Dynamical Fractional and Multifractal Fields
Dynamical Fractional and Multifractal Fields
复制标题
动态分形场和多重分形场
DOI：
10.1007/s10955-021-02867-2
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发表时间：
2022
影响因子：
1.6
通讯作者：
Mourrat, Jean-Christophe
中科院分区：
文献类型：
--
作者：
Apolinário, Gabriel B.;Chevillard, Laurent;Mourrat, Jean-Christophe
受三维流体湍流建模的启发，我们定义并研究了一类随机偏微分方程（SPDE），它们由空间平滑且时间强迫项不相关的随机搅拌。为了重现完全发展的湍流的分数（更具体地说是多重分形）规律性，这些动力学演化结合了 0 次同质伪微分线性算子，负责根据级联机制将大尺度注入系统的能量转移到较小尺度。在涉及线性和高斯框架中分数正则性发展的最简单情况下，我们对有限和无限时间内解的统计行为得出明确的预测。这样做，我们利用线性但非局部的相互作用实现了能量的级联转移。这些演化可以被视为最近提出的受迫波系统的随机版本，旨在模拟分层流和旋转流中的弱波湍流状态。为了包括多重分形（即间歇性）对这张图片的修正，我们从高斯乘法混沌（已知是多重分形）中获得了一些灵感，以激发在这些动态演化中引入额外的二次相互作用。由于所获得的一类非线性 SPDE 的理论分析要求更高，因此我们进行数值模拟并观察其解的非高斯性质，特别是偏斜性质。
Motivated by the modeling of three-dimensional fluid turbulence, we define and study a class of stochastic partial differential equations (SPDEs) that are randomly stirred by a spatially smooth and uncorrelated in time forcing term. To reproduce the fractional, and more specifically multifractal, regularity nature of fully developed turbulence, these dynamical evolutions incorporate an homogenous pseudo-differential linear operator of degree 0 that takes care of transferring energy that is injected at large scales in the system, towards smaller scales according to a cascading mechanism. In the simplest situation which concerns the development of fractional regularity in a linear and Gaussian framework, we derive explicit predictions for the statistical behaviors of the solution at finite and infinite time. Doing so, we realize a cascading transfer of energy using linear, although non local, interactions. These evolutions can be seen as a stochastic version of recently proposed systems of forced waves intended to model the regime of weak wave turbulence in stratified and rotational flows. To include multifractal, i.e. intermittent, corrections to this picture, we get some inspiration from the Gaussian multiplicative chaos, which is known to be multifractal, to motivate the introduction of an additional quadratic interaction in these dynamical evolutions. Because the theoretical analysis of the obtained class of nonlinear SPDEs is much more demanding, we perform numerical simulations and observe the non-Gaussian and in particular skewed nature of their solution.
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影响因子：
1.7
作者：
D. Barbato;F. Morandin;M. Romito
通讯作者：
M. Romito
湍流中傅立叶模态的统计。
DOI：
--
发表时间：
2001
期刊：
Physical review. E, Statistical, nonlinear, and soft matter physics
影响因子：
--
作者：
C. Brun;A. Pumir
通讯作者：
A. Pumir
树上的二元模型
DOI：
--
发表时间：
2012
期刊：
影响因子：
--
作者：
D. Barbato;L. Bianchi;F. Flandoli;F. Morandin
通讯作者：
F. Morandin
湍流壳模型的解析研究
DOI：
10.1016/j.physd.2006.05.015
发表时间：
2005
期刊：
Physica D: Nonlinear Phenomena
影响因子：
--
作者：
P. Constantin;B. Levant;E. Titi
通讯作者：
E. Titi
DOI：
--
发表时间：
2009
期刊：
影响因子：
--
作者：
L. Chevillard;Raoul Robert;Vincent Vargas
通讯作者：
Vincent Vargas