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A similarity transformation for the mean velocity profiles is obtained insink flow turbulent boundary layers (TBL), including effects of blowing andsuction. It is based on symmetry analysis which transforms the governingpartial differential equations (for mean mass and momentum) into an ordinarydifferential equation and yields a new result including an exact, linearrelation between the mean normal ($V$) and streamwise ($U$) velocities. Acharacteristic length is further introduced which, under a first orderexpansion in wall blowing/suction velocity, leads to the similaritytransformation for $U$. This transformation is shown to be a group invariantunder a generalized symmetry analysis and maps different $U$ profiles underdifferent blowing/suction conditions into a (universal) profile under noblowing/suction. Its inverse transformation enables predictions of all meanquantities in the mean mass and momentum equations - $U$, $V$ and the Reynoldsshear stress - in good agreement with direct numerical simulation (DNS) data.

Similarity transformation for equilibrium flows, including effects of blowing and suction