An experimental and numerical study of turbulent oscillatory flow over an irregular rough wall

Danny Dunbar, Dominic Van der A* (Corresponding Author), Pietro Scandura, Thomas O'Donoghue

*Corresponding author for this work

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The hydrodynamics of turbulent oscillatory flow over a gravel-based irregular rough wall are investigated using laser-Doppler anemometry (LDA) measurements of velocities in a large oscillatory flow tunnel and direct numerical simulation (DNS) of the Navier-Stokes equations. The same periodic irregular roughness was used for both experiments and DNS. Four flow shapes are investigated: sinusoidal, skewed, asymmetric, and combined skewed-asymmetric. The experiments were conducted for target Reynolds number (based on the Stokes length and standard deviation of free-stream velocity) of ๐‘…๐›ฟ, ๐œŽ = 800 and ๐‘…๐›ฟ, ๐œŽ = 1549; DNS was conducted for flows with target ๐‘…๐›ฟ, ๐œŽ = 800. Boundary layer thickness, bottom phase lead and friction factor are in good agreement with previous studies. For the first time, evidence of Prandtlโ€™s secondary flows of the second kind in oscillatory flow is presented. Turbulence
structure is visualised using isosurfaces of ๐œ†2 (Jeong & Hussain 1995), revealing densely packed structures that grow stronger and weaker in correspondence with the free-stream velocity. Reynolds and dispersive stresses peak just below the highest roughness crest, with dispersive stress vanishing a short distance above the roughness. Bursts of turbulence kinetic energy and wake kinetic energy are generated each flow half-cycle, with variable behaviour depending on flow shape. Non-Gaussian turbulence statistics are observed that originate
near the wall, becoming increasingly non-Gaussian far from the wall. Probability density functions of turbulence statistics can be closely approximated by a 4th -order Gram-Charlier distribution at most phases and elevations, though when statistics deviate more strongly from Gaussian, streamwise and wall-normal (spanwise) statistics are better described by a Pearson type IV (VII) distribution.
Original languageEnglish
Article numberA33
Number of pages47
JournalJournal of Fluid Mechanics
Early online date18 Jan 2023
Publication statusPublished - 25 Jan 2023

Bibliographical note

Open Access via the CUP Agreement
Acknowledgements. This work was conducted as part of the first authorโ€™s PhD project and is also included in Dunbar (2022). The authors are grateful for the support of the technical staff at the University of Aberdeen, particularly Fluids Lab technicians Roy Gillanders and Jack Milne. Additionally, the authors are grateful to Dr. Stuart Cameron and Dr. Mark Stewart for assistance with the design and manufacture of the experimental and numerical roughness, and Prof. Vladimir Nikora for his suggestion to look for evidence of secondary flows.

Funding. The PhD project from which this work is derived was funded by the Carnegie Trust for the Universities of Scotland (D.D., grant no. PHD00771). P.S. acknowledges the support received from the University of Catania by funding the research project โ€™Valutazione del rischio idraulico in sistemi complessi (VARIO)โ€™.

Data Availability Statement

The phase-averaged experimental and numerical datasets presented in this paper are openly available at


  • coastal engineering
  • turbulent boundary layers
  • surface gravity waves


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