The turbulent cascade in five dimensions

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.

Submitted to Science on 19th May 2017, accepted for publication on 26th July 2017. To appear in Vol 357. 14 pages, 4 figures in manuscript, 6 figures and 1 table in supplementary material

References in corpus (5)

• Emergence of a Turbulent Cascade in a Quantum Gas
• Localness of energy cascade in hydrodynamic turbulence, I. Smooth coarse-graining
• Exact Second-Order Structure-Function Relationships
• Localness of energy cascade in hydrodynamic turbulence, II. Sharp spectral filter
• The temporal evolution of the energy flux across scales in homogeneous turbulence

Cited by in corpus (36)

• A Quantum Inspired Approach to Exploit Turbulence Structures
• Variational Quantum Algorithms for Computational Fluid Dynamics
• Causality of energy-containing eddies in wall turbulence
• Decomposing causality into its synergistic, unique, and redundant components
• Quantum computing of fluid dynamics using the hydrodynamic Schrödinger equation
• The turbulent bubble break-up cascade. Part 2. Numerical simulations of breaking waves
• Machine-aided turbulence theory
• Turbulence-induced rogue waves in Kerr resonators
• The coherent structure of the kinetic energy transfer in shear turbulence
• Non-Boussinesq subgrid-scale model with dynamic tensorial coefficients
• Entropy, irreversibility and cascades in the inertial range of isotropic turbulence
• Direct assessment of Kolmogorov's first refined similarity hypothesis
• Self-similar geometries within the inertial subrange of scales in boundary layer turbulence
• Weaving classical turbulence with quantum skeleton
• Dipoles and streams in two-dimensional turbulence
• Self-similar hierarchy of coherent tubular vortices in turbulence
• A Kolmogorov spectrum for strongly vibrating plates
• Velocity gradient partitioning in turbulent flows
• Lagrangian statistics of pressure fluctuation events in homogeneous isotropic turbulence
• Identifying causal significance in three-dimensional isotropic turbulence
• Stochastic modelling of the instantaneous velocity profile in rough-wall turbulent boundary layers
• Rossby Number Effects on Columnar Eddy Formation and the Energy Dissipation Law in Homogeneous Rotating Turbulence
• Chaos, coherence and turbulence
• Entropy and fluctuation relations in isotropic turbulence
• The Role of Normal and Non-Normal Contributions to Enstrophy Production in the Near-Wall Region of a Turbulent Channel Flow
• Normality-based analysis of multiscale velocity gradients and energy transfer in direct and large-eddy simulations of isotropic turbulence
• Shot noise multifractal model for turbulent pseudo-dissipation
• Deformation of drops by outer eddies in turbulence
• A length scale for non-local multi-scale gradient interactions in isotropic turbulence
• Inter-scale energy transfer in turbulence from the viewpoint of subfilter scales
• Space-local Navier--Stokes turbulence
• Fragmentation in turbulence by small eddies
• Dimension Crossing Turbulent Cascade in an Excited Lattice Bose Gas
• Direct power spectral density estimation from structure functions without Fourier transforms
• Effect of filter kernel on scale-energetics of near-wall turbulent structures
• High Resolution and High-Speed Live Optical Flow Velocimetry