84 research outputs found
Imbalanced Weak MHD Turbulence
MHD turbulence consists of waves that propagate along magnetic fieldlines, in
both directions. When two oppositely directed waves collide, they distort each
other, without changing their respective energies. In weak MHD turbulence, a
given wave suffers many collisions before cascading. "Imbalance" means that
more energy is going in one direction than the other. In general, MHD
turbulence is imbalanced. A number of complications arise for the imbalanced
cascade that are unimportant for the balanced one.
We solve weak MHD turbulence that is imbalanced. Of crucial importance is
that the energies going in both directions are forced to equalize at the
dissipation scale. We call this the "pinning" of the energy spectra. It affects
the entire inertial range.
Weak MHD turbulence is particularly interesting because perturbation theory
is applicable. Hence it can be described with a simple kinetic equation.
Galtier et al. (2000) derived this kinetic equation. We present a simpler, more
physical derivation, based on the picture of colliding wavepackets. In the
process, we clarify the role of the zero-frequency mode. We also explain why
Goldreich & Sridhar claimed that perturbation theory is inapplicable, and why
this claim is wrong. (Our "weak" is equivalent to Goldreich & Sridhar's
"intermediate.")
We perform numerical simulations of the kinetic equation to verify our
claims. We construct simplified model equations that illustrate the main
effects. Finally, we show that a large magnetic Prandtl number does not have a
significant effect, and that hyperviscosity leads to a pronounced bottleneck
effect.Comment: 43 pages, 7 figures, submitted to Ap
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
Kolmogorov turbulence in a random-force-driven Burgers equation
The dynamics of velocity fluctuations, governed by the one-dimensional
Burgers equation, driven by a white-in-time random force with the spatial
spectrum \overline{|f(k)|^2}\proptok^{-1}, is considered. High-resolution
numerical experiments conducted in this work give the energy spectrum
with . The observed two-point
correlation function reveals with the
"dynamical exponent" . High-order moments of velocity differences
show strong intermittency and are dominated by powerful large-scale shocks. The
results are compared with predictions of the one-loop renormalized perturbation
expansion.Comment: 13 LaTeX pages, psfig.sty macros, Phys. Rev. E 51, R2739 (1995)
Ultimate-state scaling in a shell model for homogeneous turbulent convection
An interesting question in turbulent convection is how the heat transport
depends on the strength of thermal forcing in the limit of very large thermal
forcing. Kraichnan predicted [Phys. Fluids {\bf 5}, 1374 (1962)] that the heat
transport measured by the Nusselt number (Nu) would depend on the strength of
thermal forcing measured by the Rayleigh number (Ra) as Nu Ra
with possible logarithmic corrections at very high Ra. This scaling behavior is
taken as a signature of the so-called ultimate state of turbulent convection.
The ultimate state was interpreted in the Grossmann-Lohse (GL) theory [J. Fluid
Mech. {\bf 407}, 27 (2000)] as a bulk-dominated state in which both the kinetic
and thermal dissipation are dominated by contributions from the bulk of the
flow with the boundary layers either broken down or playing no role in the heat
transport. In this paper, we study the dependence of Nu and the Reynolds number
(Re) measuring the root-mean-squared velocity fluctuations on Ra and the
Prandtl number (Pr) using a shell model for homogeneous turbulent convection
where buoyancy is acting directly on most of the scales. We find that Nu
RaPr and Re RaPr, which resemble the
ultimate-state scaling behavior for fluids with moderate Pr, but the presence
of a drag acting on the large scales is crucial in giving rise to such scaling.
This suggests that if buoyancy acts on most of the scales in the bulk of
turbulent convection at very high Ra, then the ultimate state cannot be a
bulk-dominated state
Inertial- and Dissipation-Range Asymptotics in Fluid Turbulence
We propose and verify a wave-vector-space version of generalized extended
self similarity and broaden its applicability to uncover intriguing, universal
scaling in the far dissipation range by computing high-order (\leq 20\/)
structure functions numerically for: (1) the three-dimensional, incompressible
Navier Stokes equation (with and without hyperviscosity); and (2) the GOY shell
model for turbulence. Also, in case (2), with Taylor-microscale Reynolds
numbers 4 \times 10^{4} \leq Re_{\lambda} \leq 3 \times 10^{6}\/, we find
that the inertial-range exponents (\zeta_{p}\/) of the order - p\/
structure functions do not approach their Kolmogorov value p/3\/ as
Re_{\lambda}\/ increases.Comment: RevTeX file, with six postscript figures. epsf.tex macro is used for
figure insertion. Packaged using the 'uufiles' utilit
Manifestation of anisotropy persistence in the hierarchies of MHD scaling exponents
The first example of a turbulent system where the failure of the hypothesis
of small-scale isotropy restoration is detectable both in the `flattening' of
the inertial-range scaling exponent hierarchy, and in the behavior of odd-order
dimensionless ratios, e.g., skewness and hyperskewness, is presented.
Specifically, within the kinematic approximation in magnetohydrodynamical
turbulence, we show that for compressible flows, the isotropic contribution to
the scaling of magnetic correlation functions and the first anisotropic ones
may become practically indistinguishable. Moreover, skewness factor now
diverges as the P\'eclet number goes to infinity, a further indication of
small-scale anisotropy.Comment: 4 pages Latex, 1 figur
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
Polyelectrolytes in the presence of multivalent ions: gelation versus segregation
We analyze solutions of strongly charged chains bridged by linkers such as
multivalent ions. The gelation induced by the strong short range electrostatic
attractions is dramatically suppressed by the long range electrostatic
correlations due to the charge along the uncrosslinked monomers and ions. A
modified Debye-Huckel approach of crosslinked clusters of charged chains is
used to determined the mean field gelation transition self-consistently. Highly
dilute polyelectrolyte solutions tend to segregate macroscopically. Semidilute
solutions can form gels if the Bjerrum length and the distance between
neighboring charged monomers along the chain are both greater than the ion
size
Structure factor of polymers interacting via a short range repulsive potential: application to hairy wormlike micelles
We use the Random Phase Approximation (RPA) to compute the structure factor,
S(q), of a solution of chains interacting through a soft and short range
repulsive potential V. Above a threshold polymer concentration, whose magnitude
is essentially controlled by the range of the potential, S(q) exhibits a peak
whose position depends on the concentration. We take advantage of the close
analogy between polymers and wormlike micelles and apply our model, using a
Gaussian function for V, to quantitatively analyze experimental small angle
neutron scattering profiles of semi-dilute solutions of hairy wormlike
micelles. These samples, which consist in surfactant self-assembled flexible
cylinders decorated by amphiphilic copolymer, provide indeed an appropriate
experimental model system to study the structure of sterically interacting
polymer solutions
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