Velocity scales in the near-wall layer beneath reattaching turbulent separated and boundary layer flows

This paper investigates the idea that each Reynolds stress has its own velocity scale - the mean shear stress cannot provide a velocity scale for the near-wall turbulence near reattachment, for example, and cannot by definition provide a velocity scale for 'inactive' motion. Beneath a separation bubble, the tangential velocity fluctuations scale on the r.m.s. of the respective wall shear stress fluctuation and on v/y, which is the viscous velocity scale in the usual way, independent of the other flow. This paper also shows that the wall-normal direct stress and the shear stress have respective, independent velocity scales. Moreover, and quite remarkably, the scaling functions for these latter stresses appear to be universal in that they are unchanged for the boundary layer upstream of separation or downstream of reattachment, and are as in the canonical zero-pressure gradient boundary layer. The streamwise direct stress does not exhibit this universality, raising questions about the near wall structures: it is inferred that the change in form is associated with the disappearance and reappearance of the streak-like structures.