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Alternative scaling for roughness transitions in turbulent flows: The role of the internal boundary layer

Justin P. Cooke1,2,*, George I. Park1, Douglas J. Jerolmack1,3, and Paulo E. Arratia1,†

  • *Contact author: justin.cooke@uri.edu
  • †Contact author: parratia@seas.upenn.edu
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Phys. Rev. Fluids 10, 084601 – Published 4 August, 2025

DOI: https://doi.org/10.1103/tmcr-8ss1

Abstract

When turbulent boundary layer flows encounter abrupt roughness changes, an internal boundary layer (IBL) forms. Equilibrium theory breaks down in the nonequilibrium IBL, which may extend O(10) km for natural atmospheric flows. Here, we find that the IBL possesses a characteristic time scale associated with the IBL height, δi. We show that δi and the edge velocity set the scales of the mean and defect velocity profiles within the IBL, for simulation and experimental data covering a multitude of roughness transition types. For the flow within the IBL, this scaling is more appropriate than more classic scaling parameters—such as viscous and outer ones—providing an alternative scaling for this intermediate region. We present a nontrivial extension of equilibrium theory to the dynamically adjusting IBL, which can be useful for modeling a range of environmental and industrial flows.

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Phys. Rev. Fluids 10, 084601– Published 4 August, 2025
  • Received 19 November 2024
  • Accepted 8 July 2025
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