11,222 research outputs found
The Magnetohydrodynamic Kelvin-Helmholtz Instability: A Three-Dimensional Study of Nonlinear Evolution
We investigate through high resolution 3D simulations the nonlinear evolution
of compressible magnetohydrodynamic flows subject to the Kelvin-Helmholtz
instability. We confirm in 3D flows the conclusion from our 2D work that even
apparently weak magnetic fields embedded in Kelvin-Helmholtz unstable plasma
flows can be fundamentally important to nonlinear evolution of the instability.
In fact, that statement is strengthened in 3D by this work, because it shows
how field line bundles can be stretched and twisted in 3D as the quasi-2D Cat's
Eye vortex forms out of the hydrodynamical motions. In our simulations twisting
of the field may increase the maximum field strength by more than a factor of
two over the 2D effect. If, by these developments, the Alfv\'en Mach number of
flows around the Cat's Eye drops to unity or less, our simulations suggest
magnetic stresses will eventually destroy the Cat's Eye and cause the plasma
flow to self-organize into a relatively smooth and apparently stable flow that
retains memory of the original shear. For our flow configurations the regime in
3D for such reorganization is , expressed in
terms of the Alfv\'en Mach number of the original velocity transition and the
initial Alfv\'en speed projected to the flow plan. For weaker fields the
instability remains essentially hydrodynamic in early stages, and the Cat's Eye
is destroyed by the hydrodynamic secondary instabilities of a 3D nature. Then,
the flows evolve into chaotic structures that approach decaying isotropic
turbulence. In this stage, there is considerable enhancement to the magnetic
energy due to stretching, twisting, and turbulent amplification, which is
retained long afterwards. The magnetic energy eventually catches up to the
kinetic energy, and the nature of flows become magnetohydrodynamic.Comment: 11 pages, 12 figures in degraded jpg format (2 in color), paper with
original quality figures available via ftp at
ftp://ftp.msi.umn.edu/pub/users/twj/mhdkh3dd.ps.gz or
ftp://canopus.chungnam.ac.kr/ryu/mhdkh3dd.ps.gz, to appear in The
Astrophysical Journa
Extraction of coherent structures in a rotating turbulent flow experiment
The discrete wavelet packet transform (DWPT) and discrete wavelet transform
(DWT) are used to extract and study the dynamics of coherent structures in a
turbulent rotating fluid. Three-dimensional (3D) turbulence is generated by
strong pumping through tubes at the bottom of a rotating tank (48.4 cm high,
39.4 cm diameter). This flow evolves toward two-dimensional (2D) turbulence
with increasing height in the tank. Particle Image Velocimetry (PIV)
measurements on the quasi-2D flow reveal many long-lived coherent vortices with
a wide range of sizes. The vorticity fields exhibit vortex birth, merger,
scattering, and destruction. We separate the flow into a low-entropy
``coherent'' and a high-entropy ``incoherent'' component by thresholding the
coefficients of the DWPT and DWT of the vorticity fields. Similar thresholdings
using the Fourier transform and JPEG compression together with the Okubo-Weiss
criterion are also tested for comparison. We find that the DWPT and DWT yield
similar results and are much more efficient at representing the total flow than
a Fourier-based method. Only about 3% of the large-amplitude coefficients of
the DWPT and DWT are necessary to represent the coherent component and preserve
the vorticity probability density function, transport properties, and spatial
and temporal correlations. The remaining small amplitude coefficients represent
the incoherent component, which has near Gaussian vorticity PDF, contains no
coherent structures, rapidly loses correlation in time, and does not contribute
significantly to the transport properties of the flow. This suggests that one
can describe and simulate such turbulent flow using a relatively small number
of wavelet or wavelet packet modes.Comment: experimental work aprox 17 pages, 11 figures, accepted to appear in
PRE, last few figures appear at the end. clarifications, added references,
fixed typo
On the small-scale structure of turbulence and its impact on the pressure field
Understanding the small-scale structure of incompressible turbulence and its
implications for the non-local pressure field is one of the fundamental
challenges in fluid mechanics. Intense velocity gradient structures tend to
cluster on a range of scales which affects the pressure through a Poisson
equation. Here we present a quantitative investigation of the spatial
distribution of these structures conditional on their intensity for
Taylor-based Reynolds numbers in the range [160, 380]. We find that the
correlation length, the second invariant of the velocity gradient, is
proportional to the Kolmogorov scale. It also is a good indicator for the
spatial localization of intense enstrophy and strain-dominated regions, as well
as the separation between them. We describe and quantify the differences in the
two-point statistics of these regions and the impact they have on the
non-locality of the pressure field as a function of the intensity of the
regions. Specifically, across the examined range of Reynolds numbers, the
pressure in strong rotation-dominated regions is governed by a
dissipation-scale neighbourhood. In strong strain-dominated regions, on the
other hand, it is determined primarily by a larger neighbourhood reaching
inertial scales.Comment: Accepted for publication by the Journal of Fluid Mechanic
Compressed Exponential Relaxation as Superposition of Dual Structure in Pattern Dynamics of Nematic Liquid Crystals
Soft-mode turbulence (SMT) is the spatiotemporal chaos observed in
homeotropically aligned nematic liquid crystals, where non-thermal fluctuations
are induced by nonlinear coupling between the Nambu-Goldstone and convective
modes. The net and modal relaxations of the disorder pattern dynamics in SMT
have been studied to construct the statistical physics of nonlinear
nonequilibrium systems. The net relaxation dynamics is well-described by a
compressed exponential function and the modal one satisfies a dual structure,
dynamic crossover accompanied by a breaking of time-reversal invariance.
