Transient vortex events in the initial value problem for turbulence

Abstract

A vorticity surge event that could be a paradigm for a wide class of bursting events in turbulence is studied to examine how the energy cascade is established and how this event could serve as a new test of LES turbulence models. This vorticity surge event is tied to the formation of the energy cascade in a direct numerical simulation by the traditional signatures of a turbulent energy cascade such as spectra approaching -5/3 and strongly Beltramized vortex tubes. A coherent mechanism is suggested by the nearly simultaneous development of a maximum of the peak vorticity $\|\omega\|_\infty$, growth of the dissipation, the appearance of a helically aligned local vortex configuration and strong, transient oscillations in the helicity wavenumber spectrum. This coherence is also examined for two LES models, a traditional purely dissipative eddy viscosity model and a modern method (LANS$-\alpha$) that respects the nonlinear transport properties of fluids. Both LES models properly represent the spectral energy and energy dissipation associated with this vorticity surge event. However, only the model that preserves nonlinear fluid transport properties reproduces the helical properties, including Beltrami-like vortex tubes.