Related papers: "Locally homogeneous turbulence" Is it an inconsis…
Fully developed turbulence is analised with the lattice model employing vortex tube representation which is introduced recently by the authors. Several characteric features observed in experiments and direct numeric integrations are…
Turbulence is a fundamental flow phenomenon, typically anisotropic at large scales and approximately isotropic at small scales. The classical Kolmogorov scaling laws (2/3, -5/3 and 4/5) have been well-established for turbulence without…
High-resolution numerical experiments, described in this work, show that velocity fluctuations governed by the one-dimensional Burgers equation driven by a white-in-time random noise with the spectrum $\overline{|f(k)|^2}\propto k^{-1}$…
The process of star formation in interstellar molecular clouds is believed to be controlled by driven supersonic magnetohydrodynamic turbulence. We suggest that in the inertial range such turbulence obeys the Kolmogorov law, while in the…
We are concerned with the inviscid limit of the Navier-Stokes equations to the Euler equations for compressible fluids in $\mathbb{R}^3$. Motivated by the Kolmogorov hypothesis (1941) for incompressible flow, we introduce a Kolmogorov-type…
A defining feature of 3D hydrodynamic turbulence is that the rate of energy dissipation is bounded away from zero as viscosity is decreased (Reynolds number increased). This phenomenon - anomalous dissipation - is sometimes called the…
This paper is a synopsis of the recent book A. Boritchev, S. Kuksin, \textit{One-Dimensional Turbulence and the Stochastic Burgers Equation}, AMS Publications, 2021 (to appear). The book is dedicated to the stochastic Burgers equation as a…
From a simple path integral involving a variable volatility in the velocity differences, we obtain velocity probability density functions with exponential tails, resembling those observed in fully developed turbulence. The model yields…
Kolmogorov's theory for turbulence in 1941 is based on a hypothesis that small-scale statistics are uniquely determined by the kinematic viscosity and the mean rate of energy dissipation. Landau remarked that the local rate of energy…
A lagrangian approach to Burgers turbulence is carried out along the lines of the field theoretical Martin-Siggia-Rose formalism of stochastic hydrodynamics. We derive, from an analysis based on the hypothesis of unbroken galilean…
We study the homogeneous isotropic turbulence of a shear-thinning fluid modeled by the Carreau model and show how the variable viscosity affects the multiscale behaviour of the turbulent flow. We show that Kolmogorov theory can be extended…
Exact solutions of conformal turbulence restricted on a upper half plane are obtained. We show that the inertial range of homogeneous and isotropic turbulence with constant enstrophy flux develops in a distant region from the boundary. Thus…
We present the first measurements of anisotropic statistical fluctuations in perfectly homogeneous turbulent flows. We address both problems of intermittency in anisotropic sectors and hierarchical ordering of anisotropies on a direct…
We study the homogeneous turbulence in the presence of a constant average velocity gradient in an infinite fluid domain, with a novel finite-scale Lyapunov analysis, presented in a previous work dealing with the homogeneous isotropic…
Kolmogorov's similarity turbulence theory in a Lagrangian frame is assessed with new direct numerical simulations (DNS) of isotropic turbulence with and without hyperviscosity, which attain higher Reynolds numbers than previously available.…
We consider the generalised Burgers equation $$ \frac{\partial u}{\partial t} + f'(u)\frac{\partial u}{\partial x} - \nu \frac{\partial^2 u}{\partial x^2}=0,\ t \geq 0,\ x \in S^1, $$ where $f$ is strongly convex and $\nu$ is small and…
By analogy with recent arguments concerning the mean velocity profile of wall-bounded turbulent shear flows, we suggest that there may exist corrections to the 2/3 law of Kolmogorov, which are proportional to $(\ln\,\Re)^{-1}$ at large Re.…
The addition of polymers fundamentally alters the dynamics of turbulent flows in a way that defies Kolmogorov predictions. However, we now present a formalism that reconciles our understanding of polymeric turbulence with the classical…
The internal interactions of fluids occur at all scales therefore the resulting force fields have no reason to be smooth and differentiable. The release of the differentiability hypothesis has important mathematical consequences, like scale…
Coherent structures are solutions to reaction-diffusion systems that are time-periodic in an appropriate moving frame and spatially asymptotic at $x=\pm\infty$ to spatially periodic travelling waves. This paper is concerned with sources…