Because the net relaxation is described by a weighted mean of the modal ones
with respect to the wave number, the compressed-exponential behavior emerges as
a superposition of the dual structure. Here, we present experimental results of
the power spectra to discuss the compressed-exponential behavior and the dual
structure from a viewpoint of the harmonic analysis. We also derive a
relationship of the power spectra from the evolution equation of the modal
autocorrelation function. The formula will be helpful to study non-thermal
fluctuations in experiments such as the scattering methods.Comment: 17pages, 3 figures, to be published on AIP conference proceedings for
"The 4th International Symposium on Slow Dynamics in Complex Systems
Large-scale anisotropy in scalar turbulence
The effect of anisotropy on the statistics of a passive tracer transported by
a turbulent flow is investigated. We show that under broad conditions an
arbitrarily small amount of anisotropy propagates to the large scales where it
eventually dominates the structure of the concentration field. This result is
obtained analytically in the framework of an exactly solvable model and
confirmed by numerical simulations of scalar transport in two-dimensional
turbulence
Heterogeneous volatility cascade in financial markets
Using high frequency data, we have studied empirically the change of
volatility, also called volatility derivative, for various time horizons. In
particular, the correlation between the volatility derivative and the
volatility realized in the next time period is a measure of the response
function of the market participants. This correlation shows explicitly the
heterogeneous structure of the market according to the characteristic time
horizons of the differents agents. It reveals a volatility cascade from long to
short time horizons, with a structure different from the one observed in
turbulence. Moreover, we have developed a new ARCH-type model which
incorporates the different groups of agents, with their characteristic memory.
This model reproduces well the empirical response function, and allows us to
quantify the importance of each group.Comment: 10 pages, 2 figures, To be published in Physica
Endogeneous Versus Exogeneous Shocks in Systems with Memory
Systems with long-range persistence and memory are shown to exhibit different
precursory as well as recovery patterns in response to shocks of exogeneous
versus endogeneous origins. By endogeneous, we envision either fluctuations
resulting from an underlying chaotic dynamics or from a stochastic forcing
origin which may be external or be an effective coarse-grained description of
the microscopic fluctuations. In this scenario, endogeneous shocks result from
a kind of constructive interference of accumulated fluctuations whose impacts
survive longer than the large shocks themselves. As a consequence, the recovery
after an endogeneous shock is in general slower at early times and can be at
long times either slower or faster than after an exogeneous perturbation. This
offers the tantalizing possibility of distinguishing between an endogeneous
versus exogeneous cause of a given shock, even when there is no ``smoking
gun.'' This could help in investigating the exogeneous versus self-organized
origins in problems such as the causes of major biological extinctions, of
change of weather regimes and of the climate, in tracing the source of social
upheaval and wars, and so on. Sornette, Malevergne and Muzy have already shown
how this concept can be applied concretely to differentiate the effects on
financial markets of the Sept. 11, 2001 attack or of the coup against Gorbachev
on Aug., 19, 1991 (exogeneous) from financial crashes such as Oct. 1987
(endogeneous).Comment: Latex document of 14 pages with 3 eps figure
Anomalous transport in Charney-Hasegawa-Mima flows
Transport properties of particles evolving in a system governed by the
Charney-Hasegawa-Mima equation are investigated. Transport is found to be
anomalous with a non linear evolution of the second moments with time. The
origin of this anomaly is traced back to the presence of chaotic jets within
the flow. All characteristic transport exponents have a similar value around
, which is also the one found for simple point vortex flows in the
literature, indicating some kind of universality. Moreover the law
linking the trapping time exponent within jets to the transport
exponent is confirmed and an accumulation towards zero of the spectrum of
finite time Lyapunov exponent is observed. The localization of a jet is
performed, and its structure is analyzed. It is clearly shown that despite a
regular coarse grained picture of the jet, motion within the jet appears as
chaotic but chaos is bounded on successive small scales.Comment: revised versio
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