9,234 research outputs found
Lagrangian and Eulerian velocity structure functions in hydrodynamic turbulence
The Lagrangian and Eulerian transversal velocity structure functions of fully
developed fluid turbulence are found basing on the Navier-Stokes equation. The
structure functions are shown to obey the scaling relations inside the inertial
range. The scaling exponents are calculated analytically without using
dimensional considerations. The obtained values are in a very good agreement
with recent numerical and experimental data.Comment: 4 pages, 1 figur
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
Locality and stability of the cascades of two-dimensional turbulence
We investigate and clarify the notion of locality as it pertains to the
cascades of two-dimensional turbulence. The mathematical framework underlying
our analysis is the infinite system of balance equations that govern the
generalized unfused structure functions, first introduced by L'vov and
Procaccia. As a point of departure we use a revised version of the system of
hypotheses that was proposed by Frisch for three-dimensional turbulence. We
show that both the enstrophy cascade and the inverse energy cascade are local
in the sense of non-perturbative statistical locality. We also investigate the
stability conditions for both cascades. We have shown that statistical
stability with respect to forcing applies unconditionally for the inverse
energy cascade. For the enstrophy cascade, statistical stability requires
large-scale dissipation and a vanishing downscale energy dissipation. A careful
discussion of the subtle notion of locality is given at the end of the paper.Comment: v2: 23 pages; 4 figures; minor revisions; resubmitted to Phys. Rev.
The supercluster--void network III. The correlation function as a geometrical statistic
We investigate properties of the correlation function of clusters of galaxies
using geometrical models. On small scales the correlation function depends on
the shape and the size of superclusters. On large scales it describes the
geometry of the distribution of superclusters. If superclusters are distributed
randomly then the correlation function on large scales is featureless. If
superclusters and voids have a tendency to form a regular lattice then the
correlation function on large scales has quasi-regularly spaced maxima and
minima of decaying amplitude; i.e., it is oscillating. The period of
oscillations is equal to the step size of the grid of the lattice.
We calculate the power spectrum for our models and compare the geometrical
information of the correlation function with other statistics. We find that
geometric properties (the regularity of the distribution of clusters on large
scales) are better quantified by the correlation function. We also analyse
errors in the correlation function and the power spectrum by generating random
realizations of models and finding the scatter of these realizations.Comment: MNRAS LaTex style, 12 pages, 7 PostScript figures embedded, accepted
by MNRA
On the intermittent energy transfer at viscous scales in turbulent flows
In this letter we present numerical and experimental results on the scaling
properties of velocity turbulent fields in the range of scales where viscous
effects are acting. A generalized version of Extended Self Similarity capable
of describing scaling laws of the velocity structure functions down to the
smallest resolvable scales is introduced. Our findings suggest the absence of
any sharp viscous cutoff in the intermittent transfer of energy.Comment: 10 pages, plain Latex, 6 figures available upon request to
[email protected]
Time-variability in the Interstellar Boundary Conditions of the Heliosphere: Effect of the Solar Journey on the Galactic Cosmic Ray Flux at Earth
During the solar journey through galactic space, variations in the physical
properties of the surrounding interstellar medium (ISM) modify the heliosphere
and modulate the flux of galactic cosmic rays (GCR) at the surface of the
Earth, with consequences for the terrestrial record of cosmogenic
radionuclides. One phenomenon that needs studying is the effect on cosmogenic
isotope production of changing anomalous cosmic ray fluxes at Earth due to
variable interstellar ionizations. The possible range of interstellar ram
pressures and ionization levels in the low density solar environment generate
dramatically different possible heliosphere configurations, with a wide range
of particle fluxes of interstellar neutrals, their secondary products, and GCRs
arriving at Earth. Simple models of the distribution and densities of ISM in
the downwind direction give cloud transition timescales that can be directly
compared with cosmogenic radionuclide geologic records. Both the interstellar
data and cosmogenic radionuclide data are consistent with cloud transitions
during the Holocene, with large and assumption-dependent uncertainties. The
geomagnetic timeline derived from cosmic ray fluxes at Earth may require
adjustment to account for the disappearance of anomalous cosmic rays when the
Sun is immersed in ionized gas.Comment: Submitted to Space Sciences Review
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