A description of turbulence intensity profiles for boundary layers with adverse pressure gradient

Highlights

• New diagnostic-plot scaling of the turbulence-intensity profiles is presented.

• Validity of the new approach is examined using a number of available databases.

• The complete difference function is proposed to reconstruct the inner region.

• The method works under adverse pressure gradient conditions up to $\beta$ = 14.

• The new approach was found to be insensitive to the flow-history effects.

Abstract

The paper presents an extension of the diagnostic-plot scaling (Alfredsson et al., 2012) of the turbulence-intensity profiles for the outer region of adverse-pressure-gradient (APG) turbulent boundary layers (TBLs). An extended formula including the shape factor is proposed, which allows the diagnostic-plot scaling to be used in strong APGs at high Reynolds numbers. The validity of the new formulation is verified using several available databases. We demonstrate that the new formula allows to scale profiles in cases where the Clauser–Rotta pressure-gradient parameter $\beta$ is below 14 even in presence of very strong flow-history effects. In order to extend the scaling to the near-wall region of TBLs the adapted complete difference function is proposed. The proposed scaling yields a unified description of the turbulence-intensity profiles regardless of their flow history (as opposed to other previously proposed scalings), and is valid for a wider range of cases not only for the outer but also for the inner region.