On the role of vorticity stretching and strain self-amplification in the turbulence energy cascade

TL;DR

This paper investigates the detailed roles of vorticity stretching and strain self-amplification in the turbulence energy cascade, revealing their significant contributions and introducing a new energy transfer mechanism with implications for turbulence modeling.

Contribution

It provides a detailed analysis of vorticity stretching and strain amplification, introduces a third energy transfer mechanism, and links these processes to turbulence cascade dynamics and modeling.

Findings

Vorticity stretching and strain self-amplification account for about half of the energy cascade rate.

Multiscale strain amplification and vorticity stretching resemble eddy viscosity physics.

A new energy transfer mechanism related to vortex thinning influences backscatter and the bottleneck effect.

Abstract

The tendency of turbulent flows to produce fine-scale motions from large-scale energy injection is often viewed as a scale-wise cascade of kinetic energy driven by vorticity stretching. This has been recently evaluated by an exact, spatially-local relationship [Johnson, P. L. 2020, Phys. Rev. Lett., \textbf{124}, 104501], which also highlights the contribution of strain self-amplification. In this paper, the role of these two mechanisms is explored in more detail. Vorticity stretching and strain amplification interactions between velocity gradients filtered at the same scale account for about half of the energy cascade rate, directly connecting restricted Euler dynamics to the energy cascade. Multiscale strain amplification and vorticity stretching are equally important, however, and more closely resemble eddy viscosity physics. Moreover, ensuing evidence of a power-law decay of energy transfer contributions from disparate scales supports the notion of an energy cascade, albeit a `leaky' one. Besides vorticity stretching and strain self-amplification, a third mechanism of energy transfer is introduced and related to the vortex thinning mechanism important for the inverse cascade in two dimensions. Simulation results indicate this mechanism also provides a net source of backscatter in three-dimensional turbulence, in the range of scales associated with the bottleneck effect. Taken together, these results provide a rich set of implications for large-eddy simulation modeling.