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Published May 2021 | Published
Journal Article Open

Experiments and Modeling of a Compliant Wall Response to a Turbulent Boundary Layer with Dynamic Roughness Forcing


The response of a compliant surface in a turbulent boundary layer forced by a dynamic roughness is studied using experiments and resolvent analysis. Water tunnel experiments are carried out at a friction Reynolds number of Re_τ ≈ 410, with flow and surface measurements taken with 2D particle image velocimetry (PIV) and stereo digital image correlation (DIC). The narrow band dynamic roughness forcing enables analysis of the flow and surface responses coherent with the forcing frequency, and the corresponding Fourier modes are extracted and compared with resolvent modes. The resolvent modes capture the structures of the experimental Fourier modes and the resolvent with eddy viscosity improves the matching. The comparison of smooth and compliant wall resolvent modes predicts a virtual wall feature in the wall normal velocity of the compliant wall case. The virtual wall is revealed in experimental data using a conditional average informed by the resolvent prediction. Finally, the change to the resolvent modes due to the influence of wall compliance is studied by modeling the compliant wall boundary condition as a deterministic forcing to the smooth wall resolvent framework.

Additional Information

© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). Received: 30 March 2021 / Revised: 16 April 2021 / Accepted: 20 April 2021 / Published: 26 April 2021. (This article belongs to the Special Issue Turbulent Flows at Solid and Free Surface Boundaries in Memory of William W. Willmarth) Author Contributions. Conceptualization, D.P.H. and B.J.M.; methodology, D.P.H., Y.H. and B.J.M.; investigation, D.P.H. and Y.H.; writing, D.P.H., Y.H. and B.J.M.; supervision, B.J.M.; funding acquisition, B.J.M. All authors have read and agreed to the published version of the manuscript. The support of the U.S. Office of Naval Research under grant number N00014-17-1-2960 and the U.S. Army Research Office under W911NF-17-1-0306 is gratefully acknowledged. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement. The data reported here are available on request. The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.

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August 22, 2023
October 23, 2023