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## Dynamical bar-mode instability in rotating and magnetized relativistic stars

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 19/08/2013

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We present three-dimensional simulations of the dynamical bar-mode
instability in magnetized and differentially rotating stars in full general
relativity. Our focus is on the effects that magnetic fields have on the
dynamics and the onset of the instability. In particular, we perform
ideal-magnetohydrodynamics simulations of neutron stars that are known to be
either stable or unstable against the purely hydrodynamical instability, but to
which a poloidal magnetic field in the range of $10^{14}$--$10^{16}$ G is
superimposed initially. As expected, the differential rotation is responsible
for the shearing of the poloidal field and the consequent linear growth in time
of the toroidal magnetic field. The latter rapidly exceeds in strength the
original poloidal one, leading to a magnetic-field amplification in the the
stars. Weak initial magnetic fields, i.e. $ \lesssim 10^{15}$ G, have
negligible effects on the development of the dynamical bar-mode instability,
simply braking the stellar configuration via magnetic-field shearing, and over
a timescale for which we derived a simple algebraic expression. On the other
hand, strong magnetic fields, i.e. $\gtrsim 10^{16}$ G, can suppress the
instability completely, with the precise threshold being dependent also on the
amount of rotation. As a result...

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## Potential vorticity dynamics in the framework of disk shallow-water theory: II. Mixed Barotropic-Baroclinic Instability

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 07/03/2012

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We extend exploration of potential vorticity instabilities in cold
astrophysical disks whose mean states are baroclinic. In particular, we seek to
demonstrate the potential existence of traditional baroclinic instabilities of
meteorological studies in a simplified two-layer Philips Disk Model. Each disk
layer is of constant but differing densities. The resulting mean azimuthal
velocity profile shows a variation in the vertical direction implying that the
system is baroclinic in the mean state. The stability of the system is treated
in the context of disk shallow water theory wherein azimuthal disturbances are
much longer than the corresponding radial or vertical scales. The normal-mode
problem is solved numerically using two different methods. The results of a
symmetric single layer barotropic model is considered and it is found that
instability persists for models in which the potential vorticity profiles are
not symmetric, consistent with previous results. The instaiblity is interpreted
in terms of interacting Rossby waves. For a two layer system in which the flow
is fundamentally baroclinic we report here that instability takes on the form
of mixed barotropic-baroclinic type: instability occurs but it qualitatively
follows the pattern of instability found in the barotropic models. Instability
arises because of the phase locking and interaction of the Rossby waves between
the two layers. The strength of the instability weakens as the density contrast
between layers increases. (For full abstract see article.); Comment: Under consideration for publication in Astronomy and Astrophysics.
Comments to the author welcome

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## Spinning down newborn neutron stars: nonlinear development of the r-mode instability

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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We model the nonlinear saturation of the r-mode instability via three-mode
couplings and the effects of the instability on the spin evolution of young
neutron stars. We include one mode triplet consisting of the r-mode and two
near resonant inertial modes that couple to it. We find that the spectrum of
evolutions is more diverse than previously thought. The evolution of the star
is dynamic and initially dominated by fast neutrino cooling. Nonlinear effects
become important when the r-mode amplitude grows above its first parametric
instability threshold. The balance between neutrino cooling and viscous heating
plays an important role in the evolution. Depending on the initial r-mode
amplitude, and on the strength of the viscosity and of the cooling this balance
can occur at different temperatures. If thermal equilibrium occurs on the
r-mode stability curve, where gravitational driving equals viscous damping, the
evolution may be adequately described by a one-mode model. Otherwise, nonlinear
effects are important and lead to various more complicated scenarios. Once
thermal balance occurs, the star spins-down oscillating between thermal
equilibrium states until the instability is no longer active. For lower
viscosity we observe runaway behavior in which the r-mode amplitude passes
several parametric instability thresholds. In this case more modes need to be
included to model the evolution accurately. In the most optimistic case...

