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Neural operator-based stochastic forcing for resolvent prediction of space–time turbulence statistics in channel flows

Published online by Cambridge University Press:  25 November 2025

Chutian Wu ,
Xin-Lei Zhang Open the ORCID record for Xin-Lei Zhang [Opens in a new window]  and
Guowei He Open the ORCID record for Guowei He [Opens in a new window]
Chutian Wu
Affiliation:
The State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, PR China School of Engineering Sciences, University of Chinese Academy of Sciences, Beijing 100049, PR China
Xin-Lei Zhang*
Affiliation:
The State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, PR China School of Engineering Sciences, University of Chinese Academy of Sciences, Beijing 100049, PR China
Guowei He*
Affiliation:
The State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, PR China School of Engineering Sciences, University of Chinese Academy of Sciences, Beijing 100049, PR China
*
Corresponding authors: Guowei He, hgw@lnm.imech.ac.cn; Xin-Lei Zhang, zhangxinlei@imech.ac.cn
Corresponding authors: Guowei He, hgw@lnm.imech.ac.cn; Xin-Lei Zhang, zhangxinlei@imech.ac.cn
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Abstract

In this work we propose a neural operator-based coloured-in-time forcing model to predict space–time characteristics of large-scale turbulent structures in channel flows. The resolvent-based method has emerged as a powerful tool to capture dominant dynamics and associated spatial structures of turbulent flows. However, the method faces the difficulty in modelling the coloured-in-time nonlinear forcing, which often leads to large predictive discrepancies in the frequency spectra of velocity fluctuations. Although the eddy viscosity has been introduced to enhance the resolvent-based method by partially accounting for the forcing colour, it is still not able to accurately capture the decay rate of the time-correlation function. Also, the uncertainty in the modelled eddy viscosity can significantly limit the predictive reliability of the method. In view of these difficulties, we propose using the neural operator based on the DeepONet architecture to model the stochastic forcing as a function of mean velocity and eddy viscosity. Specifically, the DeepONet-based model is constructed to map an arbitrary eddy-viscosity profile and corresponding mean velocity to stochastic forcing spectra based on the direct numerical simulation data at $Re_\tau =180$. Furthermore, the learned forcing model is integrated with the resolvent operator, which enables predicting the space–time flow statistics based on the eddy viscosity and mean velocity from the Reynolds-averaged Navier–Stokes (RANS) method. Our results show that the proposed forcing model can accurately predict the frequency spectra of velocity in channel flows at different characteristic scales. Moreover, the model remains robust across different RANS-provided eddy viscosities and generalises well to $Re_\tau =550$.

JFM classification

Waves/Free-surface Flows: Channel flow Turbulent Flows: Turbulence modelling Mathematical Foundations: Machine learning

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JFM Papers
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Journal of Fluid Mechanics , Volume 1024 , 10 December 2025 , A1
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© The Author(s), 2025. Published by Cambridge University Press

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