amplitude equation model such as the Ginzburg–Landau model. Hence, these regimes provide some insight into the poorly known properties of the complex spatiotemporal dynamics exhibited by secondary instabilities of an Andronov–Hopf bifurcation. Full article
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Open AccessArticle Effects of Near Wall Modeling in the Improved-Delayed-Detached-Eddy-Simulation (IDDES) Methodology
Entropy 2018, 20(10), 771; https://doi.org/10.3390/e20100771
Received: 6 September 2018 / Revised: 28 September 2018 / Accepted: 29 September 2018 / Published: 8 October 2018
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Abstract
The present study aims to assess the effects of two different underlying RANS models on overall behavior of the IDDES methodology when applied to different flow configurations ranging from fully attached (plane channel flow) to separated flows (periodic hill flow). This includes investigating
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The present study aims to assess the effects of two different underlying RANS models on overall behavior of the IDDES methodology when applied to different flow configurations ranging from fully attached (plane channel flow) to separated flows (periodic hill flow). This includes investigating prediction accuracy of first and second order statistics, response to grid refinement, grey area dynamics and triggering mechanism. Further, several criteria have been investigated to assess reliability and quality of the methodology when operating in scale resolving mode. It turns out that irrespective of the near wall modeling strategy, the IDDES methodology does not satisfy all criteria required to make this methodology reliable when applied to various flow configurations at different Reynolds numbers with different grid resolutions. Further, it is found that using more advanced underlying RANS model to improve prediction accuracy of the near wall dynamics results in extension of the grey area, which may delay the transition to scale resolving mode. This systematic study for attached and separated flows suggests that the shortcomings of IDDES methodology mostly lie in inaccurate prediction of the dynamics inside the grey area and demands further investigation in this direction to make this methodology capable of dealing with different flow situations reliably. Full article
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Open AccessArticle Non-Linear Langevin and Fractional Fokker–Planck Equations for Anomalous Diffusion by Lévy Stable Processes
Entropy 2018, 20(10), 760; https://doi.org/10.3390/e20100760
Received: 28 July 2018 / Revised: 17 August 2018 / Accepted: 29 September 2018 / Published: 3 October 2018
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Abstract
The numerical solutions to a non-linear Fractional Fokker–Planck (FFP) equation are studied estimating the generalized diffusion coefficients. The aim is to model anomalous diffusion using an FFP description with fractional velocity derivatives and Langevin dynamics where Lévy fluctuations are introduced to model the
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The numerical solutions to a non-linear Fractional Fokker–Planck (FFP) equation are studied estimating the generalized diffusion coefficients. The aim is to model anomalous diffusion using an FFP description with fractional velocity derivatives and Langevin dynamics where Lévy fluctuations are introduced to model the effect of non-local transport due to fractional diffusion in velocity space. Distribution functions are found using numerical means for varying degrees of fractionality of the stable Lévy distribution as solutions to the FFP equation. The statistical properties of the distribution functions are assessed by a generalized normalized expectation measure and entropy and modified transport coefficient. The transport coefficient significantly increases with decreasing fractality which is corroborated by analysis of experimental data. Full article
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Open AccessArticle Trailing-Edge Flap Control for Mitigating Rotor Power Fluctuations of a Large-Scale Offshore Floating Wind Turbine under the Turbulent Wind Condition
Entropy 2018, 20(9), 676; https://doi.org/10.3390/e20090676
Received: 13 August 2018 / Revised: 3 September 2018 / Accepted: 4 September 2018 / Published: 6 September 2018
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Abstract
A trailing-edge flap control strategy for mitigating rotor power fluctuations of a 5 MW offshore floating wind turbine is developed under turbulent wind inflow. The wind shear must be considered because of the large rotor diameter. The trailing-edge flap control strategy is based
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A trailing-edge flap control strategy for mitigating rotor power fluctuations of a 5 MW offshore floating wind turbine is developed under turbulent wind inflow. The wind shear must be considered because of the large rotor diameter. The trailing-edge flap control strategy is based on the turbulent wind speed, the blade azimuth angle, and the platform motions. The rotor power is predicted using the free vortex wake method, coupled with the control strategy. The effect of the trailing-edge flap control on the rotor power is determined by a comparison with the rotor power of a turbine without a trailing-edge flap control. The optimal values of the three control factors are obtained. The results show that the trailing-edge flap control strategy is effective for improving the stability of the output rotor power of the floating wind turbine under the turbulent wind condition. Full article
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Open AccessArticle Time-Dependent Probability Density Functions and Attractor Structure in Self-Organised Shear Flows
Entropy 2018, 20(8), 613; https://doi.org/10.3390/e20080613
Received: 30 July 2018 / Revised: 9 August 2018 / Accepted: 16 August 2018 / Published: 17 August 2018
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Abstract
We report the time-evolution of Probability Density Functions (PDFs) in a toy model of self-organised shear flows, where the formation of shear flows is induced by a finite memory time of a stochastic forcing, manifested by the emergence of a bimodal PDF with
[...] Read more.
