Scaling laws and exact results in turbulence *

IF 1.6 2区数学 Q2 MATHEMATICS, APPLIED

Nonlinearity Pub Date : 2024-07-16 DOI:10.1088/1361-6544/ad6057

Matthew Novack

引用次数: 0

Abstract

In this note, we address the validity of certain exact results from turbulence theory in the deterministic setting. The main tools, inspired by the work of Duchon and Robert (2000 Nonlinearity13 249–55) and Eyink (2003 Nonlinearity16 137), are a number of energy balance identities for weak solutions of the incompressible Euler and Navier–Stokes equations. As a consequence, we show that certain weak solutions of the Euler and Navier–Stokes equations satisfy deterministic versions of Kolmogorov’s , , laws. We apply these computations to improve a recent result of Hofmanova et al (2023 arXiv:2304.14470), which shows that a construction of solutions of forced Navier–Stokes due to Bruè et al (2023 Commun. Pure Appl. Anal.) and exhibiting a form of anomalous dissipation satisfies asymptotic versions of Kolmogorov’s laws. In addition, we show that the globally dissipative 3D Euler flows recently constructed by Giri et al (2023 arXiv:2305.18509) satisfy the local versions of Kolmogorov’s laws.

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湍流中的缩放定律和精确结果 *

在本论文中，我们探讨了确定性环境中湍流理论某些精确结果的有效性。受 Duchon 和 Robert (2000 Nonlinearity13 249-55) 和 Eyink (2003 Nonlinearity16 137) 工作的启发，主要工具是不可压缩欧拉方程和纳维-斯托克斯方程弱解的一些能量平衡等式。因此，我们证明了欧拉方程和纳维-斯托克斯方程的某些弱解满足确定性版本的科尔莫戈罗夫Ⅳ定律。我们运用这些计算改进了霍夫曼诺娃等人（2023 arXiv:2304.14470）的最新结果，该结果表明，布鲁埃等人（2023 Commun. Pure Appl. Anal.）此外，我们还证明了吉里等人最近构建的全局耗散三维欧拉流（2023 arXiv:2305.18509）满足柯尔莫哥洛夫定律的局部版本。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Nonlinearity 物理-物理：数学物理

CiteScore

3.00

自引率

5.90%

发文量

170

审稿时长

12 months

期刊介绍： Aimed primarily at mathematicians and physicists interested in research on nonlinear phenomena, the journal''s coverage ranges from proofs of important theorems to papers presenting ideas, conjectures and numerical or physical experiments of significant physical and mathematical interest. Subject coverage: The journal publishes papers on nonlinear mathematics, mathematical physics, experimental physics, theoretical physics and other areas in the sciences where nonlinear phenomena are of fundamental importance. A more detailed indication is given by the subject interests of the Editorial Board members, which are listed in every issue of the journal. Due to the broad scope of Nonlinearity, and in order to make all papers published in the journal accessible to its wide readership, authors are required to provide sufficient introductory material in their paper. This material should contain enough detail and background information to place their research into context and to make it understandable to scientists working on nonlinear phenomena. Nonlinearity is a journal of the Institute of Physics and the London Mathematical Society.