2,665 research outputs found

### Two-point velocity average of turbulence: statistics and their implications

For turbulence, although the two-point velocity difference u(x+r)-u(x) at
each scale r has been studied in detail, the velocity average [u(x+r)+u(x)]/2
has not thus far. Theoretically or experimentally, we find interesting features
of the velocity average. It satisfies an exact scale-by-scale energy budget
equation. The flatness factor varies with the scale r in a universal manner.
These features are not consistent with the existing assumption that the
velocity average is independent of r and represents energy-containing
large-scale motions alone. We accordingly propose that it represents motions
over scales >= r as long as the velocity difference represents motions at the
scale r.Comment: 8 pages, accepted by Physics of Fluids (see http://pof.aip.org/

### Entropy and Area in Loop Quantum Gravity

Black hole thermodynamics suggests that the maximum entropy that can be
contained in a region of space is proportional to the area enclosing it rather
than its volume. I argue that this follows naturally from loop quantum gravity
and a result of Kolmogorov and Bardzin' on the the realizability of networks in
three dimensions. This represents an alternative to other approaches in which
some sort of correlation between field configurations helps limit the degrees
of freedom within a region. It also provides an approach to thinking about
black hole entropy in terms of states inside rather than on its surface.
Intuitively, a spin network complicated enough to imbue a region with volume
only lets that volume grow as quickly as the area bounding it.Comment: 7 pages, this essay received an Honourable Mention in the Gravity
Research Foundation Essay Competition 2005; reformatted for IJMP (accepted
for publication) with minor typographical corrections and some extended
discussio

### Relation between shear parameter and Reynolds number in statistically stationary turbulent shear flows

Studies of the relation between the shear parameter S^* and the Reynolds
number Re are presented for a nearly homogeneous and statistically stationary
turbulent shear flow. The parametric investigations are in line with a
generalized perspective on the return to local isotropy in shear flows that was
outlined recently [Schumacher, Sreenivasan and Yeung, Phys. Fluids, vol.15, 84
(2003)]. Therefore, two parameters, the constant shear rate S and the level of
initial turbulent fluctuations as prescribed by an energy injection rate
epsilon_{in}, are varied systematically. The investigations suggest that the
shear parameter levels off for larger Reynolds numbers which is supported by
dimensional arguments. It is found that the skewness of the transverse
derivative shows a different decay behavior with respect to Reynolds number
when the sequence of simulation runs follows different pathways across the
two-parameter plane. The study can shed new light on different interpretations
of the decay of odd order moments in high-Reynolds number experiments.Comment: 9 pages, 9 Postscript figure

### Shear Effects in Non-Homogeneous Turbulence

Motivated by recent experimental and numerical results, a simple unifying
picture of intermittency in turbulent shear flows is suggested. Integral
Structure Functions (ISF), taking into account explicitly the shear intensity,
are introduced on phenomenological grounds. ISF can exhibit a universal scaling
behavior, independent of the shear intensity. This picture is in satisfactory
agreement with both experimental and numerical data. Possible extension to
convective turbulence and implication on closure conditions for Large-Eddy
Simulation of non-homogeneous flows are briefly discussed.Comment: 4 pages, 5 figure

### The Kelvin-wave cascade in the vortex filament model

The energy transfer mechanism in zero temperature superfluid turbulence of
helium-4 is still a widely debated topic. Currently, the main hypothesis is
that weakly nonlinear interacting Kelvin waves transfer energy to sufficiently
small scales such that energy is dissipated as heat via phonon excitations.
Theoretically, there are at least two proposed theories for Kelvin-wave
interactions. We perform the most comprehensive numerical simulation of weakly
nonlinear interacting Kelvin-waves to date and show, using a specially designed
numerical algorithm incorporating the full Biot-Savart equation, that our
results are consistent with nonlocal six-wave Kelvin wave interactions as
proposed by L'vov and Nazarenko.Comment: 6 pages, 6 figure

### Scaling Relations of Compressible MHD Turbulence

We study scaling relations of compressible strongly magnetized turbulence. We
find a good correspondence of our results with the Fleck (1996) model of
compressible hydrodynamic turbulence. In particular, we find that the
density-weighted velocity, i.e. $u \equiv \rho^{1/3} v$, proposed in Kritsuk et
al. (2007) obeys the Kolmogorov scaling, i.e. $E_{u}(k)\sim k^{-5/3}$ for the
high Mach number turbulence. Similarly, we find that the exponents of the third
order structure functions for $u$ stay equal to unity for the all the Mach
numbers studied. The scaling of higher order correlations obeys the She-Leveque
(1994) scalings corresponding to the two-dimensional dissipative structures,
and this result does not change with the Mach number either. In contrast to $v$
which exhibits different scaling parallel and perpendicular to the local
magnetic field, the scaling of $u$ is similar in both directions. In addition,
we find that the peaks of density create a hierarchy in which both physical and
column densities decrease with the scale in accordance to the Fleck (1996)
predictions. This hierarchy can be related ubiquitous small ionized and neutral
structures (SINS) in the interstellar gas. We believe that studies of
statistics of the column density peaks can provide both consistency check for
the turbulence velocity studies and insight into supersonic turbulence, when
the velocity information is not available.Comment: 4 pages, 5 figure

### Self-organization in turbulence as a route to order in plasma and fluids

Transitions from turbulence to order are studied experimentally in thin fluid
layers and magnetically confined toroidal plasma. It is shown that turbulence
self-organizes through the mechanism of spectral condensation. The spectral
redistribution of the turbulent energy leads to the reduction in the turbulence
level, generation of coherent flow, reduction in the particle diffusion and
increase in the system's energy. The higher order state is sustained via the
nonlocal spectral coupling of the linearly unstable spectral range to the
large-scale mean flow. The similarity of self-organization in two-dimensional
fluids and low-to-high confinement transitions in plasma suggests the
universality of the mechanism.Comment: 5 pages, 4 figure

### Inertial Range Scaling, Karman-Howarth Theorem and Intermittency for Forced and Decaying Lagrangian Averaged MHD in 2D

We present an extension of the Karman-Howarth theorem to the Lagrangian
averaged magnetohydrodynamic (LAMHD-alpha) equations. The scaling laws
resulting as a corollary of this theorem are studied in numerical simulations,
as well as the scaling of the longitudinal structure function exponents
indicative of intermittency. Numerical simulations for a magnetic Prandtl
number equal to unity are presented both for freely decaying and for forced two
dimensional MHD turbulence, solving directly the MHD equations, and employing
the LAMHD-alpha equations at 1/2 and 1/4 resolution. Linear scaling of the
third-order structure function with length is observed. The LAMHD-alpha
equations also capture the anomalous scaling of the longitudinal structure
function exponents up to order 8.Comment: 34 pages, 7 figures author institution addresses added magnetic
Prandtl number stated clearl

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