1,987 research outputs found
Global Solutions of Viscous Transonic Flows in Kerr Geometry I: Weak Viscosity Limit
We present fully general relativistic equations governing viscous transonic
flows in vertical equilibrium in Kerr geometry. We find the complete set of
global solutions (both for Optically thick and optically thin flows) in the
weak viscosity limit. We show that for a large region of parameter space,
centrifugal pressure supported standing shocks can form in accretion and winds
very close to the black hole horizon, both for co-rotating and contra-rotating
flows. We compute the nature of the shear tensor for complete transonic
solutions and discuss the consequences of its reversal properties.Comment: Latex 10 pages, special macro psfig.tex are include
Hysteresis effects and diagnostics of the shock formation in low angular momentum axisymmetric accretion in the Kerr metric
The secular evolution of the purely general relativistic low angular momentum
accretion flow around a spinning black hole is shown to exhibit hysteresis
effects. This confirms that a stationary shock is an integral part of such an
accretion disc in the Kerr metric. The equations describing the space gradient
of the dynamical flow velocity of the accreting matter have been shown to be
equivalent to a first order autonomous dynamical systems. Fixed point analysis
ensures that such flow must be multi-transonic for certain astrophysically
relevant initial boundary conditions. Contrary to the existing consensus in the
literature, the critical points and the sonic points are proved not to be
isomorphic in general. Homoclinic orbits for the flow flow possessing multiple
critical points select the critical point with the higher entropy accretion
rate, confirming that the entropy accretion rate is the degeneracy removing
agent in the system. However, heteroclinic orbits are also observed for some
special situation, where both the saddle type critical points of the flow
configuration possesses identical entropy accretion rate. Topologies with
heteroclinic orbits are thus the only allowed non removable degenerate
solutions for accretion flow with multiple critical points, and are shown to be
structurally unstable. Depending on suitable initial boundary conditions, a
homoclinic trajectory can be combined with a standard non homoclinic orbit
through an energy preserving Rankine-Hugoniot type of stationary shock. An
effective Lyapunov index has been proposed to analytically confirm why certain
class of transonic flow can not accommodate shock solutions even if it produces
multiple critical points. (Abridged)Comment: mn2e.cls format. 24 pages. 4 figure
A study of nozzle and ejector flow problems by the method of integral relations
The application of the method of integral relations to nozzle and ejector flow problems was examined. For nozzle flow problems, the general formulation is that the approaching flow may be rotational. Particular attention was given to the phenomenon of choking under nonuniform flow conditions. Numerical integration of the governing ordinary differential equations was also investigated. This scheme of analysis was also applied to study the interacting flow field within an ejector system
Properties of Interstellar Turbulence from Gradients of Linear Radio Polarization Maps
Faraday rotation of linearly polarized radio signals provides a very
sensitive probe of fluctuations in the interstellar magnetic field and ionized
gas density resulting from magnetohydrodynamic (MHD) turbulence. We used a set
of statistical tools to analyze images of the spatial gradient of linearly
polarized radio emission () from the ISM for both
observational data from a test image of the Southern Galactic Plane Survey
(SGPS) and isothermal simulations of MHD turbulence. We compared the
observational data with results of synthetic observations obtained with the
simulations of 3D turbulence. Visually, in both data sets, a complex network of
filamentary structures is seen. Our analysis shows that the filaments in the
gradient can be produced by shocks as well as random fluctuations
characterizing the non-differentiable field of MHD turbulence. The latter
dominates for subsonic turbulence, while the former dominates for supersonic
turbulence. In order to quantitatively characterize these differences we use
the topology tool known as a genus curve as well as the moments of the image
distribution. We find that higher values for the moments correspond to cases of
with larger Mach numbers, but the strength of the
dependency is connected to the telescope angular resolution. In regards to the
topology, the supersonic filaments observed in have a
positive genus shift, which indicates a "swisscheese" like topology, while the
subsonic cases show a negative genus, indicating a "clump" like topology. In
the case of the genus, the dependency on the telescope resolution is not as
strong. The SGPS test region data has a distribution and morphology that
matches subsonic to transsonic type turbulence, which independently confirms
what is now expected for the WIM.Comment: Submitted to Ap
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