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## A search for non-pulsating, chemically normal stars in the $\delta$ Scuti instability strip using Kepler data

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 23/12/2014

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We identify stars in the $\delta$ Sct instability strip that do not pulsate
in p modes at the 50-$\mu$mag limit, using Kepler data. Spectral classification
and abundance analyses from high-resolution spectroscopy allow us to identify
chemically peculiar stars, in which the absence of pulsations is not
surprising. The remaining stars are chemically normal, yet they are not
$\delta$ Sct stars. Their lack of observed p modes cannot be explained through
any known mechanism. However, they are mostly distributed around the edges of
the $\delta$ Sct instability strip, which allows for the possibility that they
actually lie outside the strip once the uncertainties are taken into account.
We investigated the possibility that the non-pulsators inside the instability
strip could be unresolved binary systems, having components that both lie
outside the instability strip. If misinterpreted as single stars, we found that
such binaries could generate temperature discrepancies of $\sim$300 K -- larger
than the spectroscopic uncertainties, and fully consistent with the
observations. After these considerations, there remains one chemically normal
non-pulsator that lies in the middle of the instability strip. This star is a
challenge to pulsation theory. However...

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## Forming Planetesimals by Gravitational Instability: I. The Role of the Richardson Number in Triggering the Kelvin-Helmholtz Instability

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 01/10/2010

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Gravitational instability (GI) of a dust-rich layer at the midplane of a
gaseous circumstellar disk is one proposed mechanism to form planetesimals, the
building blocks of rocky planets and gas giant cores. Self-gravity competes
against the Kelvin-Helmholtz instability (KHI): gradients in dust content drive
a vertical shear which risks overturning the dusty subdisk and forestalling GI.
To understand the conditions under which the disk can resist the KHI, we
perform 3D simulations of stratified subdisks in the limit that dust particles
are small and aerodynamically well coupled to gas. This limit screens out the
streaming instability and isolates the KHI. Each subdisk is assumed to have a
vertical density profile given by a spatially constant Richardson number Ri. We
vary Ri and the midplane dust-to-gas ratio mu and find that the critical
Richardson number dividing KH-unstable from KH-stable flows is not unique;
rather Ri_crit grows nearly linearly with mu for mu=0.3-10. Only for disks of
bulk solar metallicity is Ri_crit ~ 0.2, close to the classical value. Our
results suggest that a dusty sublayer can gravitationally fragment and
presumably spawn planetesimals if embedded within a solar metallicity gas disk
~4x more massive than the minimum-mass solar nebula; or a minimum-mass disk
having ~3x solar metallicity; or some intermediate combination of these two
possibilities. Gravitational instability seems possible without resorting to
the streaming instability or to turbulent concentration of particles.; Comment: Accepted to ApJ

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## Thermo-Resistive Instability of Hot Planetary Atmospheres

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 14/06/2012

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The atmospheres of hot Jupiters and other strongly-forced exoplanets are
susceptible to a thermal instability in the presence of ohmic dissipation, weak
magnetic drag and strong winds. The instability occurs in radiatively-dominated
atmospheric regions when the ohmic dissipation rate increases with temperature
faster than the radiative (cooling) rate. The instability domain covers a
specific range of atmospheric pressures and temperatures, typically P ~ 3-300
mbar and T ~ 1500-2500K for hot Jupiters, which makes it a candidate mechanism
to explain the dayside thermal "inversions" inferred for a number of such
exoplanets. The instability is suppressed by high levels of non-thermal
photoionization, in possible agreement with a recently established
observational trend. We highlight several shortcomings of the instability
treatment presented here. Understanding the emergence and outcome of the
instability, which should result in locally hotter atmospheres with stronger
levels of drag, will require global non-linear atmospheric models with adequate
MHD prescriptions.; Comment: 13 pages, 3 figures, accepted for publication in ApJL

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## On the linear growth mechanism driving the stationary accretion shock instability

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 06/12/2011

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During stellar core collapse, which eventually leads to a supernovae
explosion, the stalled shock is unstable due to the standing accretion shock
instability (SASI). This instability induces large-scale non spherical
oscillations of the shock, which have crucial consequences on the dynamics and
the geometry of the explosion. While the existence of this instability has been
firmly established, its physical origin remains somewhat uncertain. Two
mechanisms have indeed been proposed to explain its linear growth. The first is
an advective-acoustic cycle, where the instability results from the interplay
between advected perturbations (entropy and vorticity) and an acoustic wave.
The second mechanism is purely acoustic and assumes that the shock is able to
amplify trapped acoustic waves. Several arguments favouring the
advective-acoustic cycle have already been proposed, however none was entirely
conclusive for realistic flow parameters. In this article we give two new
arguments which unambiguously show that the instability is not purely acoustic,
and should be attributed to the advective-acoustic cycle. First, we extract a
radial propagation timescale by comparing the frequencies of several unstable
harmonics that differ only by their radial structure. The extracted time
matches the advective-acoustic time but strongly disagrees with a purely
acoustic interpretation. Second...

