23,715 research outputs found
Advection-Dominated Accretion: Self-Similarity and Bipolar Outflows
We consider axisymmetric viscous accretion flows where a fraction f of the
viscously dissipated energy is advected with the accreting gas as stored
entropy and a fraction 1-f is radiated. When f is small (i.e. very little
advection), our solutions resemble standard thin disks in many respects except
that they have a hot tenuous corona above. In the opposite {\it
advection-dominated} limit (), the solutions approach nearly
spherical accretion. The gas is almost at virial temperature, rotates at much
below the Keplerian rate, and the flow is much more akin to Bondi accretion
than to disk accretion. We compare our exact self-similar solutions with
approximate solutions previously obtained using a height-integrated system of
equations. We conclude that the height- integration approximation is excellent
for a wide range of conditions. We find that the Bernoulli parameter is
positive in all our solutions, especially close to the rotation axis. This
effect is produced by viscous transport of energy from small to large radii and
from the equator to the poles. In addition, all the solutions are convectively
unstable and the convection is especially important near the rotation axis. For
both reasons we suggest that a bipolar outflow will develop along the axis of
the flows, fed by material from the the surface layers of the equatorial
inflow.Comment: 22 Pages, 5 Figures are available by request to [email protected],
Plain Tex, CfA Preprint No. 3931, To Appear in Astrophysical Journal 5/1/9
Navier-Stokes calculations with a coupled strongly implicit method. Part 2: Spline solutions
A coupled strongly implicit method is combined with a deferred-corrector spline solver for the vorticity-stream function form of the Navier-Stokes equation. Solutions for cavity, channel and cylinder flows are obtained with the fourth-order spline 4 procedure. The strongly coupled spline corrector method converges as rapidly as the finite difference calculations and also allows for arbitrary large time increments for the Reynolds numbers considered. In some cases fourth-order smoothing or filtering is required in order to suppress high frequency oscillations
A Further Result on the Instability of Solutions to a Class of Non-Autonomous Ordinary Differential Equations of Sixth Order
The aim of the present paper is to establish a new result, which guarantees the instability of zero solution to a certain class of non-autonomous ordinary differential equations of sixth order. Our result includes and improves some well-known results in the literature
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