Anomalous scaling in two and three dimensions for a passive vector field advected by a turbulent flow

A model of the passive vector field advected by the uncorrelated in time Gaussian velocity with power-like covariance is studied by means of the renormalization group and the operator product expansion. The structure functions of the admixture demonstrate essential power-like dependence on the external scale in the inertial range (the case of an anomalous scaling). The method of finding of independent tensor invariants in the cases of two and three dimensions is proposed to eliminate linear dependencies between the operators entering into the operator product expansions of the structure functions. The constructed operator bases, which include the powers of the dissipation operator and the enstrophy operator, provide the possibility to calculate the exponents of the anomalous scaling.Comment: 9 pages, LaTeX2e(iopart.sty), submitted to J. Phys. A: Math. Ge

Performance characteristics of wind profiling radars

Doppler radars used to measure winds in the troposphere and lower stratosphere for weather analysis and forecasting are lower-sensitivity versions of mesosphere-stratosphere-troposphere radars widely used for research. The term wind profiler is used to denote these radars because measurements of vertical profiles of horizontal and vertical wind are their primary function. It is clear that wind profilers will be in widespread use within five years: procurement of a network of 30 wind profilers is underway. The Wave Propagation Laboratory (WPL) has operated a small research network of radar wind profilers in Colorado for about two and one-half years. The transmitted power and antenna aperture for these radars is given. Data archiving procedures have been in place for about one year, and this data base is used to evaluate the performance of the radars. One of the prime concerns of potential wind profilers users is how often and how long wind measurements are lacking at a given height. Since these outages constitute an important part of the performance of the wind profilers, they are calculated at three radar frequencies, 50-, 405-, and 915-MHz, (wavelengths of 6-, 0.74-, and 0.33-m) at monthly intervals to determine both the number of outages at each frequency and annual variations in outages

"Locally homogeneous turbulence" Is it an inconsistent framework?

In his first 1941 paper Kolmogorov assumed that the velocity has increments which are homogeneous and independent of the velocity at a suitable reference point. This assumption of local homogeneity is consistent with the nonlinear dynamics only in an asymptotic sense when the reference point is far away. The inconsistency is illustrated numerically using the Burgers equation. Kolmogorov's derivation of the four-fifths law for the third-order structure function and its anisotropic generalization are actually valid only for homogeneous turbulence, but a local version due to Duchon and Robert still holds. A Kolomogorov--Landau approach is proposed to handle the effect of fluctuations in the large-scale velocity on small-scale statistical properties; it is is only a mild extension of the 1941 theory and does not incorporate intermittency effects.Comment: 4 pages, 2 figure

Statistics of mixing in three-dimensional Rayleigh--Taylor turbulence at low Atwood number and Prandtl number one

Three-dimensional miscible Rayleigh--Taylor (RT) turbulence at small Atwood number and at Prandtl number one is investigated by means of high resolution direct numerical simulations of the Boussinesq equations. RT turbulence is a paradigmatic time-dependent turbulent system in which the integral scale grows in time following the evolution of the mixing region. In order to fully characterize the statistical properties of the flow, both temporal and spatial behavior of relevant statistical indicators have been analyzed. Scaling of both global quantities ({\it e.g.}, Rayleigh, Nusselt and Reynolds numbers) and scale dependent observables built in terms of velocity and temperature fluctuations are considered. We extend the mean-field analysis for velocity and temperature fluctuations to take into account intermittency, both in time and space domains. We show that the resulting scaling exponents are compatible with those of classical Navier--Stokes turbulence advecting a passive scalar at comparable Reynolds number. Our results support the scenario of universality of turbulence with respect to both the injection mechanism and the geometry of the flow

The Viscous Lengths in Hydrodynamic Turbulence are Anomalous Scaling Functions

It is shown that the idea that scaling behavior in turbulence is limited by one outer length $L$ and one inner length $\eta$ is untenable. Every n'th order correlation function of velocity differences \bbox{\cal F}_n(\B.R_1,\B.R_2,\dots) exhibits its own cross-over length $\eta_{n}$ to dissipative behavior as a function of, say, $R_1$. This length depends on $n$ {and on the remaining separations} $R_2,R_3,\dots$. One result of this Letter is that when all these separations are of the same order $R$ this length scales like $\eta_n(R)\sim \eta (R/L)^{x_n}$ with $x_n=(\zeta_n-\zeta_{n+1}+\zeta_3-\zeta_2)/(2-\zeta_2)$, with $\zeta_n$ being the scaling exponent of the $n$'th order structure function. We derive a class of scaling relations including the ``bridge relation" for the scaling exponent of dissipation fluctuations $\mu=2-\zeta_6$.Comment: PRL, Submitted. REVTeX, 4 pages, I fig. (not included) PS Source of the paper with figure avalable at http://lvov.weizmann.ac.il/onlinelist.htm

Effect of helicity and rotation on the free decay of turbulent flows

The self-similar decay of energy in a turbulent flow is studied in direct numerical simulations with and without rotation. Two initial conditions are considered: one non-helical (mirror-symmetric), and one with maximal helicity. The results show that, while in the absence of rotation the energy in the helical and non-helical cases decays with the same rate, in rotating flows the helicity content has a major impact on the decay rate. These differences are associated with differences in the energy and helicity cascades when rotation is present. Properties of the structures that arise in the flow at late times in each time are also discussed.Comment: 4 pages, 4 figure

Real-space Manifestations of Bottlenecks in Turbulence Spectra

An energy-spectrum bottleneck, a bump in the turbulence spectrum between the inertial and dissipation ranges, is shown to occur in the non-turbulent, one-dimensional, hyperviscous Burgers equation and found to be the Fourier-space signature of oscillations in the real-space velocity, which are explained by boundary-layer-expansion techniques. Pseudospectral simulations are used to show that such oscillations occur in velocity correlation functions in one- and three-dimensional hyperviscous hydrodynamical equations that display genuine turbulence.Comment: 5 pages, 2 figure

A digital computer program for the dynamic interaction simulation of controls and structure (DISCOS), volume 1

A theoretical development and associated digital computer program system for the dynamic simulation and stability analysis of passive and actively controlled spacecraft are presented. The dynamic system (spacecraft) is modeled as an assembly of rigid and/or flexible bodies not necessarily in a topological tree configuration. The computer program system is used to investigate total system dynamic characteristics, including interaction effects between rigid and/or flexible bodies, control systems, and a wide range of environmental loadings. In addition, the program system is used for designing attitude control systems and for evaluating total dynamic system performance, including time domain response and frequency domain stability analyses