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=See Also=
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<li>[[User:Tohline/Apps/ImamuraHadleyCollaboration#Characteristics_of_Unstable_Eigenvectors_in_Self-Gravitating_Tori|Characteristics of Unstable Eigenvectors in Self-Gravitating Tori]]</li>
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Revision as of 16:45, 11 March 2020

The Stability of Self-Gravitating Polytropic Tori

Whitworth's (1981) Isothermal Free-Energy Surface
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J. W. Woodward, J. E. Tohline, & I. Hachisu (1994; hereafter WTH94) used nonlinear numerical hydrodynamic techniques to examine the relative stability of self-gravitating, polytropic tori toward the development of nonaxisymmetric structure. The following pair of tables list key properties of the set of model tori that were examined: Table 5 gives characteristics of the initial models and Table 6 presents results ascertained from the numerical stability analyses.

Table extracted from J. W. Woodward, J. E. Tohline & I. Hachisu (1994)

"The Stability of Thick, Self-gravitating Disks in Protostellar Systems"

ApJ, vol. 420, pp. 247-267 © American Astronomical Society

Woodward, Tohline & Hachisu (1994, ApJ, 420, 247)

Woodward, Tohline & Hachisu (1994, ApJ, 420, 247)

Online Movies

Figure 1: Animation Sequences to Supplement Figure 10 of WTH94

(click on security-lock icon or caption model name to go to YouTube)

Click for YouTube Video

Figure 10 from WTH94

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Table 5, Model O15 Table 5, Model O14

Click for YouTube Video

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Table 5, Model E17 Table 5, Model E29

Caption to Fig. 10 from WTH94:  "<math>~\phi_m - r</math>" diagrams illustrating the azimuthal structure of the four specific eigenmodes that were found to be dynamically unstable in our modeled disks.  (a) The m = 1 P-mode, shown here as it developed in model O15 <math>~[M_d/M_c = 1; ~T/|W| = 0.316];</math>  (b) The m = 1 A-mode, shown here as it developed in model O14 <math>~[M_d/M_c = 1; ~T/|W| = 0.251];</math>  (c) The m = 2 I-mode, shown here as it developed in model E17 <math>~[M_d/M_c = 5; ~T/|W| = 0.256];</math>  (d) The m = 2 L-mode, shown here as it developed in model E29 <math>~[M_d/M_c = 0.2; ~T/|W| = 0.447]\, .</math>


Figure 2: Five Additional Animation Sequences to Supplement Table 5 of WTH94

(click on security-lock icon or caption model name to go to YouTube)

Click for YouTube Video

Click for YouTube Video

Click for YouTube Video

Click for YouTube Video

Click for YouTube Video

Table 5, Model O13 Table 5, Model O16 Table 5, Model O17 Table 5, Model O18 Table 5, Model O22

See Also

 

Whitworth's (1981) Isothermal Free-Energy Surface

© 2014 - 2021 by Joel E. Tohline
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Recommended citation:   Tohline, Joel E. (2021), The Structure, Stability, & Dynamics of Self-Gravitating Fluids, a (MediaWiki-based) Vistrails.org publication, https://www.vistrails.org/index.php/User:Tohline/citation