2,882 research outputs found
Energy dynamics in a simulation of LAPD turbulence
Energy dynamics calculations in a 3D fluid simulation of drift wave
turbulence in the linear Large Plasma Device (LAPD) [W. Gekelman et al., Rev.
Sci. Inst. 62, 2875 (1991)] illuminate processes that drive and dissipate the
turbulence. These calculations reveal that a nonlinear instability dominates
the injection of energy into the turbulence by overtaking the linear drift wave
instability that dominates when fluctuations about the equilibrium are small.
The nonlinear instability drives flute-like () density
fluctuations using free energy from the background density gradient. Through
nonlinear axial wavenumber transfer to fluctuations, the
nonlinear instability accesses the adiabatic response, which provides the
requisite energy transfer channel from density to potential fluctuations as
well as the phase shift that causes instability. The turbulence characteristics
in the simulations agree remarkably well with experiment. When the nonlinear
instability is artificially removed from the system through suppressing
modes, the turbulence develops a coherent frequency spectrum
which is inconsistent with experimental data
Metastability of a granular surface in a spinning bucket
The surface shape of a spinning bucket of granular material is studied using
a continuum model of surface flow developed by Bouchaud et al. and Mehta et al.
An experimentally observed central subcritical region is reproduced by the
model. The subcritical region occurs when a metastable surface becomes unstable
via a nonlinear instability mechanism. The nonlinear instability mechanism
destabilizes the surface in large systems while a linear instability mechanism
is relevant for smaller systems. The range of angles in which the granular
surface is metastable vanishes with increasing system size.Comment: 8 pages with postscript figures, RevTex, to appear in Phys. Rev.
On the nonlinear instability of confined geometries
The discovery of a "weakly-turbulent" instability of anti-de Sitter spacetime
supports the idea that confined fluctuations eventually collapse to black holes
and suggests that similar phenomena might be possible in asymptotically-flat
spacetime, for example in the context of spherically symmetric oscillations of
stars or nonradial pulsations of ultracompact objects. Here we present a
detailed study of the evolution of the Einstein-Klein-Gordon system in a
cavity, with different types of deformations of the spectrum, including a mass
term for the scalar and Neumann conditions at the boundary. We provide
numerical evidence that gravitational collapse always occurs, at least for
amplitudes that are three orders of magnitude smaller than Choptuik's critical
value and corresponding to more than reflections before collapse. The
collapse time scales as the inverse square of the initial amplitude in the
small-amplitude limit. In addition, we find that fields with nonresonant
spectrum collapse earlier than in the fully-resonant case, a result that is at
odds with the current understanding of the process. Energy is transferred
through a direct cascade to high frequencies when the spectrum is resonant, but
we observe both direct- and inverse-cascade effects for nonresonant spectra.
Our results indicate that a fully-resonant spectrum might not be a crucial
ingredient of the conjectured turbulent instability and that other mechanisms
might be relevant. We discuss how a definitive answer to this problem is
essentially impossible within the present framework.Comment: 14 pages, 9 figures; v2:Some improvements in convergence results,
accepted for publication in Physical Review
AdS nonlinear instability: moving beyond spherical symmetry
Anti-de Sitter (AdS) is conjectured to be nonlinear unstable to a weakly
turbulent mechanism that develops a cascade towards high frequencies, leading
to black hole formation [1,2]. We give evidence that the gravitational sector
of perturbations behaves differently from the scalar one studied in [2]. In
contrast with [2], we find that not all gravitational normal modes of AdS can
be nonlinearly extended into periodic horizonless smooth solutions of the
Einstein equation. In particular, we show that even seeds with a single normal
mode can develop secular resonances, unlike the spherically symmetric scalar
field collapse studied in [2]. Moreover, if the seed has two normal modes, more
than one resonance can be generated at third order, unlike the spherical
collapse of [2]. We also show that weak turbulent perturbative theory predicts
the existence of direct and inverse cascades, with the former dominating the
latter for equal energy two-mode seeds.Comment: 7 pages, no figures, 2 table
Spectral theory for the failure of linear control in a nonlinear stochastic system
We consider the failure of localized control in a nonlinear spatially
extended system caused by extremely small amounts of noise. It is shown that
this failure occurs as a result of a nonlinear instability. Nonlinear
instabilities can occur in systems described by linearly stable but strongly
nonnormal evolution operators. In spatially extended systems the nonnormality
manifests itself in two different but complementary ways: transient
amplification and spectral focusing of disturbances. We show that temporal and
spatial aspects of the nonnormality and the type of nonlinearity are all
crucially important to understanding and describing the mechanism of nonlinear
instability. Presented results are expected to apply equally to other physical
systems where strong nonnormality is due to the presence of mean flow rather
than the action of control.Comment: Submitted to Physical Review
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