537 research outputs found
Passive Scalar Structures in Supersonic Turbulence
We conduct a systematic numerical study of passive scalar structures in
supersonic turbulent flows. We find that the degree of intermittency in the
scalar structures increases only slightly as the flow changes from transonic to
highly supersonic, while the velocity structures become significantly more
intermittent. This difference is due to the absence of shock-like
discontinuities in the scalar field. The structure functions of the scalar
field are well described by the intermittency model of She and L\'{e}v\^{e}que
[Phys. Rev. Lett. 72, 336 (1994)], and the most intense scalar structures are
found to be sheet-like at all Mach numbers.Comment: 4 pages, 3 figures, to appear in PR
On the von Karman-Howarth equations for Hall MHD flows
The von Karman-Howarth equations are derived for three-dimensional (3D) Hall
magnetohydrodynamics (MHD) in the case of an homogeneous and isotropic
turbulence. From these equations, we derive exact scaling laws for the
third-order correlation tensors. We show how these relations are compatible
with previous heuristic and numerical results. These multi-scale laws provide a
relevant tool to investigate the non-linear nature of the high frequency
magnetic field fluctuations in the solar wind or, more generally, in any plasma
where the Hall effect is important.Comment: 11 page
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 Microstructure of Turbulent Flow
In 1941 a general theory of locally isotropic turbulence was proposed by Kolmogoroff which permitted the prediction of a number of laws of turbulent flow for large Reynolds numbers. The most important of these laws, the dependence of the mean square of the difference in velocities at two points on their distance and the dependence of the coefficient of turbulence diffusion on the scale of the phenomenon, were obtained by both Kolmogoroff and Obukhoff in the same year. At the present time these laws have been experimentally confirmed by direct measurements carried out in aerodynamic wind tunnels in the laboratory, in the atmosphere, and also on the ocean. In recent years in the Laboratory of Atmospheric Turbulence of the Geophysics Institute of the Soviet Academy of Sciences, a number of investigations have been conducted in which this theory was further developed. The results of several of these investigations are presented
One-Parameter Homothetic Motion in the Hyperbolic Plane and Euler-Savary Formula
In \cite{Mul} one-parameter planar motion was first introduced and the
relations between absolute, relative, sliding velocities (and accelerations) in
the Euclidean plane were obtained. Moreover, the relations
between the Complex velocities one-parameter motion in the Complex plane were
provided by \cite{Mul}. One-parameter planar homothetic motion was defined in
the Complex plane, \cite{Kur}. In this paper, analogous to homothetic motion in
the Complex plane given by \cite{Kur}, one-parameter planar homothetic motion
is defined in the Hyperbolic plane. Some characteristic properties about the
velocity vectors, the acceleration vectors and the pole curves are given.
Moreover, in the case of homothetic scale identically equal to 1, the
results given in \cite{Yuc} are obtained as a special case. In addition, three
hyperbolic planes, of which two are moving and the other one is fixed, are
taken into consideration and a canonical relative system for one-parameter
planar hyperbolic homothetic motion is defined. Euler-Savary formula, which
gives the relationship between the curvatures of trajectory curves, is obtained
with the help of this relative system
Spartan Random Processes in Time Series Modeling
A Spartan random process (SRP) is used to estimate the correlation structure
of time series and to predict (extrapolate) the data values. SRP's are
motivated from statistical physics, and they can be viewed as Ginzburg-Landau
models. The temporal correlations of the SRP are modeled in terms of
`interactions' between the field values. Model parameter inference employs the
computationally fast modified method of moments, which is based on matching
sample energy moments with the respective stochastic constraints. The
parameters thus inferred are then compared with those obtained by means of the
maximum likelihood method. The performance of the Spartan predictor (SP) is
investigated using real time series of the quarterly S&P 500 index. SP
prediction errors are compared with those of the Kolmogorov-Wiener predictor.
Two predictors, one of which explicit, are derived and used for extrapolation.
