Related papers: Robert H. Kraichnan
High resolution direct numerical simulations of two-dimensional turbulence in stationary conditions are presented. The development of an energy-enstrophy double cascade is studied and found to be compatible with the classical Kraichnan…
We study the inverse energy transfer in forced two-dimensional (2D) Navier--Stokes turbulence in a doubly periodic domain. It is shown that an inverse energy cascade that carries a nonzero fraction of the injected energy to the large scales…
The paper {\it On the multifractal nature of fully developed turbulence and chaotic systems}, by R. Benzi {\it et al.} published in this journal in 1984 (vol {\bf 17}, page 3521) has been a starting point of many investigations on the…
Kraichnan seminal ideas on inverse cascades yielded new tools to study common phenomena in geophysical turbulent flows. In the atmosphere and the oceans, rotation and stratification result in a flow that can be approximated as…
A widely used statistical theory of 2D turbulence developed by Kraichnan, Leith, and Batchelor (KLB) predicts a power-law scaling for the energy, $E(k)\propto k^\alpha$ with an integral exponent $\alpha={-3}$, in the inertial range…
Statistical characteristics of the Kraichnan direct cascade for two-dimensional hydrodynamic turbulence are numerically studied (with spatial resolution $8192\times 8192$) in the presence of pumping and viscous-like damping. It is shown…
Fluid turbulence is a far-from-equilibrium phenomenon and remains one of the most challenging problems in physics. Two-dimensional, fully developed turbulence may possess the largest possible symmetry, the conformal symmetry. We focus on…
Rotating turbulence is an example of a three-dimensional system in which an inverse cascade of energy, from the small to the large scales, can be formed. While usually understood as a byproduct of the typical bidimensionalization of…
This is an introductory course on fully developed turbulence. It discusses: in Lecture 1: the Navier Stokes equations, existence of solutions, statistical description, energy balance and cascade picture; in Lecture 2: the Kolmogorov theory…
Inertial range energy transfer in three dimensional fully developed binary fluid turbulence is studied under the assumption of statistical homogeneity. Using two point statistics, exact relations corresponding to the energy cascade are…
We report the generation of large coherent vortices via inverse energy cascade in Faraday wave driven turbulence. The motion of floaters in the Faraday waves is three dimensional but its horizontal velocity fluctuations show unexpected…
The ultimate regime of thermal convection, the so called Kraichnan regime (R. H. Kraichnan, Phys. Fluids 5, 1374 (1962)), hitherto has been elusive. Here, numerical evidence for that regime is presented by performing simulations of the bulk…
In the period of 1948-1955, Chandrasekhar wrote four papers on magnetohydrodynamic (MHD) turbulence, which are the first set of papers in the area. The field moved on following these pioneering efforts. In this paper, I will briefly…
The cascade of energy in turbulent flows, i.e., the transfer of kinetic energy from large to small flow scales or vice versa (backward cascade), is the cornerstone of most theories and models of turbulence since the 1940s. Yet,…
To answer the question whether a cascade of energy exists or not in turbulence, we propose a set of correlation functions able to test if there is an irreversible transfert of energy, step by step, from large to small structures. These…
Statistical characteristics of freely decaying two-dimensional hydrodynamic turbulence at high Reynolds numbers are numerically studied. In particular, numerical experiments (with resolution up to $8192\times 8192$) provide a Kraichnan-type…
A major challenge in turbulence research is to understand from first principles the origin of anomalous scaling of the velocity fluctuations in high-Reynolds-number turbulent flows. One important idea was proposed by Kolmogorov [J. Fluid…
The American physicist Robert Dicke (1916-1997) is primarily known for his important contributions to gravitation, cosmology, and microwave physics. Much less known is his work in geophysics and related areas of the earth sciences in which…
Biskamp and Schwarz [Phys. Plasmas, 8, 3282 (2001)] have reported that the energy spectrum of two-dimensional magnetohydrodynamic turbulence is proportional to $k^{-3/2}$, which is a prediction of Iroshnikov-Kraichnan phenomenology. In this…
We present experimental evidence for a double cascade of kinetic energy in a statistically stationary rotating turbulence experiment. Turbulence is generated by a set of vertical flaps which continuously injects velocity fluctuations…