Related papers: Extreme events and instantons in Lagrangian passiv…
The reduction of dimensionality of physical systems, specially in fluid dynamics, leads in many situations to nonlinear ordinary differential equations which have global invariant manifolds with algebraic expressions containing relevant…
We develop a stochastic model for the velocity gradients dynamics along a Lagrangian trajectory. Comparing with different attempts proposed in the literature, the present model, at the cost of introducing a free parameter known in…
We consider statistics of the passive scalar on distances much larger than the pumping scale. Such statistics is determined by statistics of Lagrangian contraction that is by probabilities of initially distant fluid particles to come close.…
The role of instantons is investigated in the Lagrangian model for the velocity gradient evolution known as the Recent Fluid Deformation approximation. After recasting the model into the path-integral formalism, the probability distribution…
A precise characterization of structures occurring in turbulent fluid flows at high Reynolds numbers is one of the last open problems of classical physics. In this review we discuss recent developments related to the application of…
Lagrangian turbulence lies at the core of numerous applied and fundamental problems related to the physics of dispersion and mixing in engineering, bio-fluids, atmosphere, oceans, and astrophysics. Despite exceptional theoretical,…
In the context of instanton method for stochastic system this paper purposes a modification of the arclength parametrization of the Hamilton's equations allowing for an arbitrary instanton speed. The main results of the paper are: (i) it…
The scaling of acceleration statistics in turbulence is examined by combining data from the literature with new data from well-resolved direct numerical simulations of isotropic turbulence, significantly extending the Reynolds number range.…
The equation for the fluid velocity gradient along a Lagrangian trajectory immediately follows from the Navier-Stokes equation. However, such an equation involves two terms that cannot be determined from the velocity gradient along the…
We develop a stochastic model for Lagrangian velocity as it is observed in experimental and numerical fully developed turbulent flows. We define it as the unique statistically stationary solution of a causal dynamics, given by a stochastic…
The Lagrangian view of passive scalar turbulence has recently produced interesting results and interpretations. Innovations in theory, experiments, simulations and data analysis of Lagrangian turbulence are reviewed here in brief. Part of…
The local statistical and geometric structure of three-dimensional turbulent flow can be described by properties of the velocity gradient tensor. A stochastic model is developed for the Lagrangian time evolution of this tensor, in which the…
Extreme events play a crucial role in fluid turbulence. Inspired by methods from field theory, these extreme events, their evolution and probability can be computed with help of the instanton formalism as minimizers of a suitable action…
Particles in turbulence frequently encounter extreme accelerations between extended periods of quiescence. The occurrence of extreme events is closely related to the intermittent spatial distribution of intense flow structures such as…
An exact relation is derived between scalar dissipation due to molecular diffusivity and the randomness of stochastic Lagrangian trajectories for flows without bounding walls. This "Lagrangian fluctuation-dissipation relation" equates the…
Sampling synthetic turbulent fields as a computationally tractable surrogate for direct numerical simulations (DNS) is an important practical problem in various applications, and allows to test our physical understanding of the main…
We revisit the well-known problem of multiscaling in substances passively advected by homogeneous and isotropic turbulent flows or passive scalar turbulence. To that end we propose a two-parameter continuum hydrodynamic model for an…
We present direct numerical simulations (DNS) of the mixing of the passive scalar at modest Reynolds numbers (10 =< R_\lambda =< 42) and Schmidt numbers larger than unity (2 =< Sc =< 32). The simulations resolve below the Batchelor scale up…
We show that multiscaling properties of developed turbulence in shell models, which lead to anomalous scaling exponents in the inertial range, are determined exclusively by instanton dynamics. Instantons represent correlated extreme events…
We consider a passive scalar field under the action of pumping, diffusion and advection by a smooth flow with a Lagrangian chaos. We present theoretical arguments showing that scalar statistics is not conformal invariant and formulate new…