Related papers: Kubo Combinatorics for Turbulence Scaling Laws
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…
Intermittency phenomena are known to be among the main reasons why Kolmogorov's theory of fully developed Turbulence is not in accordance with several experimental results. This is why some \emph{fractal} statistical models have been…
We consider particle acceleration by large-scale incompressible turbulence with a lengthscale larger than the particle mean free path. We derive an ensemble-averaged transport equation of energetic charged particles from an extended…
The asymptotic energy dissipation is connected to the third-order scaling of the longitudinal velocity increment magnitude in three-dimensional turbulence via the Kolmogorov $4/5$ law. It is shown that the third-order longitudinal absolute…
Shell model turbulence is a simplified mathematical framework that captures essential features of incompressible fluid turbulence such as the energy cascade, intermittency and anomalous scaling of the fluid observables. We perform a…
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…
Statistical features of homogeneous, isotropic, two-dimensional turbulence is discussed on the basis of a set of direct numerical simulations up to the unprecedented resolution $32768^2$. By forcing the system at intermediate scales, narrow…
Shell models provide a simplified mathematical framework that captures essential features of incompressible fluid turbulence, such as the energy cascade and scaling of the fluid observables. We perform a precision analysis of the direct and…
In this note, we address the validity of certain exact results from turbulence theory in the deterministic setting. The main tools, inspired by the work of Duchon-Robert (Inertial energy dissipation for weak solutions of incompressible…
A landmark of turbulence is the emergence of universal scaling laws, such as Kolmogorov's $E(q)\sim q^{-5/3}$ scaling of the kinetic energy spectrum of inertial turbulence with the wave vector $q$. In recent years, active fluids have been…
In recent papers Benzi et al. presented experimental data and an analysis to the effect that the well-known "2/3" Kolmogorov-Obukhov exponent in the inertial range of local structure in turbulence should be corrected by a small but…
We argue on the basis of empirical data that Kolmogorov's refined similarity hypothesis (RSH) needs to be modified for transverse velocity increments, and propose an alternative. In this new form, transverse velocity increments bear the…
In this paper, we investigate the statistical features of the fully developed, forced, rapidly rotating, {turbulent} system using numerical simulations, and model {the} energy {spectrum} that {fits} well with the numerical data. Among the…
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.…
The largely open problem of scaling laws in fully developed turbulence is discussed, with the stress put on similarities and differences with scaling in field theory. A soluble model of the passive advection is examined in more detail in…
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,…
1-D scalar conservation laws with convex flux and Markov initial data are now known to yield a completely integrable Hamiltonian system. In this article, we rederive the analogue of Loitsiansky's invariant in hydrodynamic turbulence from…
In the standard picture of fully-developed turbulence, highly intermittent hydrodynamic fields are nonlinearly coupled across scales, where local energy cascades from large scales into dissipative vortices and large density gradients.…
We apply a simple method to provide explicit expressions for different scaling exponents in intermittent fully developed turbulence, that before were only given through a Legendre transform. This includes predictability exponents for…
We establish exact inequalities for the structure-function scaling exponents of a passively advected scalar in both the inertial-convective and viscous-convective ranges. These inequalities involve the scaling exponents of the velocity…