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## The Role of the Radial Orbit Instability in Dark Matter Halo Formation and Structure

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 20/06/2008

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For a decade, N-body simulations have revealed a nearly universal dark matter
density profile, which appears to be robust to changes in the overall density
of the universe and the underlying power spectrum. Despite its universality,
the physical origin of this profile has not yet been well understood.
Semi--analytic models by Barnes et al. (2005) have suggested that the density
structure of dark matter halos is determined by the onset of the radial orbit
instability (ROI). We have tested this hypothesis using N-body simulations of
collapsing dark matter halos with a variety of initial conditions. For
dynamically cold initial conditions, the resulting halo structures are triaxial
in shape, due to the mild aspect of the instability. We examine how variations
in initial velocity dispersion affect the onset of the instability, and find
that an isotropic velocity dispersion can suppress the ROI entirely, while a
purely radial dispersion does not. The quantity sigma^2/vc^2 is a criterion for
instability, where regions with sigma^2/vc^2 <~1 become triaxial due to the ROI
or other perturbations. We also find that the radial orbit instability sets a
scale length at which the velocity dispersion changes rapidly from isotropic to
radially anisotropic. This scale length is proportional to the radius at which
the density profile changes shape...

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## Growth rate and the cutoff wavelength of the Darrieus-Landau instability in laser ablation

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 13/05/2009

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The main characteristics of the linear Darrieus-Landau instability in the
laser ablation flow are investigated. The dispersion relation of the
instability is found numerically as a solution to an eigenvalue stability
problem, taking into account the continuous structure of the flow. The results
are compared to the classical Darrieus-Landau instability of a usual slow
flame. The difference between the two cases is due to the specific features of
laser ablation: high plasma compression and strong temperature dependence of
electron thermal conduction. It is demonstrated that the Darrieus-Landau
instability in laser ablation is much stronger than in the classical case. In
particular, the maximum growth rate in the case of laser ablation is about
three times larger than that for slow flames. The characteristic length scale
of the Darrieus-Landau instability in the ablation flow is comparable to the
total distance from the ablation zone to the critical zone of laser light
absorption. The possibility of experimental observations of the Darrieus-Landau
instability in laser ablation is discussed.; Comment: 16 pages, 10 figures

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## Equilibrium Electro-osmotic Instability

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 18/03/2014

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Since its prediction fifteen years ago, electro-osmotic instability has been
attributed to non-equilibrium electro-osmosis related to the extended space
charge which develops at the limiting current in the course of concentration
polarization at a charge-selective interface. This attribution had a double
basis. Firstly, it has been recognized that equilibrium electro-osmosis cannot
yield instability for a perfectly charge-selective solid. Secondly, it has been
shown that non-equilibrium electro-osmosis can. First theoretical studies in
which electro-osmotic instability was predicted and analyzed employed the
assumption of perfect charge-selectivity for the sake of simplicity and so did
the subsequent numerical studies of various time-dependent and nonlinear
features of electro-osmotic instability. In this letter, we show that relaxing
the assumption of perfect charge-selectivity (tantamount to fixing the
electrochemical potential in the solid) allows for equilibrium electro-osmotic
instability. Moreover, we suggest a simple experimental test for determining
the true, either equilibrium or non-equilibrium, origin of electro-osmotic
instability.; Comment: 5 pages, 4 figures, submitted

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## Dependence of the large-scale vortex instability on latitude, stratification and domain size

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Relevância na Pesquisa

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In an earlier study, we reported on the excitation of large-scale vortices in
Cartesian hydrodynamical convection models subject to rapid enough rotation. In
that study, the conditions of the onset of the instability were investigated in
terms of the Reynolds (Re) and Coriolis (Co) numbers in models located at the
stellar North pole. In this study, we extend our investigation to varying
domain sizes, increasing stratification and place the box at different
latitudes. The effect of the increasing box size is to increase the sizes of
the generated structures, so that the principal vortex always fills roughly
half of the computational domain. The instability becomes stronger in the sense
that the temperature anomaly and change in the radial velocity are observed to
be enhanced. The model with the smallest box size is found to be stable against
the instability, suggesting that a sufficient scale separation between the
convective eddies and the scale of the domain is required for the instability
to work. The instability can be seen upto the co-latitude of 30 degrees, above
which value the flow becomes dominated by other types of mean flows. The
instability can also be seen in a model with larger stratification. Unlike the
weakly stratified cases...

