Efficiency of energy and enstrophy transfers in periodical flows

Abstract

We apply a coarse-graining technique to understand the efficiency of scale-to-scale transport of energy and enstrophy in a quasi-two-dimensional weakly turbulent periodic flow. The investigated periodic flow resembles the propagation of a monochromatic tide in a tidal channel, connected to open sea through an inlet. The interaction of the periodic flow with the inlet mouth generates vortical structures in a wide spectrum of scales, and recently, how the corresponding energy and enstrophy fluxes change their signs depending on the tidal phase has been shown. In the present study, we are interested to extend the analysis to the efficiency of the nonlinear transfer rates by analyzing the geometric alignment between the turbulent stresses and the strain rates for the energy, and the vorticity stress and large-scale vorticity gradient for the enstrophy. Our results suggest that, depending on the phase of the period, energy is efficiently transferred to larger scales (inverse cascade) in a finite range of scales, whereas the observed direct energy cascade for very small and very large scales is much less efficient. Enstrophy shows similar behaviors in terms of transitions between direct and inverse cascading; however, all transfers seem to be relatively inefficient.