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Effect of thermal fluctuations on spectra and predictability in compressible decaying isotropic turbulence

Published online by Cambridge University Press:  21 May 2024

Qihan Ma Open the ORCID record for Qihan Ma [Opens in a new window] ,
Chunxin Yang ,
Song Chen ,
Kaikai Feng ,
Ziqi Cui  and
Jun Zhang Open the ORCID record for Jun Zhang [Opens in a new window]
Qihan Ma
Affiliation:
School of Aeronautic Science and Engineering, Beihang University, Beijing 100191, PR China
Chunxin Yang
Affiliation:
School of Aeronautic Science and Engineering, Beihang University, Beijing 100191, PR China
Song Chen
Affiliation:
Sino-French Engineer School/School of General Engineering, Beihang University, Beijing 100191, PR China
Kaikai Feng
Affiliation:
School of Aeronautic Science and Engineering, Beihang University, Beijing 100191, PR China
Ziqi Cui
Affiliation:
School of Aeronautic Science and Engineering, Beihang University, Beijing 100191, PR China
Jun Zhang*
Affiliation:
School of Aeronautic Science and Engineering, Beihang University, Beijing 100191, PR China
*
†Email address for correspondence: jun.zhang@buaa.edu.cn
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Abstract

This study investigates the impact of molecular thermal fluctuations on compressible decaying isotropic turbulence using the unified stochastic particle (USP) method, encompassing both two-dimensional (2-D) and three-dimensional (3-D) scenarios. The findings reveal that the turbulent spectra of velocity and thermodynamic variables follow the wavenumber (k) scaling law of ${k}^{(d-1)}$ for different spatial dimensions $d$ within the high wavenumber range, indicating the impact of thermal fluctuations on small-scale turbulent statistics. With the application of Helmholtz decomposition, it is found that the thermal fluctuation spectra of solenoidal and compressible velocity components (${\boldsymbol {u}}_{s}$ and ${\boldsymbol {u}}_{c}$) follow an energy ratio of 1 : 1 for 2-D cases, while the ratio changes to 2 : 1 for 3-D cases. Comparisons between 3-D turbulent spectra obtained through USP simulations and direct numerical simulations of the Navier–Stokes equations demonstrate that thermal fluctuations dominate the spectra at length scales comparable to the Kolmogorov length scale. Additionally, the effect of thermal fluctuations on the spectrum of ${\boldsymbol {u}}_{c}$ is significantly influenced by variations in the turbulent Mach number. We further study the impact of thermal fluctuations on the predictability of turbulence. With initial differences caused by thermal fluctuations, different flow realizations display significant disparities in velocity and thermodynamic fields at larger scales after a certain period of time, which can be characterized by ‘inverse error cascades’. Moreover, the results suggest a strong correlation between the predictabilities of thermodynamic fields and the predictability of ${\boldsymbol {u}}_{c}$.

JFM classification

Turbulent Flows: Isotropic turbulence Turbulent Flows: Homogeneous turbulence
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 987 , 25 May 2024 , A29
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Copyright
© The Author(s), 2024. Published by Cambridge University Press

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