On the singular nature of turbulent boundary layers

Abstract

An estimate is derived for the rate at which, with increasing Reynolds number, the vorticity in turbulent boundary layers is confined to a diminishing fraction of the overall flow domain. For laminar boundary layers this rate is reflected in the self-similar coordinate stretching that determines the Reynolds number scalings for boundary layer growth and skin friction. For the turbulent boundary layer this rate is shown to also derive from an underlying similarity structure. An accounting of the magnitude ordering of terms in the mean dynamical equation for the turbulent boundary layer reveals a four layer structure. This structure forms during the transitional regime, persists for all subseq..