The temporal evolution of the energy flux across scales in homogeneous turbulence

TL;DR

This study investigates how energy moves across different scales in turbulence, revealing that energy transfer is a scale-local process with disturbances propagating at a consistent velocity, independent of external forcing.

Contribution

It provides a detailed temporal analysis of energy flux evolution in turbulence, demonstrating the additive nature of flux travel times and the scale-local cascade process.

Findings

Energy flux disturbances propagate at a scale-independent velocity.

Energy transfer between scales is additive and consistent.

The cascade process is predominantly scale-local and continuous.

Abstract

A temporal study of energy transfer across length scales is performed in 3D numerical simulations of homogeneous shear flow and isotropic turbulence. The average time taken by perturbations in the energy flux to travel between scales is measured and shown to be additive. Our data suggests that the propagation of disturbances in the energy flux is independent of the forcing and that it defines a `velocity' that determines the energy flux itself. These results support that the cascade is, on average, a scale-local process where energy is continuously transmitted from one scale to the next in order of decreasing size.