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Effect of shock waves on the statistics and scaling in compressible isotropic turbulence

Jianchun Wang, Minping Wan, Song Chen, Chenyue Xie, and Shiyi Chen
Phys. Rev. E 97, 043108 – Published 11 April 2018

Abstract

The statistics and scaling of compressible isotropic turbulence in the presence of large-scale shock waves are investigated by using numerical simulations at turbulent Mach number Mt ranging from 0.30 to 0.65. The spectra of the compressible velocity component, density, pressure, and temperature exhibit a k2 scaling at different turbulent Mach numbers. The scaling exponents for structure functions of the compressible velocity component and thermodynamic variables are close to 1 at high orders n3. The probability density functions of increments of the compressible velocity component and thermodynamic variables exhibit a power-law region with the exponent 2. Models for the conditional average of increments of the compressible velocity component and thermodynamic variables are developed based on the ideal shock relations and are verified by numerical simulations. The overall statistics of the compressible velocity component and thermodynamic variables are similar to one another at different turbulent Mach numbers. It is shown that the effect of shock waves on the compressible velocity spectrum and kinetic energy transfer is different from that of acoustic waves.

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  • Received 3 January 2018

DOI:https://doi.org/10.1103/PhysRevE.97.043108

©2018 American Physical Society

Physics Subject Headings (PhySH)

  1. Research Areas
Fluid Dynamics

Authors & Affiliations

Jianchun Wang1,*, Minping Wan1,†, Song Chen1, Chenyue Xie1, and Shiyi Chen1,2

  • 1Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen, Guangdong 518055, People's Republic of China
  • 2State Key Laboratory of Turbulence and Complex Systems, Center for Applied Physics and Technology, College of Engineering, Peking University, Beijing 100871, People's Republic of China

  • *wangjc@sustc.edu.cn
  • wanmp@sustc.edu.cn

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Issue

Vol. 97, Iss. 4 — April 2018

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