AxisymmetricConfigurations/SolvingPE

Solving the Poisson Equation

Solving the Poisson Equation

When constructing rotating equilibrium configurations that obey a barotropic equation of state, keep in mind that certain physical variable profiles should be avoided because they will lead to structures that are unstable toward the dynamical development of shape-distorting or convective-type motions. Here are a few well-known examples.  
 
 
 
 

See Also

• Lord Rayleigh (1917, Proc. Royal Society of London. Series A, 93, 148-154) — On the Dynamics of Revolving Fluids
• P. S. Marcus, W. H. Press, & S. A. Teukolsky (1977, ApJ, 214, 584- 597) — Stablest Shapes for an Axisymmetric Body of Gravitating, Incompressible Fluid (includes torus with non-uniform rotation)

1. Shortly after their equation (3.2), Marcus, Press & Teukolsky make the following statement: "… we know that an equilibrium incompressible configuration must rotate uniformly on cylinders (the famous "Poincaré-Wavre" theorem, cf. Tassoul 1977, &Sect;4.3) …"

• Referring to our accompanying discussion of Type 1 Riemann ellipsoids, it seems that uniform rotation on cylinders is not required. What's going on?