Time-evolution and time-scales of topological structures in a turbulent boundary layer through conditional mean trajectory analysis

The Lagrangian evolution of the invariants of the velocity gradient tensor in wall-bounded turbulence is examined using conditional mean trajectories (CMT). Fields from direct numerical simulations of a turbulent boundary layer developing over a flat plate with fully turbulent flow over a Reynolds number range of Re$_{\theta} = 730$ to 1954 are used to extract the CMT in the invariant space of the velocity gradient tensor $(Q_A,R_A)$, the invariant space of the strain-rate tensor $(Q_S,R_S)$ and the invariant space of the rate-of-rotation tensor $(Q_W,R_W)$. CMT are considered for the full boundary layer, the log layer and the log and buffer layers. Results show a cyclic evolution of local topology. Associated time scales are extracted and compared with homogeneous isotropic turbulence.