Dynamics of the velocity gradient tensor invariants in isotropic turbulence

Abstract

The evolution of the invariants (R and Q) of the velocity gradient tensor in homogeneous isotropic turbulence is investigated using data from direct numerical simulation (DNS). The concepts of conditional average time rate of change of the invariants and conditional mean trajectories (CMT) in invariant phase space are introduced to study the dynamics of this flow. The resulting dynamical system in the (R,Q) phase space is a clockwise spiral with a stable focus at the origin, illustrating that in the mean, the cyclic sequence of topological evolution following a fluid particle is unstable-node/saddle/saddle (UN/S/S)→stable-node/saddle/saddle (SN/S/S)→stable-focus/stretching (SF/S)→unstable-fo..