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    Turbulent boundary layer over multiscale urban roughness

    Cameron Southgate-Ash1,2,* and Marco Placidi1,†

    • 1Faculty of Engineering and Physical Sciences, Centre for Aerodynamics and Environmental Flow (EnFlo), University of Surrey, Guildford, United Kingdom
    • 2Department of Meteorology, University of Reading, Reading, United Kingdom

    • *Contact author: c.g.southgate-ash@reading.ac.uk
    • †Contact author: m.placidi@surrey.ac.uk

    Phys. Rev. Fluids 11, 114605 – Published 12 November, 2026

    DOI: https://doi.org/10.1103/fkjl-jq96

    Abstract

    Wind tunnel experiments were conducted on six multiscale rough walls immersed in deep turbulent boundary layers. The multiscale features are introduced by fractal iteration of two reference cuboid models of aspect ratio 1 (Standard) and 3 (Tall), systematically adding smaller model length scales. Through these iterations, the frontal and plan solidities, λf and λp, respectively, and the roughness mean height are kept the same. Spatially averaged three-dimensional velocity and pressure fields allow for a direct and indirect estimation of the friction velocity and aerodynamic parameters. Results show that the boundary layer height and roughness aerodynamic parameters experience significant changes across fractal iterations, despite the fixed solidities and average height of the arrays; this is in disagreement with many morphometric methods. Mean velocity profiles collapse well when plotted in velocity defect form, supporting Townsend's similarity hypothesis. However, a departure from outer layer similarity for the streamwise fluctuating velocity is observed. Changes are recorded in both roughness and inertial sublayer depths with the additional model length scales. Dispersive stresses are found to be contributing up to 20% of the overall momentum flux for the reference cuboid models; however, these contributions decrease with each fractal iteration down to below 10%. Finally, quadrant and spectral analysis show that the additional length scales act to dampen turbulent mixing below the canopy layer, while they enhance it above the canopy height.

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