298 research outputs found
On the dual cascade in two-dimensional turbulence
We study the dual cascade scenario for two-dimensional turbulence driven by a
spectrally localized forcing applied over a finite wavenumber range
[k_\min,k_\max] (with k_\min > 0) such that the respective energy and
enstrophy injection rates and satisfy
k_\min^2\epsilon\le\eta\le k_\max^2\epsilon. The classical
Kraichnan--Leith--Batchelor paradigm, based on the simultaneous conservation of
energy and enstrophy and the scale-selectivity of the molecular viscosity,
requires that the domain be unbounded in both directions. For two-dimensional
turbulence either in a doubly periodic domain or in an unbounded channel with a
periodic boundary condition in the across-channel direction, a direct enstrophy
cascade is not possible. In the usual case where the forcing wavenumber is no
greater than the geometric mean of the integral and dissipation wavenumbers,
constant spectral slopes must satisfy and , where
() is the asymptotic slope of the range of wavenumbers lower
(higher) than the forcing wavenumber. The influence of a large-scale
dissipation on the realizability of a dual cascade is analyzed. We discuss the
consequences for numerical simulations attempting to mimic the classical
unbounded picture in a bounded domain.Comment: 22 pages, to appear in Physica
Experimental study of Taylor's hypothesis in a turbulent soap film
An experimental study of Taylor's hypothesis in a quasi-two-dimensional
turbulent soap film is presented. A two probe laser Doppler velocimeter enables
a non-intrusive simultaneous measurement of the velocity at spatially separated
points. The breakdown of Taylor's hypothesis is quantified using the cross
correlation between two points displaced in both space and time; correlation is
better than 90% for scales less than the integral scale. A quantitative study
of the decorrelation beyond the integral scale is presented, including an
analysis of the failure of Taylor's hypothesis using techniques from
predictability studies of turbulent flows. Our results are compared with
similar studies of 3D turbulence.Comment: 27 pages, + 19 figure
Improved emotion regulation after neurofeedback: A single-arm trial in patients with borderline personality disorder
Real-time functional magnetic resonance imaging (fMRI) neurofeedback training of amygdala hemodynamic activity directly targets a neurobiological mechanism, which contributes to emotion regulation problems in borderline personality disorder (BPD). However, it remains unknown which outcome measures can assess changes in emotion regulation and affective instability, associated with amygdala downregulation in a clinical trial. The current study directly addresses this question. Twenty-four female patients with a DSM-IV BPD diagnosis underwent four runs of amygdala neurofeedback. Before and after the training, as well as at a six-weeks follow-up assessment, participants completed measures of emotion dysregulation and affective instability at diverse levels of analysis (verbal report, clinical interview, ecological momentary assessment, emotion-modulated startle, heart rate variability, and fMRI). Participants were able to downregulate their amygdala blood oxygen-dependent (BOLD) response with neurofeedback. There was a decrease of BPD symptoms as assessed with the Zanarini rating scale for BPD (ZAN-BPD) and a decrease in emotion-modulated startle to negative pictures after training. Further explorative analyses suggest that patients indicated less affective instability, as seen by lower hour-to-hour variability in negative affect and inner tension in daily life. If replicated by an independent study, our results imply changes in emotion regulation and affective instability for several systems levels, including behavior and verbal report. Conclusions are limited due to the lack of a control group. A randomized controlled trial (RCT) will be needed to confirm effectiveness of the training
Inverse velocity statistics in two dimensional turbulence
We present a numerical study of two-dimensional turbulent flows in the
enstrophy cascade regime, with different large-scale forcings and energy sinks.
In particular, we study the statistics of more-than-differentiable velocity
fluctuations by means of two recently introduced sets of statistical
estimators, namely {\it inverse statistics} and {\it second order differences}.
We show that the 2D turbulent velocity field, , cannot be simply
characterized by its spectrum behavior, . There
exists a whole set of exponents associated to the non-trivial smooth
fluctuations of the velocity field at all scales. We also present a numerical
investigation of the temporal properties of measured in different
spatial locations.Comment: 9 pages, 12 figure
Dynamical equations for high-order structure functions, and a comparison of a mean field theory with experiments in three-dimensional turbulence
Two recent publications [V. Yakhot, Phys. Rev. E {\bf 63}, 026307, (2001) and
R.J. Hill, J. Fluid Mech. {\bf 434}, 379, (2001)] derive, through two different
approaches that have the Navier-Stokes equations as the common starting point,
a set of steady-state dynamic equations for structure functions of arbitrary
order in hydrodynamic turbulence. These equations are not closed. Yakhot
proposed a "mean field theory" to close the equations for locally isotropic
turbulence, and obtained scaling exponents of structure functions and an
expression for the tails of the probability density function of transverse
velocity increments. At high Reynolds numbers, we present some relevant
experimental data on pressure and dissipation terms that are needed to provide
closure, as well as on aspects predicted by the theory. Comparison between the
theory and the data shows varying levels of agreement, and reveals gaps
inherent to the implementation of the theory.Comment: 16 pages, 23 figure
Universality and saturation of intermittency in passive scalar turbulence
The statistical properties of a scalar field advected by the non-intermittent
Navier-Stokes flow arising from a two-dimensional inverse energy cascade are
investigated. The universality properties of the scalar field are directly
probed by comparing the results obtained with two different types of injection
mechanisms. Scaling properties are shown to be universal, even though
anisotropies injected at large scales persist down to the smallest scales and
local isotropy is not fully restored. Scalar statistics is strongly
intermittent and scaling exponents saturate to a constant for sufficiently high
orders. This is observed also for the advection by a velocity field rapidly
changing in time, pointing to the genericity of the phenomenon. The persistence
of anisotropies and the saturation are both statistical signatures of the
ramp-and-cliff structures observed in the scalar field.Comment: 4 pages, 8 figure
A striking correspondence between the dynamics generated by the vector fields and by the scalar parabolic equations
The purpose of this paper is to enhance a correspondence between the dynamics
of the differential equations on and those
of the parabolic equations on a bounded
domain . We give details on the similarities of these dynamics in the
cases , and and in the corresponding cases ,
and dim() respectively. In addition to
the beauty of such a correspondence, this could serve as a guideline for future
research on the dynamics of parabolic equations
Recent Developments in Understanding Two-dimensional Turbulence and the Nastrom-Gage Spectrum
Two-dimensional turbulence appears to be a more formidable problem than
three-dimensional turbulence despite the numerical advantage of working with
one less dimension. In the present paper we review recent numerical
investigations of the phenomenology of two-dimensional turbulence as well as
recent theoretical breakthroughs by various leading researchers. We also review
efforts to reconcile the observed energy spectrum of the atmosphere (the
spectrum) with the predictions of two-dimensional turbulence and
quasi-geostrophic turbulence.Comment: Invited review; accepted by J. Low Temp. Phys.; Proceedings for
Warwick Turbulence Symposium Workshop on Universal features in turbulence:
from quantum to cosmological scales, 200
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