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Modelling transitional rough-wall turbulence with quasi-linear approximations

Published online by Cambridge University Press:  29 July 2025

Yuxin Jiao Open the ORCID record for Yuxin Jiao [Opens in a new window] ,
Zecheng Zou Open the ORCID record for Zecheng Zou [Opens in a new window] ,
Shervin Bagheri Open the ORCID record for Shervin Bagheri [Opens in a new window]  and
Yongyun Hwang Open the ORCID record for Yongyun Hwang [Opens in a new window]
Yuxin Jiao*
Affiliation:
Department of Aeronautics, Imperial College London, London SW7 2AZ, UK CAPT-HEDPS, SKLTCS, Department of Mechanics and Engineering Science College of Engineering, Peking University, Beijing 100871, PR China
Zecheng Zou
Affiliation:
Department of Aeronautics, Imperial College London, London SW7 2AZ, UK
Shervin Bagheri
Affiliation:
FLOW, Department of Engineering Mechanics, KTH Royal Institute of Technology, Stockholm 100 44, Sweden
Yongyun Hwang
Affiliation:
Department of Aeronautics, Imperial College London, London SW7 2AZ, UK
*
Corresponding author: Yuxin Jiao, y.jiao17@pku.edu.cn
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Abstract

The effects of surface roughness in the transitionally rough regime on the overlying near-wall turbulence are modelled using quasi-linear approximations proposed recently: minimal quasi-linear approximation (MQLA) (Hwang & Ekchardt, 2020, J. Fluid Mech., vol. 894, A23), data-driven quasi-linear approximation (DQLA) (Holford et al., 2024, J. Fluid Mech., vol. 980, A12) and a newly established variant of MQLA (M2QLA, minimal two-mode quasi-linear approximation). The transpiration-resistance model (TRM) for boundary conditions is applied to account for the surface roughness (Lācis et al., 2020, J. Fluid Mech., vol. 884, A21). It is shown that many essential near-wall turbulence statistics are fairly well captured by the quasi-linear approximations in a wide range of slip and transpiration lengths for the TRM boundary conditions. In particular, the virtual origins and the resulting roughness functions are well predicted, showing good agreement with those from previous direct numerical simulations (DNS) in mild roughness cases. The DQLA and M2QLA, which incorporate streamwise-dependent Fourier modes in the approximations, are also shown to perform a little better than MQLA, especially with DQLA reproducing the two-dimensional energy spectra qualitatively consistent with the DNS. Finally, with a computational cost much lower than DNS, it is shown that the proposed quasi-linear approximation frameworks offer an efficient tool to rapidly explore the roughness effects within a large parameter space.

JFM classification

Turbulent Flows: Turbulence control Turbulent Flows: Turbulence modelling Nonlinear Dynamical Systems: Low-dimensional models

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JFM Papers
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Journal of Fluid Mechanics , Volume 1016 , 10 August 2025 , A7
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© The Author(s), 2025. Published by Cambridge University Press

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