Editing 2DStructure/AxisymmetricInstabilities (section)

==Rayleigh-Taylor Instability==
Referencing both p. 101 of [ <b>[[Appendix/References#Shu92|<font color="red">Shu92</font>]] </b>], and volume I, p. 410 of [ <b>[[Appendix/References#P00|<font color="red">P00</font>]] </b>], a [https://en.wikipedia.org/wiki/Rayleigh%E2%80%93Taylor_instability Rayleigh-Taylor] instability is a bouyancy-driven instability that arises when a heavy fluid rests on top of a light fluid in an effective gravitational field, <math>~\vec{g}</math>.   In the simplest case of spherically symmetric, self-gravitating configurations, the condition for stability against a Rayleigh-Taylor instability may be written as,
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<table border="0" cellpadding="5" align="center">

<tr>
  <td align="right">
<math>~(- \vec{g} ) \cdot \nabla\rho</math>
  </td>
  <td align="center">
<math>~< </math>
  </td>
  <td align="left">
<math>~0 </math>
  </td>
  <td align="center">&nbsp; &nbsp;&nbsp;&nbsp;[stable] ,</td>
</tr>
</table>
</div>
that is to say, the mass density ''must decrease outward.''  In an expanded discussion, [ <b>[[Appendix/References#P00|<font color="red">P00</font>]] </b>] &#8212; see pp. 410 - 413 &#8212; derives a dispersion relation that describes the development of the Rayleigh-Taylor instability in a plane-parallel fluid layer that initially contains a discontinuous jump/drop in the density. 

In addition, [ <b>[[Appendix/References#P00|<font color="red">P00</font>]] </b>] &#8212; see pp. 413 - 416 &#8212; and [ <b>[[Appendix/References#Shu92|<font color="red">Shu92</font>]] </b>] &#8212; see pp. 101 - 105 &#8212; both discuss circumstances that can give rise to the so-called ''Kelvin-Helmholtz'' instability.  It is another common two-fluid instability, but one that depends on the existence of transverse velocity flows and that is independent of the gravitational field.