369 research outputs found
Noise Correlations in Shear Flows
We consider the effects of a shear on velocity fluctuations in a flow. The
shear gives rise to a transient amplification that not only influences the
amplitude of perturbations but also their time correlations. We show that, in
the presence of white noise, time correlations of transversal velocity
components are exponential and that correlations of the longitudinal components
are exponential with an algebraic prefactor. Cross correlations between
transversal and downstream components are strongly asymmetric and provide a
clear indication of non-normal amplification. We suggest experimental tests of
our predictions.Comment: 6 pages, 2 figures, gzipped tar fil
Statistics of the inverse-cascade regime in two-dimensional magnetohydrodynamic turbulence
We present a detailed direct numerical simulation of statistically steady,
homogeneous, isotropic, two-dimensional magnetohydrodynamic (2D MHD)
turbulence. Our study concentrates on the inverse cascade of the magnetic
vector potential. We examine the dependence of the statistical properties of
such turbulence on dissipation and friction coefficients. We extend earlier
work sig- nificantly by calculating fluid and magnetic spectra, probability
distribution functions (PDFs) of the velocity, magnetic, vorticity, current,
stream-function, and magnetic-vector-potential fields and their increments. We
quantify the deviations of these PDFs from Gaussian ones by computing their
flatnesses and hyperflatnesses. We also present PDFs of the Okubo-Weiss
parameter, which distin- guishes between vortical and extensional flow regions,
and its magnetic analog. We show that the hyperflatnesses of PDFs of the
increments of the stream-function and the magnetic vector potential exhibit
significant scale dependence and we examine the implication of this for the
multiscaling of structure functions. We compare our results with those of
earlier studies
Melting of a nonequilibrium vortex crystal in a fluid film with polymers : elastic versus fluid turbulence
We perform a direct numerical simulation (DNS) of the forced, incompressible
two-dimensional Navier-Stokes equation coupled with the FENE-P equations for
the polymer-conformation tensor. The forcing is such that, without polymers and
at low Reynolds numbers \mbox{Re}, the film attains a steady state that is a
square lattice of vortices and anti-vortices. We find that, as we increase the
Weissenberg number \mbox{Wi}, a sequence of nonequilibrium phase transitions
transforms this lattice, first to spatially distorted, but temporally steady,
crystals and then to a sequence of crystals that oscillate in time,
periodically, at low \mbox{Wi}, and quasiperiodically, for slightly larger
\mbox{Wi}. Finally, the system becomes disordered and displays spatiotemporal
chaos and elastic turbulence. We then obtain the nonequilibrium phase diagram
for this system, in the \mbox{Wi} - \Omega plane, where \Omega \propto
{\mbox{Re}}, and show that (a) the boundary between the crystalline and
turbulent phases has a complicated, fractal-type character and (b) the
Okubo-Weiss parameter provides us with a natural measure for
characterizing the phases and transitions in this diagram.Comment: 16 pages, 17 figure
Multiscaling in superfluid turbulence: A shell-model study
We examine the multiscaling behavior of the normal- and superfluid-velocity
structure functions in three-dimensional superfluid turbulence by using a shell
model for the three-dimensional (3D) Hall-Vinen-Bekharevich-Khalatnikov (HVBK)
equations. Our 3D-HVBK shell model is based on the Gledzer-Okhitani-Yamada
(GOY) shell model. We examine the dependence of the multiscaling exponents on
the normal-fluid fraction and the mutual-friction coefficients. Our extensive
study of the 3D-HVBK shell model shows that the multiscaling behavior of the
velocity structure functions in superfluid turbulence is more complicated than
it is in fluid turbulence.Comment: 12 pages, 6 figure
Instability of spiral and scroll waves in the presence of a gradient in the fibroblast density: the effects of fibroblast-myocyte coupling
Fibroblast-myocyte coupling can modulate electrical-wave dynamics in cardiac
tissue. In diseased hearts, the distribution of fibroblasts is heterogeneous,
so there can be gradients in the fibroblast density (henceforth we call this
GFD) especially from highly injured regions, like infarcted or ischemic zones,
to less-wounded regions of the tissue. Fibrotic hearts are known to be prone to
