205 research outputs found
Suppression of lift-up effect in the 3D Boussinesq equations around a stably stratified Couette flow
Vortex axisymmetrization, inviscid damping, and vorticity depletion in the linearized 2D Euler equations
Coherent vortices are often observed to persist for long times in turbulent 2D flows even at very high Reynolds numbers and are observed in experiments and computer simulations to potentially be asymptotically stable in a weak sense for the 2D Euler equations. We consider the incompressible 2D Euler equations linearized around a radially symmetric, strictly monotone decreasing vorticity distribution. For sufficiently regular data, we prove the inviscid damping of the Īø-dependent radial and angular velocity fields with the optimal rates ā„ur(t)ā„ā²āØtā©ā1 and ā„ā„uĪø(t)ā„ā„ā²āØtā©ā2 in the appropriate radially weighted L2 spaces. We moreover prove that the vorticity weakly converges back to radial symmetry as tāā, a phenomenon known as vortex axisymmetrization in the physics literature, and characterize the dynamics in higher Sobolev spaces. Furthermore, we prove that the Īø-dependent angular Fourier modes in the vorticity are ejected from the origin as tāā, resulting in faster inviscid damping rates than those possible with passive scalar evolution. This non-local effect is called vorticity depletion. Our work appears to be the first to find vorticity depletion relevant for the dynamics of vortices
Stationary Structures Near the Kolmogorov and Poiseuille Flows in the 2d Euler Equations
We study the behavior of solutions to the incompressible 2d Euler equations near two canonical shear flows with critical points, the Kolmogorov and Poiseuille flows, with consequences for the associated NavierāStokes problems. We exhibit a large family of new, non-trivial stationary states that are arbitrarily close to the Kolmogorov flow on the square torus in analytic regularity. This situation contrasts strongly with the setting of some monotone shear flows, such as the Couette flow: there the linearized problem exhibits an āinviscid dampingā mechanism that leads to relaxation of perturbations of the base flows back to nearby shear flows. Our results show that such a simple description of the long-time behavior is not possible for solutions near the Kolmogorov flow on . Our construction of the new stationary states builds on a degeneracy in the global structure of the Kolmogorov flow on , and we also show a lack of correspondence between the linearized description of the set of steady states and its true nonlinear structure. Both the Kolmogorov flow on a rectangular torus and the Poiseuille flow in a channel are very different. We show that the only stationary states near them must indeed be shears, even in relatively low regularity. In addition, we show that this behavior is mirrored closely in the related NavierāStokes settings: the linearized problems near the Poiseuille and Kolmogorov flows both exhibit an enhanced rate of dissipation. Previous work by us and others shows that this effect survives in the full, nonlinear problem near the Poiseuille flow and near the Kolmogorov flow on rectangular tori, provided that the perturbations lie below a certain threshold. However, we show here that the corresponding result cannot hold near the Kolmogorov flow on
Different twins in the millisecond pulsar recycling scenario: optical polarimetry of PSR J1023+0038 and XSS J12270-4859
We present the first optical polarimetric study of the two transitional
pulsars PSR J1023+0038 and XSS J12270-4859. This work is focused on the search
for intrinsical linear polarisation (LP) in the optical emission from the two
systems. We carried out multiband optical and NIR photo-polarimetry of the two
systems using the ESO NTT at La Silla (Chile), equipped with the EFOSC2 and the
SOFI instruments. XSS J12270-4859 was observed during its radio-pulsar state;
we did not detect LP in all bands, with 3 sigma upper limits of, e.g., 1.4% in
the R-band. We built the NIR-optical averaged spectral energy distribution
(SED) of the system, that could be well described by an irradiated black body
with radius and albedo ,
without the need of further components (thus excluding the visible presence of
an extended accretion disc and/or of relativistic jets). The case was different
for PSR J1023+0038, that was in its accretion phase during our campaign. We
measured a LP of and in the V and R bands,
respectively. The phase-resolved polarimetric curve of the source in the R-band
reveals a hint of a sinusoidal modulation at the source 4.75 hr orbital period,
peaked at the same orbital phase as the light curve. The measured LP of PSR
J1023+0038 could in principle be interpreted as scattering with free electrons
(that can be found in the accretion disc of the system or even in the hot
corona that surrounds the disc itself) or to synchrotron emission from a
relativistic particles jet or outflow. However, the NIR-optical SED of the
system built starting from our dataset did not suggest the presence of a jet.
