相关论文: From Burgers to Navier-Stokes turbulence
Since Kolmogorov's theory, turbulence has been studied using various methods, many of which could be now be understood in a probabilistic framework. Herein, a comprehensive review of the advances made on stochastic theory of turbulence…
The classical turbulence theory by Kolmogorov is reconsidered using Navier-Stokes' equation generalized to 6D physical-plus-eddy space. Strong pseudo-singularity is shown to reveal itself along the boundary `ridge' line separating 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…
Recent studies of turbulence in superfluid Helium indicate that turbulence in quantum fluids obeys a Kolmogorov scaling law. Such a law was previously attributed to classical solutions of the Navier-Stokes equations of motion. It is…
This work is a review with proofs of a group of results on the stochastic Burgers equation with small viscosity, obtained during the last two decades. These results jointly show that the equation makes a surprisingly good model of…
The Kolmogorov approach to turbulence is applied to the Burgers turbulence in the stochastic adhesion model of large-scale structure formation. As the perturbative approach to this model is unreliable, here is proposed a new,…
We present results for the 1 dimensional stochastically forced Burgers equation when the spatial range of the forcing varies. As the range of forcing moves from small scales to large scales, the system goes from a chaotic, structureless…
In this thesis, we use some methods of theory of stochastic process to approach turbulence in fluid dynamics. We discuss the Kolmogorov model for fully developed homogeneous turbulence, some recent analytical results to the 1-D Burgers'…
This PhD thesis is devoted to deterministic study of the turbulence in the Navier- Stokes equations. The thesis is divided in four independent chapters.The first chapter involves a rigorous discussion about the energy's dissipation law,…
We study the three dimensional Navier-Stokes equation with a random Gaussian force acting on large wavelengths. Our work has been inspired by Polyakov's analysis of steady states of two dimensional turbulence. We investigate the time…
We consider the steady-state statistics of turbulence sustained by a large-scale force. The Kolmogorov flux relation (4/5-law) is shown to be a particular case of the general relation on the current-density correlation function. Using that,…
We analyze the statistical properties of three-dimensional ($3d$) turbulence in a rotating fluid. To this end we introduce a generating functional to study the statistical properties of the velocity field $\bf v$. We obtain the master…
In the limit $d\to\infty$ the role of pressure gradients and that of the incompressibility constraint decreases, thus blurring the difference between transverse and longitudinal velocity correlation functions. Using Polyakov's expression…
Turbulence is an ubiquitous phenomenon in natural and industrial flows. Since the celebrated work of Kolmogorov in 1941, understanding the statistical properties of fully developed turbulence has remained a major quest. In particular,…
We propose a theoretical framework where the dissipative structures of turbulence emerge from microscopic path uncertainty. By modeling fluid parcels as stochastic tracers governed by the Schr\"odinger Bridge (SB) variational principle, we…
In this visualisation the instantaneous local velocity is expressed in terms of four components to capture the development of and interactions between coherent structures in turbulent flows. It is then possible to isolate the terms linked…
The Navier-Stokes equation for incompressible liquid is considered in the limit of infinitely large Reynolds number. It is assumed that the flow instability leads to generation of steady-state large-scale pulsations. The excitation and…
We are concerned with the inviscid limit of the Navier-Stokes equations to the Euler equations in $\R^3$. We first observe that a pathwise Kolmogorov hypothesis implies the uniform boundedness of the $\alpha^{th}$-order fractional…
This Resource Letter provides a guide to the literature on fully developed turbulence in fluids. It is restricted to mechanically driven turbulence in an incompressible fluid described by the Navier-Stokes equations of hydrodynamics, and…
The hydrodynamics of Newtonian fluids has been the subject of a tremendous amount of work over the past eighty years, both in physics and mathematics. Sadly, however, a mutual feeling of incomprehension has often hindered scientific…