scholarly journals Spectral Methods for Time‐dependent Studies of Accretion Flows. II. Two‐dimensional Hydrodynamic Disks with Self‐Gravity

2006 ◽  
Vol 645 (1) ◽  
pp. 506-518 ◽  
Author(s):  
Chi‐kwan Chan ◽  
Dimitrios Psaltis ◽  
Feryal Ozel
Keyword(s):  
Spectral Methods ◽  
Time Dependent ◽  
Two Dimensional ◽  
Accretion Flows ◽  
Self Gravity

scholarly journals Integrable unsteady motion with an application to ocean eddies

1998 ◽  
Vol 5 (3) ◽  
pp. 145-151
Author(s):  
A. D. Kirwan, Jr. ◽  
B. L. Lipphardt, Jr.
Keyword(s):  
Potential Vorticity ◽  
Particle Motion ◽  
Gulf Stream ◽  
Incompressible Flows ◽  
Unsteady Motion ◽  
Ring System ◽  
Time Dependent ◽  
Two Dimensional ◽  
Ocean Eddies ◽  
Multilayered Systems

Abstract. Application of the Brown-Samelson theorem, which shows that particle motion is integrable in a class of vorticity-conserving, two-dimensional incompressible flows, is extended here to a class of explicit time dependent dynamically balanced flows in multilayered systems. Particle motion for nonsteady two-dimensional flows with discontinuities in the vorticity or potential vorticity fields (modon solutions) is shown to be integrable. An example of a two-layer modon solution constrained by observations of a Gulf Stream ring system is discussed.

Two‐dimensional time‐dependent analysis of the switching of a thyristor

1977 ◽  
Vol 48 (1) ◽  
pp. 270-278 ◽  
Author(s):  
Shih‐Pei Hu ◽  
Benjamin M. Rabinovici
Keyword(s):  
Time Dependent ◽  
Two Dimensional ◽  
Time Dependent Analysis

Upstream motions in stratified flow

1988 ◽  
Vol 187 ◽  
pp. 487-506 ◽  
Author(s):  
I. P. Castro ◽  
W. H. Snyder
Keyword(s):  
Body Height ◽  
Three Dimensional ◽  
Time Dependent ◽  
Experimental Measurements ◽  
Two Dimensional ◽  
Towing Tank ◽  
First Order ◽  
Density Perturbations ◽  
Small Obstacle ◽  
Obstacle Height

In this paper experimental measurements of the time-dependent velocity and density perturbations upstream of obstacles towed through linearly stratified fluid are presented. Attention is concentrated on two-dimensional obstacles which generate turbulent separated wakes at Froude numbers, based on velocity and body height, of less than 0.5. The form of the upstream columnar modes is shown to be largely that of first-order unattenuating disturbances, which have little resemblance to the perturbations described by small-obstacle-height theories. For two-dimensional obstacles the disturbances are similar to those found by Wei, Kao & Pao (1975) and it is shown that provided a suitable obstacle drag coefficient is specified, the lowest-order modes (at least) are quantitatively consistent with the results of the Oseen inviscid model.Discussion of some results of similar measurements upstream of three-dimensional obstacles, the importance of towing tank endwalls and the relevance of the Foster & Saffman (1970) theory for the limit of zero Froude number is also included.

scholarly journals Two-dimensional modeling of density and thermal structure of dense circumstellar outflowing disks

2018 ◽  
Vol 613 ◽  
pp. A75 ◽  
Author(s):  
P. Kurfürst ◽  
A. Feldmeier ◽  
J. Krtička
Keyword(s):  
Mass Loss ◽  
Optical Depth ◽  
Massive Stars ◽  
Thermal Structure ◽  
Time Dependent ◽  
Navier Stokes ◽  
Viscous Heating ◽  
Two Dimensional ◽  
Dense Region ◽  
Loss Rates

Context. Evolution of massive stars is affected by a significant loss of mass either via (nearly) spherically symmetric stellar winds or by aspherical mass-loss mechanisms, namely the outflowing equatorial disks. However, the scenario that leads to the formation of a disk or rings of gas and dust around massive stars is still under debate. It is also unclear how various forming physical mechanisms of the circumstellar environment affect its shape and density, as well as its kinematic and thermal structure. Aims. We study the hydrodynamic and thermal structure of optically thick, dense parts of outflowing circumstellar disks that may be formed around various types of critically rotating massive stars, for example, Be stars, B[e] supergiant (sgB[e]) stars or Pop III stars. We calculate self-consistent time-dependent models of temperature and density structure in the disk’s inner dense region that is strongly affected by irradiation from a rotationally oblate central star and by viscous heating. Methods. Using the method of short characteristics, we specify the optical depth of the disk along the line-of-sight from stellar poles. Within the optically thick dense region with an optical depth of τ > 2∕3 we calculate the vertical disk thermal structure using the diffusion approximation while for the optically thin outer layers we assume a local thermodynamic equilibrium with the impinging stellar irradiation. For time-dependent hydrodynamic modeling, we use two of our own types of hydrodynamic codes: two-dimensional operator-split numerical code based on an explicit Eulerian finite volume scheme on a staggered grid, and unsplit code based on the Roe’s method, both including full second-order Navier-Stokes shear viscosity. Results. Our models show the geometric distribution and contribution of viscous heating that begins to dominate in the central part of the disk for mass-loss rates higher than Ṁ ≳ 10−10 M⊙ yr−1. In the models of dense viscous disks with Ṁ > 10−8 M⊙ yr−1, the viscosity increases the central temperature up to several tens of thousands of Kelvins, however the temperature rapidly drops with radius and with distance from the disk midplane. The high mass-loss rates and high viscosity lead to instabilities with significant waves or bumps in density and temperature in the very inner disk region. Conclusions. The two-dimensional radial-vertical models of dense outflowing disks including the full Navier-Stokes viscosity terms show very high temperatures that are however limited to only the central disk cores inside the optically thick area, while near the edge of the optically thick region the temperature may be low enough for the existence of neutral hydrogen, for example.

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