We report the time-evolution of Probability Density Functions (PDFs) in a toy model of self-organised shear flows, where the formation of shear flows is induced by a finite memory time of a stochastic forcing, manifested by the emergence of a bimodal PDF with the two peaks representing non-zero mean values of a shear flow. Using theoretical analyses of limiting cases, as well as numerical solutions of the full Fokker–Planck equation, we present a thorough parameter study of PDFs for different values of the correlation time and amplitude of stochastic forcing. From time-dependent PDFs, we calculate the information length ( L ), which is the total number of statistically different states that a system passes through in time and utilise it to understand the information geometry associated with the formation of bimodal or unimodal PDFs. We identify the difference between the relaxation and build-up of the shear gradient in view of information change and discuss the total information length ( L = L ( t ) ) which maps out the underlying attractor structures, highlighting a unique property of L which depends on the trajectory/history of a PDF’s evolution. Full article
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Open AccessArticle Turbulence through the Spyglass of Bilocal Kinetics
Entropy 2018, 20(7), 539; https://doi.org/10.3390/e20070539
Received: 13 June 2018 / Revised: 13 July 2018 / Accepted: 16 July 2018 / Published: 20 July 2018
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Abstract
In two recent papers we introduced a generalization of Boltzmann’s assumption of molecular chaos based on a criterion of maximum entropy, which allowed setting up a bilocal version of Boltzmann’s kinetic equation. The present paper aims to investigate how the essentially non-local character
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In two recent papers we introduced a generalization of Boltzmann’s assumption of molecular chaos based on a criterion of maximum entropy, which allowed setting up a bilocal version of Boltzmann’s kinetic equation. The present paper aims to investigate how the essentially non-local character of turbulent flows can be addressed through this bilocal kinetic description, instead of the more standard approach through the local Euler/Navier–Stokes equation. Balance equations appropriate to this kinetic scheme are derived and closed so as to provide bilocal hydrodynamical equations at the non-viscous order. These equations essentially consist of two copies of the usual local equations, but coupled through a bilocal pressure tensor. Interestingly, our formalism automatically produces a closed transport equation for this coupling term. Full article
Open AccessArticle Transition of Transient Channel Flow with High Reynolds Number Ratios
Entropy 2018, 20(5), 375; https://doi.org/10.3390/e20050375
Received: 24 March 2018 / Revised: 14 May 2018 / Accepted: 15 May 2018 / Published: 17 May 2018
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Abstract
Large-eddy simulations of turbulent channel flow subjected to a step-like acceleration have been performed to investigate the effect of high Reynolds number ratios on the transient behaviour of turbulence. It is shown that the response of the flow exhibits the same fundamental characteristics
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Large-eddy simulations of turbulent channel flow subjected to a step-like acceleration have been performed to investigate the effect of high Reynolds number ratios on the transient behaviour of turbulence. It is shown that the response of the flow exhibits the same fundamental characteristics described in He & Seddighi (J. Fluid Mech., vol. 715, 2013, pp. 60–102 and vol. 764, 2015, pp. 395–427)—a three-stage response resembling that of the bypass transition of boundary layer flows. The features of transition are seen to become more striking as the Re-ratio increases—the elongated streaks become stronger and longer, and the initial turbulent spot sites at the onset of transition become increasingly sparse. The critical Reynolds number of transition and the transition period Reynolds number for those cases are shown to deviate from the trends of He & Seddighi (2015). The high Re-ratio cases show double peaks in the transient response of streamwise fluctuation profiles shortly after the onset of transition. Conditionally-averaged turbulent statistics based on a λ_2-criterion are used to show that the two peaks in the fluctuation profiles are due to separate contributions of the active and inactive regions of turbulence generation. The peak closer to the wall is attributed to the generation of “new” turbulence in the active region, whereas the peak farther away from the wall is attributed to the elongated streaks in the inactive region. In the low Re-ratio cases, the peaks of these two regions are close to each other during the entire transient, resulting in a single peak in the domain-averaged profile. Full article
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