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

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