Related papers: Two-point velocity average of turbulence: statisti…
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…
Turbulence exhibits significant velocity fluctuations even if the scale is much larger than the scale of the energy supply. Since any spatial correlation is negligible, these large-scale fluctuations have many degrees of freedom and are…
We consider two-particle dispersion in a velocity field, where the relative two-point velocity scales according to $v^{2}(r)\propto r^{\alpha}$ and the corresponding correlation time scales as $\tau (r)\propto r^{\beta}$, and fix $\alpha…
The mean rate of energy dissipation in turbulence is traditionally assumed to scale with parameters of the energy-containing large scales, i.e., the root-mean-square fluctuation of the longitudinal velocity u and its correlation length…
Turbulent flows in three dimensions are characterized by the transport of energy from large to small scales through the energy cascade. Since the small scales are the result of the nonlinear dynamics across the scales, they are often…
Traditionally, trends of universal turbulence statistics are presented versus R-lambda, which is the Reynolds number based on Taylor's scale, lambda, and the root-mean-squared (rms) velocity component, u'. Taylor's scale and u', and hence…
We propose an alternative formulation of structure functions for the velocity field in fully developed turbulence. Instead of averaging moments of the velocity differences as a function of the distance, we suggest to average moments of the…
We extend our earlier work on turbulence-induced relative velocity between equal-size particles (Pan and Padoan, Paper I) to particles of arbitrarily different sizes. The Pan and Padoan (PP10) model shows that the relative velocity between…
Two-dimensional turbulence generated in a finite box produces large-scale coherent vortices coexisting with small-scale fluctuations. We present a rigorous theory explaining the $\eta=1/4$ scaling in the $V\propto r^{-\eta}$ law of the…
Many questions remain in turbulence research---and related fields---about the underlying physical processes that transfer scalar quantities, such as the kinetic energy, between different length scales. Measurement of an ensemble-averaged…
This paper is devoted to a statistical analysis of the fluctuations of velocity and acceleration produced by a random distribution of point vortices in two-dimensional turbulence. We show that the velocity probability density function…
The statistical properties of turbulence are considered to be universal at sufficiently small length scales, i. e., independent of boundary conditions and large-scale forces acting on the fluid. Analyzing data from numerical simulations of…
To study subregions of a turbulence velocity field, a long record of velocity data of grid turbulence is divided into smaller segments. For each segment, we calculate statistics such as the mean rate of energy dissipation and the mean…
The numerical experiments of turbulence conducted by Gotoh et al. are analyzed precisely with the help of the formulae for the scaling exponents of velocity structure function and for the probability density function (PDF) of velocity…
We consider the two-dimensional (2D) flow in a flat free-slip surface that bounds a three-dimensional (3D) volume in which the flow is turbulent. The equations of motion for the two-dimensional flow in the surface are neither compressible…
Studies in the literature on plane turbulent wall jets on flat surfaces, have invariably considered either the nozzle initial conditions or the asymptotic conditions far downstream, as scaling parameters for the streamwise variations of…
We present theory of two-dimensional turbulence excited by an external force in thin fluid films on scales larger than the film thickness. The principal feature of two-dimensional turbulence is the tendency of producing motions of larger…
The velocity fluctuations for point vortex models are studied for the {\alpha}-turbulence equations, which are characterized by a fractional Laplacian relation between active scalar and the streamfunction. In particular, we focus on the…
We present a numerical study of two-dimensional turbulent flows in the enstrophy cascade regime, with different large-scale forcings and energy sinks. In particular, we study the statistics of more-than-differentiable velocity fluctuations…
The phenomenology of the scaling behavior of higher order structure functions of velocity differences across a scale $R$ in turbulence should be built around the irreducible representations of the rotation symmetry group. Every irreducible…