A quantitative nonequilibrium phase transition theory for analyzing the turbulence development process

Author:

Zhou Zhuo1,Wu Jiu Hui1,Liang Xiao1,Yuan Xiaoyang2,Lin Mei3,Ma Fuyin1

Affiliation:

1. School of Mechanical Engineering and State Key Laboratory for Strength and Vibration of Mechanical Structure, Xi’an Jiaotong University, Xi’an, Shanxi 710049, P. R. China

2. Key Laboratory of Education Ministry for Modem Design and Rotor-Bearing System, Xi’an Jiaotong University, Xi’an 710049, P. R. China

3. School of Energy and Power Engineering, Xi’an Jiaotong University, Xi’an 710049, P. R. China

Abstract

In this paper, a quantitative nonequilibrium multi-dimensional phase transition theory is proposed for describing the turbulence spectrum (energy E with wave number k and scaling index [Formula: see text]) of the turbulence development process by a fold catastrophe model. Each of the control variables in this catastrophe model is subtly expressed into a relative multi-parameter multiplication, and then the state variable can be quantitatively described by these parameters. By using this nonequilibrium phase transition theory, the quantitative relationship in the process of turbulence formation can be strictly derived through dimensionless analysis. Therefore, the turbulence development process can be described with respect to a scaling index [Formula: see text], in which there exists an energy containing range with −1.12 power law (E [Formula: see text] k[Formula: see text]) when [Formula: see text] varies from −2 to −1.2, and an inertial subrange with −1.69 power law (E [Formula: see text] k[Formula: see text]) that is almost identical with the famous Kolmogorov’s −5/3 power law when [Formula: see text] varies from −1.2 to −0.8, and then the dissipation range with −2.52 power law (E [Formula: see text] k[Formula: see text]) when [Formula: see text] varies from −0.8 to 0. Furthermore, this quantitative nonequilibrium phase transition theory has been verified by the corresponding theoretical comparison and experiment. This theory provides not only a new understanding of turbulence, but also a new perspective for other complex nonequilibrium phase transitions.

Funder

National Natural Science Foundation of China

Publisher

World Scientific Pub Co Pte Lt

Subject

Condensed Matter Physics,Statistical and Nonlinear Physics

Cited by 1 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Quantitative analysis method for laminar-turbulence transition process of mechanical seal by a catastrophic model;Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science;2021-05-18

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3