Breakdown toward turbulence in Poiseuille flows: Evolution of small-scale anisotropy and structure-function tensors.

Direct numerical simulations (DNS) of perturbation evolution in plane Poiseuille flow is performed in different parameter regimes. The development of perturbations from linear to non-linear stages through to breakdown (to turbulence) is examined in terms of velocity gradient field behavior. Three key velocity gradient statistics are monitored – dissipation anisotropy, structure function tensors and Q-R invariant map, where Q and R are second and third invariants of the velocity gradient tensor. Dissipation anisotropy tensor represents the dimensionality of the perturbation field, while the structure function tensor quantifies its componentiality. As is well established, the Q-R invariants specify the local perturbation streamline topology. The characteristic features of perturbation componentiality, dimensionality and topology are established. It is also demonstrated that the sequence of breakdown events and velocity-gradient behavior change with the initial amplitude magnitude and orientation of the initial perturbations.