Particles and fields in fluid turbulence
arXiv:cond-mat/0105199 · doi:10.1103/RevModPhys.73.913
Abstract
The understanding of fluid turbulence has considerably progressed in recent years. The application of the methods of statistical mechanics to the description of the motion of fluid particles, i.e. to the Lagrangian dynamics, has led to a new quantitative theory of intermittency in turbulent transport. The first analytical description of anomalous scaling laws in turbulence has been obtained. The underlying physical mechanism reveals the role of statistical integrals of motion in non-equilibrium systems. For turbulent transport, the statistical conservation laws are hidden in the evolution of groups of fluid particles and arise from the competition between the expansion of a group and the change of its geometry. By breaking the scale-invariance symmetry, the statistically conserved quantities lead to the observed anomalous scaling of transported fields. Lagrangian methods also shed new light on some practical issues, such as mixing and turbulent magnetic dynamo.
165 pages, review article for Rev. Mod. Phys
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- Fluctuations of separation of trajectories in chaos and correlation dimension
- Puff turbulence in the limit of strong buoyancy
- Rotation matters - Direct numerical simulations of rectangular particles in suspensions at low to intermediate solid fraction
- Stochastic Lagrangian Dynamics of Vorticity. I. General Theory
- Lagrangian view of time irreversibility of fluid turbulence
- Irreversibility and small-scale generation in 3D turbulent flows
- Stretching vortices as a basis for the theory of turbulence
- Scaling behavior in interacting systems: joint effect of anisotropy and compressibility
- Perturbative anomalous exponents from Kolmogorov multipliers
- Advection by Compressible Turbulent Flows: Renormalization Group Study of Vector and Tracer Admixture
- Modelling the growth rate of a tracer gradient using stochastic differential equations
- Experimental investigation into Lagrangian statistics of droplets in homogeneous isotropic turbulence
- Dispersion and reaction in random flows: single realisation vs ensemble average
- Turbulent stretching of dumbbells with hydrodynamic interactions: an analytical study
- Velocity alignment explains Lagrangian irreversibility in turbulence
- Clustering of advected passive sliders on a fluctuating surface
- Numerical Coalescence of Chaotic Trajectories
- Assigning probabilities to non-Lipschitz mechanical systems
- Single particle Lagrangian dispersion in Bolgiano turbulence
- An upper critical dimension for dynamo action: A -dimensional closure model study
- Dynamics of inertial particles in a random flow with strong permanent shear
- Fluid-particle separation in the Batchelor regime with telegraph model of noise
- Non-Kolmogorov scaling for two-particle relative velocity in two-dimensional inverse energy-cascade turbulence
- Anomalous Regularization in Kraichnan's Passive Scalar Model
- Point-source dispersion of quasi-neutrally-buoyant inertial particles
- New equation for lagrangian incompressible fluid flows applied to turbulence
- Heat equilibrium distribution in a turbulent flow
- Universality classes of surface wave turbulence as probed by laser Doppler velocimetry in viscous fluids
- "Life after death" in ordinary differential equations with a non-Lipschitz singularity