621 research outputs found
Multi-time, multi-scale correlation functions in turbulence and in turbulent models
A multifractal-like representation for multi-time multi-scale velocity
correlation in turbulence and dynamical turbulent models is proposed. The
importance of subleading contributions to time correlations is highlighted. The
fulfillment of the dynamical constraints due to the equations of motion is
thoroughly discussed. The prediction stemming from this representation are
tested within the framework of shell models for turbulence.Comment: 18 pages, 4 eps figure
On the elimination of the sweeping interactions from theories of hydrodynamic turbulence
In this paper, we revisit the claim that the Eulerian and quasi-Lagrangian
same time correlation tensors are equal. This statement allows us to transform
the results of an MSR quasi-Lagrangian statistical theory of hydrodynamic
turbulence back to the Eulerian representation. We define a hierarchy of
homogeneity symmetries between incremental homogeneity and global homogeneity.
It is shown that both the elimination of the sweeping interactions and the
derivation of the 4/5-law require a homogeneity assumption stronger than
incremental homogeneity but weaker than global homogeneity. The
quasi-Lagrangian transformation, on the other hand, requires an even stronger
homogeneity assumption which is many-time rather than one-time but still weaker
than many-time global homogeneity. We argue that it is possible to relax this
stronger assumption and still preserve the conclusions derived from theoretical
work based on the quasi-Lagrangian transformation.Comment: v1: submitted to Physica D. v2: major revisions; resubmitted to
Physica D. v3: minor revisions requested by referee
On role of symmetries in Kelvin wave turbulence
E.V. Kozik and B.V. Svistunov (KS) paper "Symmetries and Interaction
Coefficients of Kelvin waves", arXiv:1006.1789v1, [cond-mat.other] 9 Jun 2010,
contains a comment on paper "Symmetries and Interaction coefficients of Kelvin
waves", V. V. Lebedev and V. S. L'vov, arXiv:1005.4575, 25 May 2010. It relies
mainly on the KS text "Geometric Symmetries in Superfluid Vortex Dynamics}",
arXiv:1006.0506v1 [cond-mat.other] 2 Jun 2010. The main claim of KS is that a
symmetry argument prevents linear in wavenumber infrared asymptotics of the
interaction vertex and thereby implies locality of the Kelvin wave spectrum
previously obtained by these authors. In the present note we reply to their
arguments. We conclude that there is neither proof of locality nor any
refutation of the possibility of linear asymptotic behavior of interaction
vertices in the texts of KS
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
Fluctuation-response relation in turbulent systems
We address the problem of measuring time-properties of Response Functions
(Green functions) in Gaussian models (Orszag-McLaughin) and strongly
non-Gaussian models (shell models for turbulence). We introduce the concept of
{\it halving time statistics} to have a statistically stable tool to quantify
the time decay of Response Functions and Generalized Response Functions of high
order. We show numerically that in shell models for three dimensional
turbulence Response Functions are inertial range quantities. This is a strong
indication that the invariant measure describing the shell-velocity
fluctuations is characterized by short range interactions between neighboring
shells
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.
Symmetries and Interaction coefficients of Kelvin waves
We considered symmetry restriction on the interaction coefficients of Kelvin
waves and demonstrated that linear in small wave vector asymptotic is not
forbidden, as one can expect by naive reasoning.Comment: 4 pages, submitted to J. of Low Temp. Phy
- …