The cascade of energy in homogeneous turbulence: a 5D approach

The inherent multi-dimensional nature of the turbulent cascade is a major challenge to its study. In order to characterize a process occurring in space, time and scale, we present a new approach where we track coherent structures representing energy in different scales from a time-resolved simulation of isotropic turbulence lasting $66$ large-eddy turnovers. We couple the dynamics at different scales by computing the geometric intersection between individual coherent structures from any two scales. Statistically, we find that eddies at scale $r$ intersect those at scales $2r$ and $r/2$ preferentially at the beginning and at the end of their life, respectively. With our simulation at $Re_{\lambda}=315$, we could check this trend to hold for $r$ values spanning a ratio of $8$. We thus report on $4$ generations of eddies that trace the transfer of energy from scale $8r$ to scale $r$ via intermediate steps through a scale-local, spatially-localized process. We found the geometric intersection between scales separated by ratios of $4$ or larger to be of the same order of magnitude as the random intersection levels found for those scale combinations.