The turbulent cascade in five dimensions

TL;DR

This paper investigates the energy cascade in five-dimensional turbulent flows, revealing a cross-scale link where energy lumps grow and decay across scales, providing new insights into turbulence modeling.

Contribution

It introduces a novel approach to track energy regions across scales in five-dimensional turbulence, uncovering a key cross-scale link in a water-like fluid.

Findings

Identified a statistical predominance of energy lumps appearing at scale 2Δ and dying at Δ/2.

Uncovered the energy cascade process in a simple water-like fluid.

Provided insights applicable to geophysical, industrial, and plasma flows.

Abstract

To the naked eye, turbulent flows exhibit whirls of many different sizes. To each size, or scale, corresponds a fraction of the total energy resulting from a cascade in five dimensions: scale, time and three-dimensional space. Understanding this process is critical to modeling strategies of geophysical and industrial flows. By tracking the flow regions containing energy in different scales, we have evidenced the statistical predominance of a cross-scale link whereby fluid lumps of energy at scale $\Delta$ appear within lumps of scale $2\Delta$ and die within those of scale $\Delta/2$. Our approach uncovers the energy cascade in a simple water-like fluid, offering new insights to turbulence models while paving the way to similar analysis in conducting fluids, quantum fluids and plasmas.