Particles and fields in fluid turbulence

By Gregory Falkovich, K. Gawȩdzki, Massimo Vergassola. 2001

1,062 citations recorded by the source corpus.

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.

Subfields: Computational Mechanics, Global and Planetary Change, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/f8e818340a71b01f9f8b116f4dbc523a8e024dd8

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

In Global and Planetary Change

In Statistical and Nonlinear Physics

Citations in the corpus

Dynamics and bifurcations of nonsmooth systems: A survey (2012, neutral): “Falkovich-Gawedzki-Vergassola [116], and”
Odor Landscapes in Turbulent Environments (2014, methodology): “The statistics of the concentration of odors for the Kraichnan flow [26] [panel (a)] and jet-flow experiments [3] (all other panels).”
Beyond Kolmogorov cascades (2019, methodology): “These results provide a support to an initial work by Jucha et al. (2014) and relies on a rigorous version of the Ott–Mann–Gawedzki relation (Ott & Mann 2000; Falkovich et al. 2001), sometimes described as a “Lagrangian analogue of the 4/3-law”.”
Convex integration and phenomenologies in turbulence (2019, background): “(10)We also note here that the 4/5-law has an analogue in Lagrangian variables, the so-called Ott-Mann-Gawȩdzki relation [158, 73].”
Statistics from Lagrangian observations (2008, background): “Triplets have been studied recently in the context of Richardson dispersion (Celani and Vergassola, 2001; Falkovich et al., 2001).”
Cascades and transitions in turbulent flows (2018, background): “Both recovery of smallscale isotropy and universality of scaling exponents can be proved rigorously in the case of passive scalar and magnetic advection by a Kraichnan flow [134, 418].”
Acceleration of rain initiation by cloud turbulence (2002, methodology): “Here we derive a formula for the collision rate of small heavy particles in a turbulent flow, using a recently developed formalism for tracing random trajectorie”
Short term fluctuations of wind and solar power systems (2016, background): “This can also be quantified by higher order structure functions [29, 30, 31, 32, 33, 34].”
The large deviation approach to statistical mechanics (2008, background): “Stochastic field equations of this form are known as hydrodynamic equations, and are used to model turbulent fluids [160–162], as well as the macroscopic dynamics of particles evolving and interacting on lattices [12,163,164]; see Section 6.”
Frontiers of chaotic advection (2014, background): “…constant is not, however, simply the average rate of stretching (infinite-time Lyapunov exponent), but is obtained from the distribution of finite-time Lyapunov exponents in a nontrivial manner (Antonsen, Jr. et al., 1995, 1996; Balkovsky and Fouxon, 1999; Falkovich et al., 2001; Thiffeault, 2008).”
Mixing Versus Stirring (2019, background): “…e.g. Donzis et al. (2005)), the correction F (Pe) is nevertheless singular (it is infinite in the limit D → 0, sometimes coined a ‘dissipative anomaly’ (Falkovich et al. 2001)), and this makes sense : The decay rate of the scalar fluctuations is solely prescribed by the stirring strength γ, but it…”
Fluctuation Relations for Diffusion Processes (2007, methodology): “A discussion of the case with D(x, y) non-smooth around the diagonal, pertaining to the fully developed turbulence, may be found in [29], or, on the mathematical level, in [60].”