Stochastic models of Lagrangian acceleration of fluid particle in developed turbulence
arXiv:cond-mat/0408018 · doi:10.1142/S0217979204026433
Abstract
Modeling statistical properties of motion of a Lagrangian particle advected by a high-Reynolds-number flow is of much practical interest and complement traditional studies of turbulence made in Eulerian framework. The strong and nonlocal character of Lagrangian particle coupling due to pressure effects makes the main obstacle to derive turbulence statistics from the three-dimensional Navier-Stokes equation; motion of a single fluid-particle is strongly correlated to that of the other particles. Recent breakthrough Lagrangian experiments with high resolution of Kolmogorov scale have motivated growing interest to acceleration of a fluid particle. Experimental stationary statistics of Lagrangian acceleration conditioned on Lagrangian velocity reveals essential dependence of the acceleration variance upon the velocity. This is confirmed by direct numerical simulations. Lagrangian intermittency is considerably stronger than the Eulerian one. Statistics of Lagrangian acceleration depends on Reynolds number. In this review we present description of new simple models of Lagrangian acceleration that enable data analysis and some advance in phenomenological study of the Lagrangian single-particle dynamics. Simple Lagrangian stochastic modeling by Langevin-type dynamical equations is one the widely used tools. The models are aimed particularly to describe the observed highly non-Gaussian conditional and unconditional acceleration distributions. Stochastic one-dimensional toy models capture main features of the observed stationary statistics of acceleration. We review various models and focus in a more detail on the model which has some deductive support from the Navier-Stokes equation. Comparative analysis on the basis of the experimental data and direct numerical simulations is made.
73 pages, 16 eps-figures, LaTeX2e
References in corpus (42)
- Particles and fields in fluid turbulence
- Interpretation of the nonextensitivity parameter in some applications of Tsallis statistics and Lévy distributions
- Measurement of Particle Accelerations in Fully Developed Turbulence
- Measurement of Lagrangian velocity in fully developed turbulence
- Anisotropy in Turbulent Flows and in Turbulent Transport
- Experimental Lagrangian Acceleration Probability Density Function Measurement
- Modelling fluctuations of financial time series: from cascade process to stochastic volatility model
- A quark-meson model for nuclear and neutron matter
- Multifractal statistics of Lagrangian velocity and acceleration in turbulence
- Growth of non-infinitesimal perturbations in turbulence
- Multifractal stationary random measures and multifractal random walks with log-infinitely divisible scaling laws
- Long time correlations in Lagrangian dynamics: a key to intermittency in turbulence
- The 3D structure of the Lagrangian acceleration in turbulent flows
- Non-locality and Intermittency in 3D Turbulence
- Lagrangian Velocity Statistics in Turbulent Flows: Effects of Dissipation
- Lagrangian acceleration statistics in turbulent flows
- Asymptotic power law of moments in a random multiplicative process with weak additive noise
- The "zeroth law" of turbulence: Isotropic turbulence simulations revisited
- Non-additivity of Tsallis entropies and fluctuations of temperature
- Turbulence and Tsallis Statistics
- Relation between shear parameter and Reynolds number in statistically stationary turbulent shear flows
- Generalized statistical mechanics and fully developed turbulence
- A model for rapid stochastic distortions of small-scale turbulence
- One-dimensional Langevin models of fluid particle acceleration in developed turbulence
- Quasicanonical Gibbs distribution and Tsallis nonextensive statistics
- A note on non-thermodynamical applications of non-extensive statistics
- The PDF of fluid particle acceleration in turbulent flow with underlying normal distribution of velocity fluctuations
- Conditional Lagrangian acceleration statistics in turbulent flows with Gaussian distributed velocities
- Vortex Tubes in Turbulence Velocity Fields at Reynolds Numbers 300-1300
- Gaussian factor in the distribution arising from the nonextensive statistics approach to fully developed turbulence
- An interpretation of Tsallis statistics based on polydispersity
- Comment on ``Dynamical Foundations of Nonextensive Statistical Mechanics"
- Multifractal Analysis of Various PDF in Turbulence based on Generalized Statistics: A Way to Tangles in Superfluid He
- Length Scales of Acceleration for Locally Isotropic Turbulence
- On the interaction between velocity increment and energy dissipation in the turbulent cascade
- Skewness of probability density functions of fluid particle acceleration in developed turbulence
- Phenomenological Gaussian screening in the nonextensive statistics approach to fully developed turbulence
- The Exact Solution of one Fokker-Planck Type Equation used by R. Friedrich and J. Peinke in the Stochastic Model of a Turbulent Cascade
- The conditional mean acceleration of fluid particle in developed turbulence
- Stochastic model of the conditional acceleration of a fluid particle in developed turbulence
- Lagrangian statistics in fully developed turbulence
- Lagrangian Vorticity and Velocity Measurements in Turbulent Jets