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## Rayleigh-Taylor Instability in a Relativistic Fireball on a Moving Computational Grid

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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We numerically calculate the growth and saturation of the Rayleigh-Taylor
instability caused by the deceleration of relativistic outflows with Lorentz
factor {\Gamma} = 10, 30, and 100. The instability generates turbulence whose
scale exhibits strong dependence on Lorentz factor, as only modes with angular
size smaller than 1/{\Gamma} can grow. We develop a simple diagnostic to
measure the kinetic energy in turbulent fluctuations, and calculate a ratio of
turbulent kinetic energy to thermal energy of .03 in the region affected by the
instability. Although our numerical calculation does not include magnetic
fields, we argue that small scale turbulent dynamo amplifies magnetic fields to
nearly this same fraction, giving a ratio of magnetic to thermal energy of ~
.01, to within a factor of two. The instability completely disrupts the contact
discontinuity between the ejecta and the swept up circumburst medium. The
reverse shock is stable, but is impacted by the Rayleigh-Taylor instability,
which strengthens the reverse shock and pushes it away from the forward shock.
The forward shock front is unaffected by the instability, but Rayleigh-Taylor
fingers can penetrate of order 10% of the way into the energetic region behind
the shock during the two-shock phase of the explosion. We calculate afterglow
emission from the explosion and find the reverse shock emission peaks at a
later time due to its reduced Lorentz factor and modified density and pressure
at the shock front. These calculations are performed using a novel numerical
technique that includes a moving computational grid. The moving grid is
essential as it maintains contact discontinuities to high precision and can
easily evolve flows with extremely large Lorentz factors.; Comment: ApJ Accepted

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## Stability of rotating magnetized jets in the solar atmosphere. I. Kelvin-Helmholtz instability

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 05/10/2015

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Observations show various jets in the solar atmosphere with significant
rotational motions, which may undergo instabilities leading to heat ambient
plasma. We study the Kelvin-Helmholtz (KH) instability of twisted and rotating
jets caused by the velocity jumps near the jet surface. We derive a dispersion
equation with appropriate boundary condition for total pressure (including
centrifugal force of tube rotation), which governs the dynamics of
incompressible jets. Then, we obtain analytical instability criteria of
Kelvin-Helmholtz instability in various cases, which were verified by numerical
solutions to the dispersion equation. We find that twisted and rotating jets
are unstable to KH instability when the kinetic energy of rotation is more than
the magnetic energy of the twist. Our analysis shows that the azimuthal
magnetic field of 1-5 G can stabilize observed rotations in
spicule/macrospicules and X-ray/EUV jets. On the other hand, non-twisted jets
are always unstable to KH instability. In this case, the instability growth
time is several seconds for spicule/macrospicules and few minutes (or less) for
EUV/X-ray jets. We also find that standing kink and torsional Alfven waves are
always unstable near the antinodes due to the jump of azimuthal velocity at the
surface...

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## On Modeling the Kelvin--Helmholtz Instability in Solar Atmosphere

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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In the present review article, we discuss the recent developments in studying
the Kelvin--Helmholtz (KH) instability of magnetohydrodynamic (MHD) waves
propagating in various solar magnetic structures. The main description is on
the modeling of KH instability developing in the coronal mass ejections (CMEs),
and contributes to the triggering of wave turbulence subsequently leading to
the coronal heating. KH instability of MHD waves in coronal active regions
recently observed and imaged in unprecedented detail in EUV high cadence,
high-resolution observations by SDO/AIA, and spectroscopic observations by
Hinode/EIS instrument, is posing now challenge for its realistic modeling. It
is shown that considering the solar mass flows of CMEs as moving cylindrical
twisted magnetic flux tubes, the observed instability can be explained in terms
of unstable m = -3 MHD mode. We also describe the occurrence of the KH
instability in solar jets. The obtained critical jet speeds for the instability
onset as well as the linear wave growth rates are in good agreement with the
observational data of solar jets.; Comment: 27 pages, 5 figures, 2 figures added, new references added, accepted.
arXiv admin note: text overlap with arXiv:1310.8106, arXiv:1301.2736 by other
authors

