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A deep learning approach to wall-shear stress quantification: from numerical training to zero-shot experimental application

Published online by Cambridge University Press:  25 June 2025

Esther Lagemann Open the ORCID record for Esther Lagemann [Opens in a new window] ,
Julia Roeb Open the ORCID record for Julia Roeb [Opens in a new window] ,
Steven L. Brunton Open the ORCID record for Steven L. Brunton [Opens in a new window]  and
Christian Lagemann Open the ORCID record for Christian Lagemann [Opens in a new window]
Esther Lagemann*
Affiliation:
AI Institute in Dynamic Systems, Department of Mechanical Engineering, University of Washington, Seattle, WA 98195, USA
Julia Roeb
Affiliation:
Engler-Bunte-Institut, Simulation of Reacting Thermo-Fluid Systems, Karlsruhe Institute for Technology, Engler-Bunte-Ring 7, Karlsruhe 76131, Germany
Steven L. Brunton
Affiliation:
AI Institute in Dynamic Systems, Department of Mechanical Engineering, University of Washington, Seattle, WA 98195, USA
Christian Lagemann
Affiliation:
AI Institute in Dynamic Systems, Department of Mechanical Engineering, University of Washington, Seattle, WA 98195, USA
*
Corresponding author: Esther Lagemann, elage@uw.edu
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Abstract

The accurate quantification of wall-shear stress dynamics is of substantial importance for various applications in fundamental and applied research, spanning areas from human health to aircraft design and optimization. Despite significant progress in experimental measurement techniques and postprocessing algorithms, temporally resolved wall-shear stress fields with adequate spatial resolution and within a suitable spatial domain remain an elusive goal. Furthermore, there is a systematic lack of universal models that can accurately replicate the instantaneous wall-shear stress dynamics in numerical simulations of multiscale systems where direct numerical simulations (DNSs) are prohibitively expensive. To address these gaps, we introduce a deep learning architecture that ingests wall-parallel streamwise velocity fields at $y^+ \approx 3.9 \sqrt {Re_\tau }$ of turbulent wall-bounded flows and outputs the corresponding two-dimensional streamwise wall-shear stress fields with identical spatial resolution and domain size. From a physical perspective, our framework acts as a surrogate model encapsulating the various mechanisms through which highly energetic outer-layer flow structures influence the governing wall-shear stress dynamics. The network is trained in a supervised fashion on a unified dataset comprising DNSs of statistically one-dimensional turbulent channel and spatially developing turbulent boundary layer flows at friction Reynolds numbers ranging from $390$ to $1500$. We demonstrate a zero-shot applicability to experimental velocity fields obtained from particle image velocimetry measurements and verify the physical accuracy of the wall-shear stress estimates with synchronized wall-shear stress measurements using the micro-pillar shear-stress sensor for Reynolds numbers up to $2000$. In summary, the presented framework lays the groundwork for extracting inaccessible experimental wall-shear stress information from readily available velocity measurements and thus, facilitates advancements in a variety of experimental applications.

JFM classification

Mathematical Foundations: Machine learning Turbulent Flows: Turbulence modelling Turbulent Flows: Turbulent boundary layers

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JFM Papers
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Journal of Fluid Mechanics , Volume 1014 , 10 July 2025 , A1
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© The Author(s), 2025. Published by Cambridge University Press

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