Statistical Properties of Turbulence: An Overview

Abstract

We present an introductory overview of several challenging problems in the statistical characterisation of turbulence. We provide examples from fluid turbulence in three and two dimensions, from the turbulent advection of passive scalars, turbulence in the one-dimensional Burgers equation, and fluid turbulence in the presence of polymer additives.

34 pages, 31 figures

References in corpus (12)

• Large scale dynamics in turbulent Rayleigh-Benard convection
• The multifractal nature of turbulent energy dissipation
• Burgers Turbulence
• Universal intermittent properties of particle trajectories in highly turbulent flows
• Hyperviscosity, Galerkin truncation and bottlenecks in turbulence
• Colloquium: Theory of Drag Reduction by Polymers in Wall Bounded Turbulence
• Sub-Kolmogorov-Scale Fluctuations in Fluid Turbulence
• Twenty-five years of multifractals in fully developed turbulence: a tribute to Giovanni Paladin
• Non-local interactions in hydrodynamic turbulence at high Reynolds numbers: the slow emergence of scaling laws
• Universal Model of Finite-Reynolds Number Turbulent Flow in Channels and Pipes
• Dynamic Multiscaling in Turbulence
• Vortex Tubes in Turbulence Velocity Fields at High Reynolds Numbers

Cited by in corpus (37)

• Cascades and transitions in turbulent flows
• Machine learning strategies for path-planning microswimmers in turbulent flows
• Two-dimensional Turbulence in Symmetric Binary-Fluid Mixtures: Coarsening Arrest by the Inverse Cascade
• Anomalous diffusion and Lévy walks distinguish active from inertial turbulence
• Systematics of the magnetic-Prandtl-number dependence of homogeneous, isotropic magnetohydrodynamic turbulence
• Direct numerical simulations of statistically steady, homogeneous, isotropic fluid turbulence with polymer additives
• Liquid velocity fluctuations and energy spectra in three-dimensional buoyancy driven bubbly flows
• Turbulence in the two-dimensional Fourier-truncated Gross-Pitaevskii equation
• Vorticity moments in four numerical simulations of the 3D Navier-Stokes equations
• On the Peterlin approximation for turbulent flows of polymer solutions
• Kinetic energy spectra and flux in turbulent phase-separating symmetric binary-fluid mixtures
• Binary-Fluid Turbulence: Signatures of Multifractal Droplet Dynamics and Dissipation Reduction
• Two-dimensional, homogeneous, isotropic fluid turbulence with polymer additives
• Flow structures govern particle collisions in turbulence
• Coarsening in the two-dimensional incompressible Toner-Tu equation: Signatures of turbulence
• Multiscaling in superfluid turbulence: A shell-model study
• Multiscaling in Hall-Magnetohydrodynamic Turbulence: Insights from a Shell Model
• Homogeneous Isotropic Superfluid Turbulence in Two Dimensions: Inverse and Forward Cascades in the Hall-Vinen-Bekharevich-Khalatnikov model
• Statistics of the inverse-cascade regime in two-dimensional magnetohydrodynamic turbulence
• Elliptical Tracers in Two-dimensional, Homogeneous, Isotropic Fluid Turbulence: the Statistics of Alignment, Rotation, and Nematic Order
• Dynamics of circular arrangements of vorticity in two dimensions
• Revisiting the SABRA Model: Statics and Dynamics
• Statistical Properties of three-dimensional Hall Magnetohydrodynamics Turbulence
• Depletion of Nonlinearity in Magnetohydrodynamic Turbulence: Insights from Analysis and Simulations
• Bridging Inertial and Dissipation Range Statistics in Rotating Turbulence
• A regularity criterion for solutions of the three-dimensional Cahn-Hilliard-Navier-Stokes equations and associated computations
• Inertia drives concentration-wave turbulence in swimmer suspensions
• Phase ordering, topological defects, and turbulence in the 3D incompressible Toner-Tu equation
• The role of BKM-type theorems in $3D$ Euler, Navier-Stokes and Cahn-Hilliard-Navier-Stokes analysis
• The spreading of viruses by airborne aerosols: lessons from a first-passage-time problem for tracers in turbulent flows
• Topology of two-dimensional turbulent flows of dust and gas
• Two-dimensional magnetohydrodynamic turbulence with large and small energy-injection length scales
• Weak-strong clustering transition in renewing compressible flows
• The Statistical Properties of Superfluid Turbulence in ${}^4$He from the Hall-Vinen-Bekharevich-Khalatnikov Model
• Dynamic Scaling in Rotating Turbulence: A Shell Model Study
• Fluid dynamics in clouds: The sum of its parts
• Analytic structure of solutions of the one-dimensional Burgers equation with modified dissipation