arrhythmias, so it is important to understand the effects of GFD in the
formation and sustenance of arrhythmic re- entrant waves, like spiral or scroll
waves. Therefore, we investigate the effects of GFD on the stability of spiral
and scroll waves of electrical activation in a state-of-the- art mathematical
model for cardiac tissue in which we also include fibroblasts. By introducing
GFD in controlled ways, we show that spiral and scroll waves can be unstable in
the presence of GFDs because of regions with varying spiral or scroll-wave
frequency {\omega}, induced by the GFD. We examine the effects of the resting
membrane potential of the fibroblast and the number of fibroblasts attached to
the myocytes on the stability of these waves. Finally, we show that the
presence of GFDs can lead to the formation of spiral waves at high-frequency
pacing.Comment: 20 pages, 15 figure
Turbulence in the two-dimensional Fourier-truncated Gross-Pitaevskii equation
We undertake a systematic, direct numerical simulation (DNS) of the
two-dimensional, Fourier-truncated, Gross-Pitaevskii equation to study the
turbulent evolutions of its solutions for a variety of initial conditions and a
wide range of parameters. We find that the time evolution of this system can be
classified into four regimes with qualitatively different statistical
properties. First, there are transients that depend on the initial conditions.
In the second regime, power-law scaling regions, in the energy and the
occupation-number spectra, appear and start to develop; the exponents of these
power-laws and the extents of the scaling regions change with time and depended
on the initial condition. In the third regime, the spectra drop rapidly for
modes with wave numbers and partial thermalization takes place for
modes with ; the self-truncation wave number depends on the
initial conditions and it grows either as a power of or as .
Finally, in the fourth regime, complete-thermalization is achieved and, if we
account for finite-size effects carefully, correlation functions and spectra
are consistent with their nontrivial Berezinskii-Kosterlitz-Thouless forms.Comment: 30 pages, 12 figure
Homogeneous Isotropic Superfluid Turbulence in Two Dimensions: Inverse and Forward Cascades in the Hall-Vinen-Bekharevich-Khalatnikov model
We present the first direct-numerical-simulation study of the statistical
properties of two-dimensional superfluid turbulence in the
Hall-Vinen-Bekharevich-Khalatnikov two-fluid model. We show that both
normal-fluid and superfluid energy spectra can exhibit two power-law regimes,
the first associated with an inverse cascade of energy and the second with the
forward cascade of enstrophy. We quantify the mutual-friction-induced alignment
of normal and superfluid velocities by obtaining probability distribution
functions of the angle between them and the ratio of their moduli. Our study
leads to specific suggestions for experiments
Particles and Fields in Superfluids: Insights from the Two-dimensional Gross-Pitaevskii Equation
We carry out extensive direct numerical simulations (DNSs) to investigate the
interaction of active particles and fields in the two-dimensional (2D)
Gross-Pitaevskii (GP) superfluid, in both simple and turbulent flows. The
particles are active in the sense that they affect the superfluid even as they
are affected by it. We tune the mass of the particles, which is an important
control parameter. At the one-particle level, we show how light, neutral, and
heavy particles move in the superfluid, when a constant external force acts on
them; in particular, beyond a critical velocity, at which a vortex-antivortex
pair is emitted, particle motion can be periodic or chaotic. We demonstrate
that the interaction of a particle with vortices leads to dynamics that depends
sensitively on the particle characteristics. We also demonstrate that
assemblies of particles and vortices can have rich, and often turbulent
spatiotemporal evolution. In particular, we consider the dynamics of the
following illustrative initial configurations: (a) one particle placed in front
of a translating vortex-antivortex pair; (b) two particles placed in front of a
translating vortex-antivortex pair; (c) a single particle moving in the
presence of counter-rotating vortex clusters; and (d) four particles in the
presence of counter-rotating vortex clusters. We compare our work with earlier
studies and examine its implications for recent experimental studies in
superfluid Helium and Bose-Einstein condensates.Comment: 24 figure
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