Three unexpected properties of the turbulent boundary layer

We shall discuss experimental and numerical evidence extracted from the literature of three unexpected features of the turbulent boundary layer: 1)  The effect of pressure gradient upon a turbulent velocity profile is opposite in sign to its effect upon a laminar velocity profile, and as a consequence cannot be predicted by mixing-length or eddy-viscosity models. 2)  The asymptotic decay of both Reynolds stresses and velocity defect at the outer edge of the turbulent boundary layer is faster than in a laminar boundary layer (and in a constant-eddy-viscosity model). 3) The verification of Clauser equilibrium (defect-layer self-similarity) through a careful interpolation highlights a different behavior of DNS and experimental results.

The effect of pressure gradient upon the logarithmic region of a turbulent velocity profile turns out to be qualitatively and quantitatively identical to the one observed in a parallel flow (in both cases opposite to the effect that takes place in laminar flow), thus testifying to its universality. It also bears an interesting similarity to a sign reversal of the same type observed in turbulent flow past an undulated bottom (P. Luchini, F. Charru. J.F.M. 871, 534-561, 2019).

The asymptotic decay of the velocity defect at the outer edge of the boundary layer is well represented by a cubic exponential, one possible explanation of which is a z^-1 decay of eddy viscosity (in place of the constant eddy viscosity most frequently assumed). A  relatively simple interpolation of the complete velocity profile using this cubic exponential well approximates DNS and experimental data and encompasses all of the above three effects.