We conclude that the optical LP observed for PSR J1023+0038 is possibly due to
Thomson scattering with electrons in the disc, as also suggested from the
possible modulation of the R-band LP at the system orbital period.Comment: 10 pages, 8 figures, 4 tables. Accepted for publication in Sec. 7.
Stellar structure and evolution of Astronomy and Astrophysic
Simultaneous Multi-band Radio & X-ray Observations of the Galactic Center Magnetar SGR 17452900
We report on multi-frequency, wideband radio observations of the Galactic
Center magnetar (SGR 17452900) with the Green Bank Telescope for 100
days immediately following its initial X-ray outburst in April 2013. We made
multiple simultaneous observations at 1.5, 2.0, and 8.9 GHz, allowing us to
examine the magnetar's flux evolution, radio spectrum, and interstellar medium
parameters (such as the dispersion measure (DM), the scattering timescale and
its index). During two epochs, we have simultaneous observations from the
Chandra X-ray Observatory, which permitted the absolute alignment of the radio
and X-ray profiles. As with the two other radio magnetars with published
alignments, the radio profile lies within the broad peak of the X-ray profile,
preceding the X-ray profile maximum by 0.2 rotations. We also find that
the radio spectral index is significantly negative between 2 and
9 GHz; during the final 30 days of our observations ,
which is typical of canonical pulsars. The radio flux has not decreased during
this outburst, whereas the long-term trends in the other radio magnetars show
concomitant fading of the radio and X-ray fluxes. Finally, our wideband
measurements of the DMs taken in adjacent frequency bands in tandem are
stochastically inconsistent with one another. Based on recent theoretical
predictions, we consider the possibility that the dispersion measure is
frequency-dependent. Despite having several properties in common with the other
radio magnetars, such as , an
increase in the radio flux during the X-ray flux decay has not been observed
thus far in other systems.Comment: 15 pages, 9 figures, 3 tables; accepted to Ap
The discovery, monitoring and environment of SGR J1935+2154
We report on the discovery of a new member of the magnetar class, SGR
J1935+2154, and on its timing and spectral properties measured by an extensive
observational campaign carried out between July 2014 and March 2015 with
Chandra and XMM-Newton (11 pointings). We discovered the spin period of SGR
J1935+2154 through the detection of coherent pulsations at a period of about
3.24s. The magnetar is slowing-down at a rate of 1.43(1)x10^{-11} s/s and with
a decreasing trend due to a negative second period derivative of
-3.5(7)x10^{-19} s/s^2. This implies a surface dipolar magnetic field strength
of about 2.2x10^{14} G, a characteristic age of about 3.6kyr and, a spin-down
luminosity L_{sd} of about 1.7x10^{34} erg/s. The source spectrum is well
modelled by a blackbody with temperature of about 500eV plus a power-law
component with photon index of about 2. The source showed a moderate long-term
variability, with a flux decay of about 25\% during the first four months since
its discovery, and a re-brightening of the same amount during the second four
months. The X-ray data were also used to study the source environment. In
particular, we discovered a diffuse emission extending on spatial scales from
about 1" up to at least 1' around SGR J1935+2154 both in Chandra and XMM-Newton
data. This component is constant in flux (at least within uncertainties) and
its spectrum is well modelled by a power-law spectrum steeper than that of the
pulsar. Though a scattering halo origin seems to be more probable we cannot
exclude that part, or all, of the diffuse emission is due to a pulsar wind
nebula.Comment: To appear in MNRAS; 10 pages, 3 color figures, 4 table
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