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A refined strong Reynolds analogy: perspectives from the transport of velocity and temperature fluctuations

Published online by Cambridge University Press:  15 September 2025

Zhikang Huang Open the ORCID record for Zhikang Huang [Opens in a new window] ,
Hongmin Su ,
Qilong Guo ,
Xianxu Yuan Open the ORCID record for Xianxu Yuan [Opens in a new window] ,
Xue-Lu Xiong Open the ORCID record for Xue-Lu Xiong [Opens in a new window]  and
Yi Zhou Open the ORCID record for Yi Zhou [Opens in a new window]
Zhikang Huang
Affiliation:
School of Energy and Power Engineering, Nanjing University of Science and Technology, Nanjing 210094, PR China State Key Laboratory of Aerodynamics, Mianyang 621000, PR China
Hongmin Su*
Affiliation:
State Key Laboratory of Aerodynamics, Mianyang 621000, PR China
Qilong Guo
Affiliation:
State Key Laboratory of Aerodynamics, Mianyang 621000, PR China
Xianxu Yuan
Affiliation:
State Key Laboratory of Aerodynamics, Mianyang 621000, PR China
Xue-Lu Xiong
Affiliation:
School of Energy and Power Engineering, Nanjing University of Science and Technology, Nanjing 210094, PR China
Yi Zhou*
Affiliation:
School of Energy and Power Engineering, Nanjing University of Science and Technology, Nanjing 210094, PR China
*
Corresponding authors: Hongmin Su, suhongmin@cardc.cn; Yi Zhou, yizhou@njust.edu.cn
Corresponding authors: Hongmin Su, suhongmin@cardc.cn; Yi Zhou, yizhou@njust.edu.cn
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Abstract

In compressible turbulent boundary layers (CTBLs), the strong Reynolds analogy (SRA) refers to a set of quantitative relationships between temperature and velocity fluctuations. The essence of the SRA is the linear relationship between these fluctuations in large-scale motions. We investigate the transport processes of the second-order statistical moments associated with temperature and velocity fluctuations to reveal the physical mechanisms underlying this linear correlation. An important finding is that there exists a strong linear mechanism between the turbulent production of velocity and temperature fluctuations. Nonlinear mechanisms, such as the viscous-thermal dissipation, the work contribution, and particularly the pressure term, lead to the failure of the existing SRAs in the outer layer. Based on the above findings, a refined SRA (RSRA) is proposed, which better describes the quantitative relation between the temperature and velocity fluctuation intensities. An approximate expression for the turbulent Prandtl number under different Mach numbers and wall-cooling conditions is derived with the newly proposed RSRA. The relations proposed in this paper are validated through the direct numerical simulation data of flat-plate zero-pressure-gradient CTBLs at different Mach numbers and wall temperatures.

JFM classification

Compressible Flows: Compressible boundary layers Turbulent Flows: Compressible turbulence Turbulent Flows: Turbulence theory

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Type
JFM Papers
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Journal of Fluid Mechanics , Volume 1019 , 25 September 2025 , A13
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© The Author(s), 2025. Published by Cambridge University Press

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