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## Secular Gravitational Instability of a Dust Layer in Shear Turbulence

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 13/11/2011

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We perform a linear stability analysis of a dust layer in a turbulent gas
disk. Youdin (2011) investigated the secular gravitational instability of a
dust layer using hydrodynamic equations with a turbulent diffusion term. We
obtain essentially the same result independently of Youdin (2011). In the
present analysis, we restrict the area of interest to small dust particles,
while investigating the secular gravitational instability in a more rigorous
manner. We discuss the time evolution of the dust surface density distribution
using a stochastic model and derive the advection-diffusion equation. The
validity of the analysis by Youdin (2011) is confirmed in the strong drag
limit. We demonstrate quantitatively that the finite thickness of a dust layer
weakens the secular gravitational instability and that the density-dependent
diffusion coefficient changes the growth rate. We apply the obtained results to
the turbulence driven by the shear instability and find that the secular
gravitational instability is faster than the radial drift when the gas density
is three times as large as that in the minimum-mass disk model. If the dust
particles are larger than chondrules, the secular gravitational instability
grows within the lifetime of a protoplanetary disk.; Comment: 32 pages...

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## Instabilities and transport in magnetized plasmas

Fonte: University of Cambridge; Department of Applied Mathematics and Theoretical Physics; Darwin College
Publicador: University of Cambridge; Department of Applied Mathematics and Theoretical Physics; Darwin College

Tipo: Thesis; doctoral; PhD

EN

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#Plasma#Magnetic field#Fluid#Kinetic#Magnetized#Firehose instability#Magnetorotational instatbility#MRI#Transport#Galaxy clusters#Accretion disc

In a magnetized plasma, naturally occurring pressure anisotropies facilitate in- stabilities that are expected to modify the transport properties of the system. In this thesis we examine two such instabilities and, where appropriate, their effects on transport.
First we consider the collisional (fluid) magnetized magnetorotational instability (MRI) in the presence of the Braginskii viscosity. We conduct a global linear analysis of the instability in a galactic rotation profile for three magnetic field configurations: purely azimuthal, purely vertical and slightly pitched. Our analysis, numerical and asymptotic, shows that the first two represent singular configurations where the Braginskii viscosity?s primary role is dissipative and the maximum growth rate is proportional to the Reynolds number when this is small. For a weak pitched field, the Braginskii viscosity is destabilising and when its effects dominate over the Lorentz force, the growth rate of the MRI can be up to 2?2 times faster than the inviscid limit. If the field is strong, an over-stability develops and both the real and imaginary parts of the frequency increase with the coefficient of the viscosity.
Second, in the context of the ICM of galaxy clusters, we consider the pressure-anisotropy-driven firehose instability. The linear instability is fast (? ion cyclotron period) and small-scale (ion Larmor radius ?i) and so fluid theory is
inapplicable. We determine its nonlinear evolution in an ab initio kinetic calculation (for parallel gradients only). We use a particular physical asymptotic ordering to derive a closed nonlinear equation for the firehose turbulence...

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## Magnetic effects on the low-T/|W| instability in differentially rotating neutron stars

Fonte: American Physical Society
Publicador: American Physical Society

Tipo: Article; PeerReviewed
Formato: application/pdf; application/pdf

Publicado em 15/11/2014

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Dynamical instabilities in protoneutron stars may produce gravitational waves whose observation could shed light on the physics of core-collapse supernovae. When born with sufficient differential rotation, these stars are susceptible to a shear instability (the “low-T/|W| instability”), but such rotation can also amplify magnetic fields to strengths where they have a considerable impact on the dynamics of the stellar matter. Using a new magnetohydrodynamics module for the Spectral Einstein Code, we have simulated a differentially-rotating neutron star in full 3D to study the effects of magnetic fields on this instability. Though strong toroidal fields were predicted to suppress the low-T/|W| instability, we find that they do so only in a small range of field strengths. Below 4×10^(13) G, poloidal seed fields do not wind up fast enough to have an effect before the instability saturates, while above 5×10^(14) G, magnetic instabilities can actually amplify a global quadrupole mode (this threshold may be even lower in reality, as small-scale magnetic instabilities remain difficult to resolve numerically). Thus, the prospects for observing gravitational waves from such systems are not in fact diminished over most of the magnetic parameter space. Additionally...

