Subensemble decomposition and Markov process analysis of Burgers turbulence.
Zhi-Xiong Zhang,Zhen-Su She +1 more
TLDR
The interconversion of shock and rarefaction waves during the equation's evolution displays in accordance with a Markov process, which has a stationary transition probability matrix with the elements satisfying universal functions and, when the time interval is much greater than the corresponding characteristic value, exhibits the scale-invariant property.Abstract:
A numerical and statistical study is performed to describe the positive and negative local subgrid energy fluxes in the one-dimensional random-force-driven Burgers turbulence (Burgulence). We use a subensemble method to decompose the field into shock wave and rarefaction wave subensembles by group velocity difference. We observe that the shock wave subensemble shows a strong intermittency which dominates the whole Burgulence field, while the rarefaction wave subensemble satisfies the Kolmogorov 1941 (K41) scaling law. We calculate the two subensemble probabilities and find that in the inertial range they maintain scale invariance, which is the important feature of turbulence self-similarity. We reveal that the interconversion of shock and rarefaction waves during the equation's evolution displays in accordance with a Markov process, which has a stationary transition probability matrix with the elements satisfying universal functions and, when the time interval is much greater than the corresponding characteristic value, exhibits the scale-invariant property.read more
Citations
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Statistics of one-dimensional compressible turbulence with random large-scale force
TL;DR: In this paper, a numerical study was performed to explore the difference between the one-dimensional compressible hydrodynamic turbulence and Burgers turbulence and found that the transition in the compressible turbulence was not in accordance with a Markovian process.
Journal ArticleDOI
Statistics of active and passive scalars in one-dimensional compressible turbulence.
Qionglin Ni,Shiyi Chen +1 more
TL;DR: The negative filtered flux at large scales and the time-increasing total variance give evidences to the existence of an inverse cascade of the passive concentration, which is induced by the implosive collapse in the Lagrangian trajectories.
Journal ArticleDOI
Universal functions for Burgers turbulence
TL;DR: In this paper , Saffman analytically solved the Burgers equation and derived universal functions for the energy spectrum, second-order structure function, and energy flux that works for any kinematic viscosity, energy injection rate, and system size.
References
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TL;DR: In this article, the authors consider the problem of finding the components of the velocity at every point of a point with rectangular cartesian coordinates x 1, x 2, x 3, x 4, x 5, x 6, x 7, x 8.
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Victor Yakhot,Steven A. Orszag +1 more
TL;DR: In this article, a dynamic renormalization group (RNG) method for hydrodynamic turbulence was developed, which uses dynamic scaling and invariance together with iterated perturbation methods, allowing us to evaluate transport coefficients and transport equations for the large scale (slow) modes.
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On a quasi-linear parabolic equation occurring in aerodynamics
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