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

Abstract

The hydrodynamics of turbulent oscillatory flow over a gravel-based irregular rough wall is investigated using laser-Doppler anemometry 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 numbers (based on the Stokes length and standard deviation of free-stream velocity) of $R_{\delta,\sigma }=800$ and $R_{\delta,\sigma }=1549$ ; DNS was conducted for flows with target $R_{\delta,\sigma }=800$ . Boundary layer thickness, bottom phase lead and friction factor are in good agreement with previous studies. For the first time, evidence of Prandtl's secondary flows of the second kind in oscillatory flow is presented. Turbulence structure is visualised using isosurfaces of $\lambda _{2}$ (Jeong & Hussain J. Fluid Mech., vol. 285, 1995, pp. 69–94), 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 fourth-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.

An empirical model for velocity in rough turbulent oscillatory boundary layers

“…However, unlike the flow under surface gravity waves, the mean flow field in an OFT is horizontally uniform and lacks a vertical component. Xie et al (2021) conducted a study of flows with 𝑅𝑒 and 𝐴∕𝑘 𝑠 values similar to van der A et al (2011), Yuan and Madsen (2014), O'Donoghue et al (2021) and Dunbar (2022) in a large wave flume. In this type of facility, the flow is naturally comprised of multiple harmonics but their relative amplitude and phase cannot be controlled.…”

“…In this article, experimental data from several previous OFT experiments (Jonsson and Carlsen, 1976;Yuan and Madsen, 2014;O'Donoghue et al, 2021;Dunbar, 2022) are used to develop and validate the empirical model. In the experiments, velocity profiles in a periodic oscillatory boundary layer over a fixed rough bed were measured using particle image velocimetry (PIV), laser Doppler anemometry (LDA), or a micropropellor.…”

“…The studies of van der A et al (2011), Yuan and Madsen (2014), O'Donoghue et al (2021), Xie et al (2021) and Dunbar (2022) primarily cover the rough turbulent regime (see Fig. 1).…”

“…King, 1991;Dibajnia and Watanabe, 1998;van der A et al, 2010;Silva et al, 2011) have demonstrated the importance of flow skewness and asymmetry for the transport of sediments. These sediment transport studies have been complemented by more recent research in which the effects of skewness and asymmetry on rough-wall boundary layer hydrodynamics have been experimentally investigated in oscillatory flow tunnel (OFT) facilities Yuan and Madsen, 2014;O'Donoghue et al, 2021;Dunbar, 2022). An OFT is a U-tube facility in which a piston is used to generate an oscillatory flow.…”

“…Salon et al, 2007) and direct numerical simulation (DNS, e.g. Jonsson and Carlsen (1976, ), Kemp andSimons (1982, ), Sleath (1987, ), Jensen et al (1989, ), Krstic and Fernando (2001, ), Mirfenderesk and Young (2003, ), Chen et al (2007, ), Dixen et al (2008, ), van der A et al (2011, ), Yuan and Madsen (2014, ), Ghodke and Apte (2016, ), Xie et al (2021, ), O'Donoghue et al (2021, ), Dunbar (2022. Delineation of flow regimes is based on Jonsson (1980) and Davies and Villaret (1997) 1987; Scandura et al, 2016;Ghodke and Apte, 2018; to simulate oscillatory boundary layer flow.…”