Strong enstrophy events and maximal growth estimates in turbulence simulations

The temporal growth of enstrophy is a question of fundamental interest which is intimately related to the open problem of uniqueness and regularity of solutions of the Navier-Stokes equations. Recently, Lu and Doering derived a rigorous upper bound for the temporal growth of enstrophy and detected the optimal structures that can cause such events. Here, we study the temporal growth of large-amplitude vortices locally, in quasi-Lagrangian frames of reference which are moving with a swarm of Lagrangian tracers. The analysis is done in situ with highly-resolved direct numerical simulations of forced homogeneous isotropic turbulence at a Taylor microscale Reynolds number of 107 with N=2048 grid points in each direction. The most rapid growth events in the simulations are found to correspond with interacting Burgers vortices.