The performance of the predictors is similarly evaluated.Comment: 10 pages, 3 figures, Proceedings of APFA
Intermittency of Magnetohydrodynamic Turbulence: Astrophysical Perspective
Intermittency is an essential property of astrophysical fluids, which
demonstrate an extended inertial range. As intermittency violates
self-similarity of motions, it gets impossible to naively extrapolate the
properties of fluid obtained computationally with relatively low resolution to
the actual astrophysical situations. In terms of Astrophysics, intermittency
affects turbulent heating, momentum transfer, interaction with cosmic rays,
radio waves and many more essential processes. Because of its significance,
studies of intermittency call for coordinated efforts from both theorists and
observers. In terms of theoretical understanding we are still just scratching a
surface of a very rich subject. We have some theoretically well justified
models that are poorly supported by experiments, we also have She-Leveque
model, which could be vulnerable on theoretical grounds, but, nevertheless, is
well supported by experimental and laboratory data. I briefly discuss a rather
mysterious property of turbulence called ``extended self-similarity'' and the
possibilities that it opens for the intermittency research. Then I analyze
simulations of MHD intermittency performed by different groups and show that
their results do not contradict to each other. Finally, I discuss the
intermittency of density, intermittency of turbulence in the
viscosity-dominated regime as well as the intermittency of polarization of
Alfvenic modes. The latter provides an attractive solution to account for a
slower cascading rate that is observed in some of the numerical experiments. I
conclude by claiming that a substantial progress in the field may be achieved
by studies of the turbulence intermittency via observations.Comment: 14 pages, 7 figures, invited lecture at Trieste, published
International Journal of Modern Physics D, July 2
KPZ in one dimensional random geometry of multiplicative cascades
We prove a formula relating the Hausdorff dimension of a subset of the unit
interval and the Hausdorff dimension of the same set with respect to a random
path matric on the interval, which is generated using a multiplicative cascade.
When the random variables generating the cascade are exponentials of Gaussians,
the well known KPZ formula of Knizhnik, Polyakov and Zamolodchikov from quantum
gravity appears. This note was inspired by the recent work of Duplantier and
Sheffield proving a somewhat different version of the KPZ formula for Liouville
gravity. In contrast with the Liouville gravity setting, the one dimensional
multiplicative cascade framework facilitates the determination of the Hausdorff
dimension, rather than some expected box count dimension.Comment: 14 page
On the noise-induced passage through an unstable periodic orbit II: General case
Consider a dynamical system given by a planar differential equation, which
exhibits an unstable periodic orbit surrounding a stable periodic orbit. It is
known that under random perturbations, the distribution of locations where the
system's first exit from the interior of the unstable orbit occurs, typically
displays the phenomenon of cycling: The distribution of first-exit locations is
translated along the unstable periodic orbit proportionally to the logarithm of
the noise intensity as the noise intensity goes to zero. We show that for a
large class of such systems, the cycling profile is given, up to a
model-dependent change of coordinates, by a universal function given by a
periodicised Gumbel distribution. Our techniques combine action-functional or
large-deviation results with properties of random Poincar\'e maps described by
continuous-space discrete-time Markov chains.Comment: 44 pages, 4 figure
Conformal compactification and cycle-preserving symmetries of spacetimes
The cycle-preserving symmetries for the nine two-dimensional real spaces of
constant curvature are collectively obtained within a Cayley-Klein framework.
This approach affords a unified and global study of the conformal structure of
the three classical Riemannian spaces as well as of the six relativistic and
non-relativistic spacetimes (Minkowskian, de Sitter, anti-de Sitter, both
Newton-Hooke and Galilean), and gives rise to general expressions holding
simultaneously for all of them. Their metric structure and cycles (lines with
constant geodesic curvature that include geodesics and circles) are explicitly
characterized. The corresponding cyclic (Mobius-like) Lie groups together with
the differential realizations of their algebras are then deduced; this
derivation is new and much simpler than the usual ones and applies to any
homogeneous space in the Cayley-Klein family, whether flat or curved and with
any signature. Laplace and wave-type differential equations with conformal
algebra symmetry are constructed. Furthermore, the conformal groups are
realized as matrix groups acting as globally defined linear transformations in
a four-dimensional "conformal ambient space", which in turn leads to an
explicit description of the "conformal completion" or compactification of the
nine spaces.Comment: 43 pages, LaTe
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