This is linear stability code that solves the Boussinesq Navier-Stokes (BNS) equations.

The idea is to take the BNS equations and derive the linear stability equations. From there, we numerically solve the equations for long term behaviour to determine the growth rate of the fastest growing mode. 

Method:
This code uses spectral methods w/ 2/3 de-aliasing rule to evaluate derivatives. Pressure is eliminated via projection in the fourier plane. The time stepping is done via a 2nd order Adams-Bashforth scheme. We solve for u,v,w,rho and the growth rate of the linear perturbation.  
The equations solved are 3.3 - 3.4 of Billant and Chomaz 2000c. 


Note:
If you want to use this code, go ahead but I make no guarantees that it will correctly solve your problem as this code has only been tested for 
a very specific problem, namely find the largest growing eigenmode of the Lamb-Chaplygin dipole in a linear approximation to the Boussinesq equations
using a spectral method. If you still want to use the code, I would greatly appreciate an e-mail.


To do:
maybe AB higher order??

This code is currently run on the supercomputing cluster Sharcnet. 

References:

Billant P. & Chomaz J.-M. 2000c "Three-Dimensional stability of a vertical columnar vortex pair in a stratified fluid" J. Fluid Mech. 418, 64