86 research outputs found
Bifractality of the Devil's staircase appearing in the Burgers equation with Brownian initial velocity
It is shown that the inverse Lagrangian map for the solution of the Burgers
equation (in the inviscid limit) with Brownian initial velocity presents a
bifractality (phase transition) similar to that of the Devil's staircase for
the standard triadic Cantor set. Both heuristic and rigorous derivations are
given. It is explained why artifacts can easily mask this phenomenon in
numerical simulations.Comment: 12 pages, LaTe
Single-point velocity distribution in turbulence
We show that the tails of the single-point velocity probability distribution
function (PDF) are generally non-Gaussian in developed turbulence. By using
instanton formalism for the Navier-Stokes equation, we establish the relation
between the PDF tails of the velocity and those of the external forcing. In
particular, we show that a Gaussian random force having correlation scale
and correlation time produces velocity PDF tails at . For a short-correlated forcing
when there is an intermediate asymptotics at .Comment: 9 pages, revtex, no figure
Observation of inertial energy cascade in interplanetary space plasma
We show in this article direct evidence for the presence of an inertial
energy cascade, the most characteristic signature of hydromagnetic turbulence
(MHD), in the solar wind as observed by the Ulysses spacecraft. After a brief
rederivation of the equivalent of Yaglom's law for MHD turbulence, we show that
a linear relation is indeed observed for the scaling of mixed third order
structure functions involving Els\"asser variables. This experimental result,
confirming the prescription stemming from a theorem for MHD turbulence, firmly
establishes the turbulent character of low-frequency velocity and magnetic
field fluctuations in the solar wind plasma
Pdf's of Derivatives and Increments for Decaying Burgers Turbulence
A Lagrangian method is used to show that the power-law with a -7/2 exponent
in the negative tail of the pdf of the velocity gradient and of velocity
increments, predicted by E, Khanin, Mazel and Sinai (1997 Phys. Rev. Lett. 78,
1904) for forced Burgers turbulence, is also present in the unforced case. The
theory is extended to the second-order space derivative whose pdf has power-law
tails with exponent -2 at both large positive and negative values and to the
time derivatives. Pdf's of space and time derivatives have the same
(asymptotic) functional forms. This is interpreted in terms of a "random Taylor
hypothesis".Comment: LATEX 8 pages, 3 figures, to appear in Phys. Rev.
Universality of Velocity Gradients in Forced Burgers Turbulence
It is demonstrated that Burgers turbulence subject to large-scale
white-noise-in-time random forcing has a universal power-law tail with exponent
-7/2 in the probability density function of negative velocity gradients, as
predicted by E, Khanin, Mazel and Sinai (1997, Phys. Rev. Lett. 78, 1904). A
particle and shock tracking numerical method gives about five decades of
scaling. Using a Lagrangian approach, the -7/2 law is related to the shape of
the unstable manifold associated to the global minimizer.Comment: 4 pages, 2 figures, RevTex4, published versio
Probability density function of turbulent velocity fluctuation
The probability density function (PDF) of velocity fluctuations is studied
experimentally for grid turbulence in a systematical manner. At small distances
from the grid, where the turbulence is still developing, the PDF is
sub-Gaussian. At intermediate distances, where the turbulence is fully
developed, the PDF is Gaussian. At large distances, where the turbulence has
decayed, the PDF is hyper-Gaussian. The Fourier transforms of the velocity
fluctuations always have Gaussian PDFs. At intermediate distances from the
grid, the Fourier transforms are statistically independent of each other. This
is the necessary and sufficient condition for Gaussianity of the velocity
fluctuations. At small and large distances, the Fourier transforms are
dependent.Comment: 7 pages, 8 figures in a PS file, to appear in Physical Review
Probability density function of turbulent velocity fluctuations in rough-wall boundary layer
The probability density function of single-point velocity fluctuations in
turbulence is studied systematically using Fourier coefficients in the
energy-containing range. In ideal turbulence where energy-containing motions
are random and independent, the Fourier coefficients tend to Gaussian and
independent of each other. Velocity fluctuations accordingly tend to Gaussian.
However, if energy-containing motions are intermittent or contaminated with
bounded-amplitude motions such as wavy wakes, the Fourier coefficients tend to
non-Gaussian and dependent of each other. Velocity fluctuations accordingly
tend to non-Gaussian. These situations are found in our experiment of a
rough-wall boundary layer.Comment: 6 pages, to appear in Physical Review
Longitudinal Structure Functions in Decaying and Forced Turbulence
In order to reliably compute the longitudinal structure functions in decaying
and forced turbulence, local isotropy is examined with the aid of the isotropic
expression of the incompressible conditions for the second and third order
structure functions. Furthermore, the Karman-Howarth-Kolmogorov relation is
investigated to examine the effects of external forcing and temporally
decreasing of the second order structure function. On the basis of these
investigations, the scaling range and exponents of the longitudinal
structure functions are determined for decaying and forced turbulence with the
aid of the extended-self-similarity (ESS) method. We find that 's are
smaller, for , in decaying turbulence than in forced turbulence. The
reasons for this discrepancy are discussed. Analysis of the local slopes of the
structure functions is used to justify the ESS method.Comment: 15 pages, 16 figure
- âŠ