Evolution and lifetimes of flow topology in a turbulent boundary layer

Abstract

The average rates of change in the invariants of the velocity gradient tensor (Q and R) have been determined experimentally in the outer layer of a turbulent boundary layer as a function of the invariants themselves. Subsequent integration yields trajectories in the QR plane describing the average evolution of the local flow topology following a fluid particle. The trajectories reveal inward spiraling orbits around and converging to the origin. The orbit’s period is nearly constant at 14.3δ/Ue corresponding to 470ν/uτ2, which may be regarded as the characteristic lifetime of the energy containing eddies in this part of the boundary layer. Furthermore, an empirical model for the average Q and R evolution is presented that reproduces the main features of the orbits in the vicinity of the origin. The deviation of the QR trajectories of individual fluid particles from the average trajectory is discussed in relation to the significant scatter observed in the rates of change in the invariants around their average.