The turbulent cascade in five dimensions

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Science  25 Aug 2017:
Vol. 357, Issue 6353, pp. 782-784
DOI: 10.1126/science.aan7933

Tackling the life and death of whirls

Energy in a turbulent system moves from large eddies to smaller ones until it is dissipated by viscous motion. The details of exactly how this works have remained obscure, in part because of the challenge of simulating fluids across many length scales in three dimensions over time. Cardesa et al. present a large numeric simulation of a water-like fluid that shows characteristic length scales for the birth and death of turbulent whirls. The approach can be extended to understand energy transfer in the atmosphere, plasmas, and other complex systems.

Science, this issue p. 782


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.

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