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Compressibility effects on drag reduction by spanwise traveling transversal surface waves in turbulent boundary layers

Xiao Shao1,*, Marian Albers1, Matthias Meinke1, and Wolfgang Schröder1,2

  • *Contact author: x.shao@aia.rwth-aachen.de
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Phys. Rev. Fluids 10, 094603 – Published 23 September, 2025

DOI: https://doi.org/10.1103/2882-bszw

Abstract

The effect of compressibility on drag reduction (DR) by spanwise traveling transversal surface waves (STTSW) is investigated in turbulent boundary layer (TBL) flow over a flat plate. Wall-resolved simulations are performed at Mach numbers M1=0.2 and M2=0.7 over a range of actuation parameters, i.e., wavelength, period, and amplitude. The results based on 36 cases simulated for each Mach number show that DR is more pronounced at higher Mach numbers with a maximum reduction of 19.2% at M1=0.2 compared to 27.5% at M2=0.7 for identical actuation parameters. This enhanced DR at M2=0.7 is mainly due to the formation of spanwise shock waves at higher phase velocities. These spanwise shock waves are generated by the actuated wall deformation that redistributes the pressure field. Upstream of the shock, in the supersonic flow region, the development of streamwise vortices is weakened, resulting in reduced turbulent mixing and dissipation. Downstream of the shock, the turbulent structures are reorganized due to the compression wave leading to locally high wall-shear stress. Integrating the wall-shear stress distribution over the complete surface wave shows that the spanwise shock waves cause significant friction drag reduction. However, the pressure variations upstream and downstream of the shock wave require an increased actuation power, which results in negative net power saving at M2=0.7.

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Phys. Rev. Fluids 10, 094603– Published 23 September, 2025
  • Received 3 February 2025
  • Accepted 25 August 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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