The turbulent cascade in five dimensions

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 strategies for modeling geophysical and industrial flows. By tracking the flow regions containing energy in different scales, we have detected the statistical predominance of a cross-scale link whereby fluid lumps of energy at scale Δ appear within lumps of scale 2Δ and die within those of scale Δ/2. Our approach uncovers the energy cascade in a simple water-like fluid, offering insights for turbulence models while paving the way for similar analyses in conducting fluids, quantum fluids, and plasmas.