Related papers: "Locally homogeneous turbulence" Is it an inconsis…
The Kolmogorov scaling law of turbulences has been considered the most important theoretical breakthrough in the last century. It is an essential approach to analyze turbulence data present in meteorological, physical, chemical, biological…
In this paper, we prove the local uniqueness of an inverse problem arising in the nonstationary flow of a nonhomogeneous incompressible asymmetric fluid in a bounded domain with smooth boundary. The direct problem is an initial-boundary…
Differential models for hydrodynamic, passive-scalar and wave turbulence given by nonlinear first- and second-order evolution equations for the energy spectrum in the $k$-space were analysed. Both types of models predict formation an…
Whether turbulence intermittencies shall be described by a log-Poisson, a log-stable pdf or other distributions is still debated nowadays. In this paper, a bridge between polymer physics, self-avoiding walk and random vortex stretching is…
This paper is the first in a series of three papers that aim at understanding the scaling behaviour of hydrodynamic turbulence. We present in this paper a perturbative theory for the structure functions and the response functions of the…
Classical theories of turbulence do not describe accurately inertial range scaling laws in turbulent convection and notably fail to model the shape of the turbulent spectrum of solar photospheric convection. To understand these…
We construct, for the first time to our knowledge, a one-dimensional stochastic field $\{u(x)\}_{x\in \mathbb{R}}$ which satisfies the following axioms which are at the core of the phenomenology of turbulence mainly due to Kolmogorov: (i)…
An exact result concerning the energy transfers between non-linear waves of thin elastic plate is derived. Following Kolmogorov's original ideas in hydrodynamical turbulence, but applied to the F\"oppl-von K\'arm\'an equation for thin…
We propose an exact analytical formula for the anomalous scaling exponents of inertial range structure functions in incompressible fluid turbulence. The formula is a gravitational Knizhnik-Polyakov-Zamolodchikov (KPZ)-type relation, and is…
A dynamical systems approach to turbulence envisions the flow as a trajectory through a high-dimensional state space transiently visiting the neighbourhoods of unstable simple invariant solutions (E. Hopf, Commun. Appl. Maths 1, 303, 1948).…
There is a striking convergence between Burgers turbulence and the continuous spontaneous localization [CSL] model of quantum mechanics. In this paper, we exploit this analogy showing the similarities in the physics of these two apparently…
A phenomenological theory of the fluctuations of velocity occurring in a fully developed homogeneous and isotropic turbulent flow is presented. The focus is made on the fluctuations of the spatial (Eulerian) and temporal (Lagrangian)…
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,…
In this course we review the theory of incompressible homogeneous turbulence at an elementary level, and discuss the similarities and differences expected in the compressible case, relevant to the interstellar medium and molecular clouds.…
We develop a new method to uniquely solve a large class of heat equations, so-called Kolmogorov equations in infinitely many variables. The equations are analyzed in spaces of sequentially weakly continuous functions weighted by proper…
The analogue of the Kolmogorov's four-fifths law is derived for two-dimensional, homogeneous, isotropic EMHD turbulence in the energy cascade inertial range. Direct numerical simulations for the freely decaying case show that this relation…
Based on direct numerical simulations with point-like inertial particles, with Stokes numbers, $\textrm{St}=0, 0.5$, $3$, and $6$, transported by homogeneous and isotropic turbulent flows, we present in this letter for the first time…
The spectral slope of strong MHD turbulence has recently been a matter of controversy. While Goldreich-Sridhar model (1995) predicts Kolmogorov's -5/3 slope of turbulence, shallower slopes were often reported by numerical studies. We argue…
We study the statistical properties of solutions to Burgers' equation, $v_t + vv_x = \nu v_{xx}$, for large times, when the initial velocity and its potential are stationary Gaussian processes. The initial power spectral density at small…
In this paper, we consider a continuous-time Markov process and prove a local limit theorem for the integral of a time-inhomogeneous function of the process. One application is in the study of the fast-oscillating perturbations of linear…