The influence of energy containing scales on spectral energy transfers locality

The locality of energy transfers in turbulent flows has been a cornerstone of turbulence theory since Kolmogorov, assuming energy transfers predominantly between neighboring scales. This study challenges this understanding by demonstrating that spectral locality is not intrinsic to the Navier-Stokes equations but is tied to the spectral location of the energy containing range.

Through direct numerical simulations (DNS), we investigate how energy-containing scale locations influence triadic energy transfers. We introduce a heuristic for the mode-to-mode energy transfer rate based on energy products of the modes involved in the triad interaction to support our hypothesis. We perform direct computation of mode-to-mode energy transfers for a set of sampling modes, and compare it to the heuristic, showing that interactions are indeed local when using conventional low wavenumber forcing (LWF).

We also present results from DNS with intermediate wavenumber forcing (IWF). In these cases, the analysis of the heuristic reveal striking ring-like structures in wavenumber space corresponding to slightly non-local transfers, which are also observed in the direct computation of the energy transfer rates.