Modelling the downstream development of a turbulent boundary layer following a step change of roughness

Mogeng Li, Charitha M. de Silva, Daniel Chung, Dale I. Pullin, Ivan Marusic, Nicholas Hutchins*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

5 Citations (Scopus)


In this study, we develop an analytical model to predict the turbulent boundary layer downstream of a step-change in the surface roughness where upstream flow conditions are given. We first revisit the classical model of Elliott (Trans. Am. Geophys. Union, vol. 39, 1958, pp. 1048-1054), who modelled the velocity distribution within and above the internal layer with a simple piecewise logarithmic profile, and evolved the velocity profile using the streamwise momentum equation. Elliott's model was originally developed for an atmospheric surface layer, and to make the model applicable to a spatially developing turbulent boundary layer with finite thickness, we propose a number of more physical refinements, including adding a wake function to the velocity profile, considering the growth of the entire boundary layer in the streamwise direction, and using a more realistic shear stress profile in the momentum equation. In particular, we implement the blending model (Li et al., J. Fluid Mech., vol. 923, 2021, p. A18) to account for the deviation of the mean flow within the internal layer from a canonical velocity profile based on the local wall condition. These refinements lead to improved agreement between the prediction and the measurement, especially in the vicinity of the rough-to-smooth change.

Original languageEnglish
Article numberA7
JournalJournal of Fluid Mechanics
Publication statusPublished - 2022
Externally publishedYes


  • turbulent boundary layers


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