9,954 research outputs found
Galilean invariance and homogeneous anisotropic randomly stirred flows
The Ward-Takahashi (WT) identities for incompressible flow implied by
Galilean invariance are derived for the randomly forced Navier-Stokes equation
(NSE), in which both the mean and fluctuating velocity components are
explicitly present. The consequences of Galilean invariance for the vertex
renormalization are drawn from this identity.Comment: REVTeX 4, 4 pages, no figures. To appear as a Brief Report in the
Physical Review
Sub-Kolmogorov-Scale Fluctuations in Fluid Turbulence
We relate the intermittent fluctuations of velocity gradients in turbulence
to a whole range of local dissipation scales generalizing the picture of a
single mean dissipation length. The statistical distribution of these local
dissipation scales as a function of Reynolds number is determined in numerical
simulations of forced homogeneous isotropic turbulence with a spectral
resolution never applied before which exceeds the standard one by at least a
factor of eight. The core of the scale distribution agrees well with a
theoretical prediction. Increasing Reynolds number causes the generation of
ever finer local dissipation scales. This is in line with a less steep decay of
the large-wavenumber energy spectra in the dissipation range. The energy
spectrum for the highest accessible Taylor microscale Reynolds number
R_lambda=107 does not show a bottleneck.Comment: 8 pages, 5 figures (Figs. 1 and 3 in reduced quality
Universal Model of Finite-Reynolds Number Turbulent Flow in Channels and Pipes
In this Letter we suggest a simple and physically transparent analytical
model of the pressure driven turbulent wall-bounded flows at high but finite
Reynolds numbers Re. The model gives accurate qualitative description of the
profiles of the mean-velocity and Reynolds-stresses (second order correlations
of velocity fluctuations) throughout the entire channel or pipe in the wide
range of Re, using only three Re-independent parameters. The model sheds light
on the long-standing controversy between supporters of the century-old log-law
theory of von-K\`arm\`an and Prandtl and proposers of a newer theory promoting
power laws to describe the intermediate region of the mean velocity profile.Comment: 4 pages, 6 figs, re-submitted PRL according to referees comment
Drag Reduction by Polymers in Wall Bounded Turbulence
We address the mechanism of drag reduction by polymers in turbulent wall
bounded flows. On the basis of the equations of fluid mechanics we present a
quantitative derivation of the "maximum drag reduction (MDR) asymptote" which
is the maximum drag reduction attained by polymers. Based on Newtonian
information only we prove the existence of drag reduction, and with one
experimental parameter we reach a quantitative agreement with the experimental
measurements.Comment: 4 pages, 1 fig., included, PRL, submitte
Particle and particle pair dispersion in turbulence modeled with spatially and temporally correlated stochastic processes
In this paper we present a new model for modeling the diffusion and relative
dispersion of particles in homogeneous isotropic turbulence. We use an
Heisenberg-like Hamiltonian to incorporate spatial correlations between fluid
particles, which are modeled by stochastic processes correlated in time. We are
able to reproduce the ballistic regime in the mean squared displacement of
single particles and the transition to a normal diffusion regime for long
times. For the dispersion of particle pairs we find a -dependence of the
mean squared separation at short times and a -dependence for long ones. For
intermediate times indications for a Richardson law are observed in
certain situations. Finally the influence of inertia of real particles on the
dispersion is investigated.Comment: 10 pages, 7 figures, 1 tabl
Gauge symmetry and Slavnov-Taylor identities for randomly stirred fluids
The path integral for randomly forced incompressible fluids is shown to have
an underlying Becchi-Rouet-Stora (BRS) symmetry as a consequence of Galilean
invariance. This symmetry must be respected to have a consistent generating
functional, free from both an overall infinite factor and spurious relations
amongst correlation functions. We present a procedure for respecting this BRS
symmetry, akin to gauge fixing in quantum field theory. Relations are derived
between correlation functions of this gauge fixed, BRS symmetric theory,
analogous to the Slavnov-Taylor identities of quantum field theory.Comment: 5 pages, no figures, In Press Physical Review Letters, 200
The Spectral Energy Distribution and Infrared Luminosities of z ≈ 2 Dust-obscured Galaxies from Herschel and Spitzer
