# Is vortex stretching the main cause of the turbulent energy cascade?

## TL;DR

This paper challenges the traditional view that vortex stretching is the primary mechanism driving the turbulent energy cascade, showing instead that strain-rate self-amplification is the main contributor, with implications for understanding turbulence physics.

## Contribution

The study derives a new theoretical result revealing the dominant role of strain-self amplification over vortex stretching in the energy cascade, supported by direct numerical simulations.

## Key findings

- Vortex stretching is not the main contributor to the average energy cascade.
- Strain-rate self-amplification dominates the energy transfer process.
- Vortex stretching may be significant during large fluctuations of the cascade.

## Abstract

In three dimensional turbulence there is on average a cascade of kinetic energy from the largest to the smallest scales of the flow. While the dominant idea is that the cascade occurs through the physical process of vortex stretching, evidence for this is debated. In the framework of the Karman-Howarth equation for the two point turbulent kinetic energy, we derive a new result for the average flux of kinetic energy between two points in the flow that reveals the role of vortex stretching. However, the result shows that vortex stretching is in fact not the main contributor to the average energy cascade; the main contributor is the self-amplification of the strain-rate field. We emphasize the need to correctly distinguish and not conflate the roles of vortex stretching and strain-self amplification in order to correctly understand the physics of the cascade, and also resolve a paradox regarding the differing role of vortex stretching on the mechanisms of the energy cascade and energy dissipation rate. Direct numerical simulations are used to confirm the results, as well as provide further results and insights on vortex stretching and strain-self amplification at different scales in the flow. Interestingly, the results imply that while vortex stretching plays a sub-leading role in the average cascade, it may play a leading order role during large fluctuations of the energy cascade about its average behavior.