# Turbulence generation supported by an inverse energy transfer through a zig-zag pattern

## TL;DR

This paper shows how turbulence can develop from small-scale vortices forming zig-zag patterns, challenging the traditional view of turbulence generation.

## Contribution

The study introduces a novel mechanism of turbulence generation through inverse energy transfer from small to large scales.

## Key findings

- Turbulent energy spectra emerge first at small scales and extend to larger ones.
- Vortex filaments form and rearrange into zig-zag patterns, enabling inverse energy transfer.
- This process challenges the traditional forward cascade model of turbulence.

## Abstract

A known feature of turbulent flow in any setting, be it in ocean currents or smoke rising from a fire, is the presence of vortices on a range of scales. As turbulence develops, kinetic energy is transferred between these different scales, leading to a power law distribution of spectral energy, of a specific form established nearly a century ago. While a universally accepted mechanistic model of this process is still missing, the long-standing dominating idea is that of a turbulent energy cascade where large vortices break down into smaller ones, to successively develop finer scales until reaching a smallest scale, where energy is dissipated by viscosity. However, we here present observations of a turbulent energy spectrum developing through an alternative process. Specifically, the following problem is addressed: how is turbulence generated from the given initial condition, and what flow structures appear that may help explain the emergence of the energy spectrum? We show, using a computer simulation supported by a stability analysis, a turbulent energy spectrum emerging first at small scales and progressively extending to larger scales. This coincides in time with the formation of vortex filaments through vortex stretching on the smallest resolvable scale, and their subsequent rearrangement into recursive zig-zag patterns. It is hypothesized that the formation of this pattern leads to an inverse energy transfer from small to large scales, contributing to the development of the power law energy distribution. This description of a turbulent energy spectrum forming initially from small scales, potentially in part due to the formation of vortex filaments and their zig-zag rearrangement, rather than a forward cascade through a break-down of vortices from large scales to small, is novel to the best of our knowledge. These findings provide critical new perspectives on the development of turbulence in fluid flow, relevant in scenarios ranging from blood flow in the heart, to fuel mixing, aerodynamics, and atmospheric turbulence.