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## Surge Instability on a Cavitating Propeller

Fonte: Instituto de Tecnologia da Califórnia
Publicador: Instituto de Tecnologia da Califórnia

Tipo: Conference or Workshop Item; PeerReviewed
Formato: application/pdf

Publicado em //2001

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This study details experiments investigating a previously unrecognized surge instability on a cavitating propeller in a water tunnel. The surge instability is furst explored through visual observation of the cavitation on the propeller blades and in the tip vortices. Similarities between the instability and previously documented cavitation phenomena are noted. Measurements of the radiated pressure are then obtained, and the acoustic signature of the instability is identified. The magnitudes of the fluctuating pressures are very large, presumably capable of producing sever hull vibration on a ship.
The origins of the instability are explored through separate investigation of the cavitation dynamics and the response of the water tunnel to volumetric displacement in the working section. Experiments are conducted to quantify the dynamics of the propeller vacitation. Finally, a model is developed for the complete system, incorporating both the cavitation and facility dynamics. The model predicts active system dynamics (linked to the mass flow gain factor familiar in the context of pump dynamics) and therefore potentially unstable behavior for two distinct frequency ranges, one of which appears to be responsible for the instability.

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## Surge Instability on a Cavitating Propeller

Fonte: Instituto de Tecnologia da Califórnia
Publicador: Instituto de Tecnologia da Califórnia

Tipo: Article; PeerReviewed
Formato: application/pdf

Publicado em /05/2000

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This study details experiments investigating a previously unrecognized surge instability on a cavitating propeller in a water tunnel. The surge instability is explored through visual observation of the cavitation on the propeller blades and in the tip vortices. Similarities between the instability and previously documented cavitation phenomena are noted. Measurements of the radiated pressure are obtained, and the acoustic signature of the instability is identified. The magnitudes of the fluctuating pressures are very large, presumably capable of producing severe hull vibration on a ship.
The origins of this instability are explored through separate investigation of the cavitation dynamics and the response of the water tunnel to volumetric displacement in the working section. Experiments are conducted to quantify the dynamics of the propeller cavitation. Finally, a model is developed for the complete system, incorporating both the cavitation and facility dynamics. The model predicts active system dynamics (linked to the mass flow gain factor familiar in the context of pump dynamics) and therefore potentially unstable behavior for two distinct frequency ranges, one of which appears to be responsible for the instability.

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## Multifrequency Instability of Cavitating Inducers

Fonte: American Society of Mechanical Engineers
Publicador: American Society of Mechanical Engineers

Tipo: Article; PeerReviewed
Formato: application/pdf

Publicado em /06/2007

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Recent testing of high-speed cavitating turbopump inducers has revealed the existence of
more complex instabilities than the previously recognized cavitating surge and rotating
cavitation. This paper explores one such instability that is uncovered by considering the
effect of a downstream asymmetry, such as a volute on a rotating disturbance similar to
(but not identical to) that which occurs in rotating cavitation. The analysis uncovers a
new instability that may be of particular concern because it occurs at cavitation numbers
well above those at which conventional surge and rotating cavitation occur. This means
that it will not necessarily be avoided by the conventional strategy of maintaining a
cavitation number well above the performance degradation level. The analysis considers
a general surge component at an arbitrary frequency ω present in a pump rotating at
frequency Ω and shows that the existence of a discharge asymmetry gives rise not only to
beat components at frequencies, Ω−ω and Ω+ω (as well as higher harmonics), but also
to rotating as well as surge components at all these frequencies. In addition, these
interactions between the frequencies and the surge and rotating modes lead to “coupling
impedances” that effect the dynamics of each of the basic frequencies. We evaluate these
coupling impedances and show not only that they can be negative (and thus promote
instability) but also are most negative for surge frequencies just a little below Ω. This
implies potential for an instability involving the coupling of a surge mode with a frequency
around 0.9 Ω and a low-frequency rotating mode about 0.1 Ω. We also examine
how such an instability would be manifest in unsteady pressure measurements at the inlet
to and discharge from a cavitating pump and establish a “footprint” for the recognition
of such an instability.

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