Energy transfer from large to small scales in turbulence by multi-scale nonlinear strain and vorticity interactions

TL;DR

This paper derives an exact relationship showing how multi-scale interactions like vorticity stretching and strain self-amplification transfer energy across scales in turbulence, with numerical evidence highlighting the significance of strain self-amplification.

Contribution

It provides a novel, exact quantitative relationship that distinguishes the roles of vorticity stretching and strain self-amplification in energy transfer in turbulence.

Findings

Strain self-amplification contributes more to energy transfer than vorticity stretching.

Numerical evidence supports the derived relationship.

The contribution of strain self-amplification is significant but not dominant.

Abstract

An intrinsic feature of turbulent flows is an enhanced rate of mixing and kinetic energy dissipation due to the rapid generation of small-scale motions from large-scale excitation. The transfer of kinetic energy from large to small scales is commonly attributed to the stretching of vorticity by the strain-rate, but strain self-amplification also plays a role. Previous treatments of this connection are phenomenological or inexact, or cannot distinguish the contribution of vorticity stretching from that of strain self-amplification. In this paper, an exact relationship is derived which quantitatively establishes how intuitive multi-scale mechanisms such as vorticity stretching and strain self-amplification together actuate the inter-scale transfer of energy in turbulence. Numerical evidence validates this result and uses it to demonstrate that the contribution of strain self-amplification to energy transfer is higher than that of vorticity stretching, but not overwhelmingly so.