Recovery of the wall-shear stress to equilibrium flow conditions after a rough-to-smooth step-change in turbulent boundary layers

TL;DR

This study investigates how the wall-shear stress in turbulent boundary layers recovers after a rough-to-smooth surface change, revealing that the near-wall region recovers quickly while outer regions take longer, with implications for measurement accuracy.

Contribution

The paper provides new experimental and numerical evidence on the spatial recovery of wall-shear stress after rough-to-smooth transitions, clarifying the extent of recovery in different flow regions.

Findings

Viscous region recovers almost immediately to equilibrium.

Buffer and outer regions take several boundary layer thicknesses to recover.

Estimating wall-shear stress from mean velocity profiles can underestimate its magnitude near the transition.

Abstract

This paper examines recovery of the wall-shear stress of a turbulent boundary layer that has undergone a sudden transition from a rough to a smooth surface. Early works of Antonia and Luxton questioned the reliability of standard smooth-wall methods to measure wall-shear stress in such conditions, and subsequent studies show significant disagreement depending on the approach used to determine the wall-shear stress downstream. Here we address this by utilising a collection of experimental databases at Re_\tau \approx 4100 that have access to both `direct' and `indirect' measures of the wall-shear stress to understand the recovery to equilibrium conditions to the new surface. Our results reveal that the viscous region (z^+\lesssim 4) recovers almost immediately to an equilibrium state with the new wall conditions, however, the buffer region and beyond takes several boundary layer thicknesses before recovering to equilibrium conditions, which is longer than previously thought. A unique direct numerical simulation database of a wall-bounded flow with a rough-to-smooth wall transition is employed to confirm these findings. In doing so, we present evidence that any estimate of the wall-shear stress from the mean velocity profile in the buffer region or further away from the wall tends to underestimate its magnitude in the near vicinity of the rough-to-smooth transition, and this is likely to be partly responsible for the large scatter of recovery lengths to equilibrium conditions reported in the literature. Our results also reveal that the smaller energetic scales in the near-wall region recover to an equilibrium state associated with the new wall conditions within one boundary layer thickness downstream of the transition, while the larger energetic scales exhibit an over-energised state for several boundary layer thicknesses downstream of the transition.