Dust-obscured galaxies (DOGs) are a subset of high-redshift (z ≈ 2) optically-faint ultra-luminous infrared galaxies (ULIRGs, e.g., L_(IR) > 10^(12) L_☉). We present new far-infrared photometry, at 250, 350, and 500 μm (observed-frame), from the Herschel Space Telescope for a large sample of 113 DOGs with spectroscopically measured redshifts. Approximately 60% of the sample are detected in the far-IR. The Herschel photometry allows the first robust determinations of the total infrared luminosities of a large sample of DOGs, confirming their high IR luminosities, which range from 10^(11.6) L_☉ 10^(13) L_☉. The rest-frame near-IR (1-3 μm) spectral energy distributions (SEDs) of the Herschel-detected DOGs are predictors of their SEDs at longer wavelengths. DOGs with "power-law" SEDs in the rest-frame near-IR show observed-frame 250/24 μm flux density ratios similar to the QSO-like local ULIRG, Mrk 231. DOGs with a stellar "bump" in their rest-frame near-IR show observed-frame 250/24 μm flux density ratios similar to local star-bursting ULIRGs like NGC 6240. None show 250/24 μm flux density ratios similar to extreme local ULIRG, Arp 220; though three show 350/24 μm flux density ratios similar to Arp 220. For the Herschel-detected DOGs, accurate estimates (within ~25%) of total IR luminosity can be predicted from their rest-frame mid-IR data alone (e.g., from Spitzer observed-frame 24 μm luminosities). Herschel-detected DOGs tend to have a high ratio of infrared luminosity to rest-frame 8 μm luminosity (the IR8 = L_(IR)(8-1000 μm)/νL_ν(8 μm) parameter of Elbaz et al.). Instead of lying on the z = 1-2 "infrared main sequence" of star-forming galaxies (like typical LIRGs and ULIRGs at those epochs) the DOGs, especially large fractions of the bump sources, tend to lie in the starburst sequence. While, Herschel-detected DOGs are similar to scaled up versions of local ULIRGs in terms of 250/24 μm flux density ratio, and IR8, they tend to have cooler far-IR dust temperatures (20-40 K for DOGs versus 40-50 K for local ULIRGs) as measured by the rest-frame 80/115 μm flux density ratios (e.g., observed-frame 250/350 μm ratios at z = 2). DOGs that are not detected by Herschel appear to have lower observed-frame 250/24 μm ratios than the detected sample, either because of warmer dust temperatures, lower IR luminosities, or both
Partition Functions, the Bekenstein Bound and Temperature Inversion in Anti-de Sitter Space and its Conformal Boundary
We reformulate the Bekenstein bound as the requirement of positivity of the
Helmholtz free energy at the minimum value of the function L=E- S/(2\pi R),
where R is some measure of the size of the system. The minimum of L occurs at
the temperature T=1/(2\pi R). In the case of n-dimensional anti-de Sitter
spacetime, the rather poorly defined size R acquires a precise definition in
terms of the AdS radius l, with R=l/(n-2). We previously found that the
Bekenstein bound holds for all known black holes in AdS. However, in this paper
we show that the Bekenstein bound is not generally valid for free quantum
fields in AdS, even if one includes the Casimir energy. Some other aspects of
thermodynamics in anti-de Sitter spacetime are briefly touched upon.Comment: Latex, 32 page
Non-local interactions in hydrodynamic turbulence at high Reynolds numbers: the slow emergence of scaling laws
We analyze the data stemming from a forced incompressible hydrodynamic
simulation on a grid of 2048^3 regularly spaced points, with a Taylor Reynolds
number of Re~1300. The forcing is given by the Taylor-Green flow, which shares
similarities with the flow in several laboratory experiments, and the
computation is run for ten turnover times in the turbulent steady state. At
this Reynolds number the anisotropic large scale flow pattern, the inertial
range, the bottleneck, and the dissipative range are clearly visible, thus
providing a good test case for the study of turbulence as it appears in nature.
Triadic interactions, the locality of energy fluxes, and structure functions of
the velocity increments are computed. A comparison with runs at lower Reynolds
numbers is performed, and shows the emergence of scaling laws for the relative
amplitude of local and non-local interactions in spectral space. The scalings
of the Kolmogorov constant, and of skewness and flatness of velocity
increments, performed as well and are consistent with previous experimental
results. Furthermore, the accumulation of energy in the small-scales associated
with the bottleneck seems to occur on a span of wavenumbers that is independent
of the Reynolds number, possibly ruling out an inertial range explanation for
it. Finally, intermittency exponents seem to depart from standard models at
high Re, leaving the interpretation of intermittency an open problem.Comment: 8 pages, 8 figure
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