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Characteristics and modelling of forcing statistics in resolvent analysis of compressible turbulent boundary layers

Published online by Cambridge University Press:  28 July 2025

Yitong Fan Open the ORCID record for Yitong Fan [Opens in a new window] ,
Melissa Kozul Open the ORCID record for Melissa Kozul [Opens in a new window] ,
Richard D. Sandberg Open the ORCID record for Richard D. Sandberg [Opens in a new window]  and
Weipeng Li Open the ORCID record for Weipeng Li [Opens in a new window]
Yitong Fan
Affiliation:
School of Aeronautics and Astronautics, Shanghai Jiao Tong University, Shanghai 200240, PR China Department of Mechanical Engineering, University of Melbourne, Parkville, VIC 3010, Australia
Melissa Kozul
Affiliation:
Department of Mechanical Engineering, University of Melbourne, Parkville, VIC 3010, Australia
Richard D. Sandberg
Affiliation:
Department of Mechanical Engineering, University of Melbourne, Parkville, VIC 3010, Australia
Weipeng Li*
Affiliation:
School of Aeronautics and Astronautics, Shanghai Jiao Tong University, Shanghai 200240, PR China
*
Corresponding author: Weipeng Li, liweipeng@sjtu.edu.cn
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Abstract

Resolvent-based modelling and estimation is critically dependent on the nonlinear forcing input and hence understanding its role in the flow response is of great significance. This study quantifies the nonlinear forcing input in the resolvent formulation and investigates its characteristics for compressible turbulent boundary layers at Mach number 5.86 and friction Reynolds number 420 subject to adiabatic- and cold-wall conditions. Results show that, with the addition of the eddy viscosity to the resolvent operator, the cross-spectral density (CSD) of the forcing tends to exhibit a spatially uncorrelated distribution, which suggests that the spatial cross-coherence may be neglected and makes the modelling of the forcing input potentially easier. Aiming to quantify the different importance of each forcing component in generating turbulent fluctuations, contributions of the eddy-viscosity-corrected forcing to the flow responses are investigated through reduced-order analysis and matrix decomposition. The streamwise motions are almost insensitive to the temperature-related forcing, and can be oppositely influenced by the wall-normal and spanwise forcing components. By retaining only the diagonal components in the CSD of the forcing input, the assumption of forcing decorrelation in space and among components is also examined in the input–output framework. It is found that this simplified input is able to capture the dominant turbulence features and the local forcing is observed to cause inner-layer responses. That is, present results suggest adequate modelling of the CSD of the forcing can be achieved retaining only its diagonal components. On the basis of the current findings, the forcing input in the resolvent-based framework is thus modelled, with the wall-normal dependence and amplitude ratio between forcing components designed for compressible turbulent boundary layers. Through an algebraic Lyapunov equation, improved estimations of the statistical spectral densities of velocity and temperature fluctuations are finally obtained, in contrast to the results by simply assuming the forcing CSD to be an identity matrix.

JFM classification

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

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Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 1016 , 10 August 2025 , A10
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© The Author(s), 2025. Published by Cambridge University Press

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