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Scaling law of structure function of Richtmyer–Meshkov turbulence

Published online by Cambridge University Press:  29 September 2023

Zhangbo Zhou ,
Juchun Ding Open the ORCID record for Juchun Ding [Opens in a new window] ,
Wan Cheng Open the ORCID record for Wan Cheng [Opens in a new window]  and
Xisheng Luo Open the ORCID record for Xisheng Luo [Opens in a new window]
Zhangbo Zhou
Affiliation:
Advanced Propulsion Laboratory, Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, PR China
Juchun Ding*
Affiliation:
Advanced Propulsion Laboratory, Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, PR China
Wan Cheng
Affiliation:
Advanced Propulsion Laboratory, Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, PR China
Xisheng Luo
Affiliation:
Advanced Propulsion Laboratory, Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, PR China
*
†Email address for correspondence: djc@ustc.edu.cn
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Abstract

The scaling law of the structure function of Richtmyer–Meshkov (RM) turbulence is investigated both numerically and theoretically. High-fidelity simulations with a minimum-dispersion, adaptive-dissipation scheme are first performed. Results show that the mixing width experiences an exponential growth and the turbulent kinetic energy has a visible $-3/2$ spectrum. The scalar field exhibits a greater degree of intermittency than the velocity field, and also the small-scale statistics suffer a larger influence of large scales. Visible differences in the scaling law of the structure function among the RM turbulence and other types of turbulence are observed, which reveal the unique characteristic of RM turbulence. A phenomenological theory, which gives the spatial and temporal scaling laws of the structure functions of velocity and scalar of RM turbulence, is developed for the first time by introducing an external agent. The spatial scaling exponents of structure functions from simulation deviate from the Kolmogorov exponents, but are quite close to the RM-modified anomalous exponents. This demonstrates the validity of the present phenomenological theory. The temporal scaling exponents of structure functions first meet the RM-modified anomalous exponents, and then approach the Kolmogorov–Obukhov–Corrsin non-intermittent ones.

JFM classification

Compressible Flows: Shock waves Mixing: Turbulent mixing
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 972 , 10 October 2023 , A18
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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