Related papers: Instanton Theory of Burgers Shocks and Intermitten…
We study the onset of intermittency in stochastic Burgers hydrodynamics, as characterized by the statistical behavior of negative velocity gradient fluctuations. The analysis is based on the response functional formalism, where specific…
We analyze the field theory of fully developed Burgers turbulence. Its key elements are shock fields, which characterize the singularity statistics of the velocity field. The shock fields enter an operator product expansion describing…
This dissertation discusses the intermitency phenomenon in three models of turbulence, employing analytical and numerical techniques in the analysis of stochastic processes and the probability distributions which they induce. The initial…
The statistics of Lagrangian particles in turbulent flows is considered in the framework of a simple vortex model. Here, the turbulent velocity field is represented by a temporal sequence of Burgers vortices of different circulation,…
Understanding intermittency of turbulent systems from the underlying differential equations is an outstanding problem in fluid dynamics. Here, in the example of Burgers turbulence as a stringent test, we introduce a method that yields…
We develop a Lagrangian approach to conservation-law anomalies in weak solutions of inviscid Burgers equation, motivated by previous work on the Kraichnan model of turbulent scalar advection. We show that the entropy solutions of Burgers…
Instanton calculations are performed in the context of stationary Burgers turbulence to estimate the tails of the probability density function (PDF) of velocity gradients. These results are then compared to those obtained from massive…
We investigate time-irreversibility from the point of view of a single particle in Burgers turbulence. Inspired by the recent work for incompressible flows [Xu et al., PNAS 111.21 (2014) 7558], we analyze the evolution of the kinetic energy…
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…
All Lie symmetries of the Burgers equation driven by an external random force are found. Besides the generalized Galilean transformations, this equation is also invariant under the time reparametrizations. It is shown that the Gaussian…
We report the experimental observation of intermittency in a regime dominated by random shock waves on the surface of a fluid. We achieved such a nondispersive surface-wave field using a magnetic fluid subjected to a high external magnetic…
We present a generalized picture of intermittency in turbulence that is based on the theory of stochastic processes. To this end, we rely on the experimentally and numerically verified finding by R.~Friedrich and J.~Peinke [Phys. Rev. Lett.…
The decay of Burgers turbulence with compactly supported Gaussian "white noise" initial conditions is studied in the limit of vanishing viscosity and large time. Probability distribution functions and moments for both velocities and…
The randomly driven Burgers equation with pressure is considered as a 1D model of strong turbulence of compressible fluid. It is shown that infinitely small pressure provides a finite effect on the velocity and density statistics and this…
The instanton solution for the forced Burgers equation is found. This solution describes the exponential tail of the probability distribution function of velocity differences in the region where shock waves are absent. The results agree…
The last decades witnessed a renewal of interest in the Burgers equation. Much activities focused on extensions of the original one-dimensional pressureless model introduced in the thirties by the Dutch scientist J.M. Burgers, and more…
The inviscid limit of the stochastic Burgers equation is discussed in terms of the level surfaces of the minimising Hamilton-Jacobi function, the classical mechanical caustic and the Maxwell set and their algebraic pre-images under the…
Lagrangian pair dispersion provides insights into mixing in turbulent flows. By direct numerical simulations (DNS) we show that the statistics of pair dispersion in the randomly forced two-dimensional Burgers equation, which is a typical…
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 one-dimensional Burgers equation in the inviscid limit for white-noise initial velocity. We derive the probability distributions of velocity and Lagrangian increments, measured on intervals of any length $x$. This also gives…