随机Burgers方程的Kolmogorov 4/5定律的弱和强版本

IF 2.9 1区数学 Q1 MATHEMATICS, APPLIED Archive for Rational Mechanics and Analysis Pub Date : 2023-11-12 DOI:10.1007/s00205-023-01940-2

Peng Gao, Sergei Kuksin

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引用次数: 1

摘要

对于空间周期随机1d Burgers方程的解，我们建立了两种版本的Kolmogorov 4/5定律;这提供了湍流速度场增量的第三矩的渐近展开式。我们还证明了这个方程的一个类似于关于柯尔莫哥罗夫湍流理论可能普适的朗道反对，并证明了第三矩是唯一允许普适渐近展开的矩。

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Weak and Strong Versions of the Kolmogorov 4/5-Law for Stochastic Burgers Equation

For solutions of the space-periodic stochastic 1d Burgers equation we establish two versions of the Kolmogorov 4/5-law; this provides an asymptotic expansion for the third moment of increments of turbulent velocity fields. We also prove for this equation an analogy of the Landau objection to possible universality of Kolmogorov’s theory of turbulence, and show that the third moment is the only one which admits a universal asymptotic expansion.

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来源期刊

Archive for Rational Mechanics and Analysis 物理-力学

CiteScore

5.10

自引率

8.00%

发文量

审稿时长

4-8 weeks

期刊介绍： The Archive for Rational Mechanics and Analysis nourishes the discipline of mechanics as a deductive, mathematical science in the classical tradition and promotes analysis, particularly in the context of application. Its purpose is to give rapid and full publication to research of exceptional moment, depth and permanence.