Thermal Instability

Intro

Thought I would play around with clumps that were marginally unstable and let them evolve without self-gravity

Setup

Box size is 4 pc and clump radius is 1 pc. Ambient and clump density are 2 part/cc and the clump has small density perturbations of order 10% but is initially in pressure equilibrium with ambient. I modified the clump module to do perturbations in r, theta, phi space instead of x-y-z space however I still used exp [ (k_r, k_theta, k_phi) dot (r, theta, phi) ] instead of the more appropriate spherical harmonics…

A	k_r	k_{\theta}	k_{\phi}	\epsilon
.1	\pi/2	0	0	0
.05	2\pi	4	2	0
.05	\pi	3	4	0

\frac{\rho}{\rho_0} = \displaystyle{\sum_i {A_icos(k^i_r r+k^i_{\theta}\theta+k^i_{\phi}\phi+\epsilon^i)}}

Results

movie​

Discussion

While the small scale perturbations grow the fastest, eventually the large scale perturbation results in the clump collapsing. Towards the end of the run material is also 'collapsing' against the boundary creating a hot rarefied spherical shell.