We present a similarity transformation for the mean velocity profiles in sink flow turbulent boundary layers, including effects of blowing and suction. It is based on symmetry analysis which transforms the governing partial differential equations (for mean mass and momentum) into an ordinary differential equation and yields a new result including an exact, linear relation between the mean normal ($V$) and streamwise ($U$) velocities. A characteristic length function is further introduced which, under a first order expansion (whose coefficient is $\eta$) in wall blowing and suction velocity, leads to the similarity transformation for $U$ with the value of $\eta \approx -1/9$. This transformation is shown to be a group invariant and maps different $U$ profiles under different blowing and suction conditions into a (universal) profile for no blowing or suction. Its inverse transformation enables predictions of all mean quantities in the mean mass and momentum equations, in good agreement with DNS data.

• Received 2 December 2016

DOI:https://doi.org/10.1103/PhysRevFluids.2.034605