Dynamics in the cylinder's wake
The first instability of the wake of a circular cylinder is to the periodic two-dimensional von Karman vortex street. I have previously carried out a numerical Floquet analysis of the vortex street to three-dimensional perturbations, and calculated the thresholds, wavenumbers, and Floquet modes of this secondary instability. I now present an instantaneous -- temporally local -- stability analysis which shows the flow to be linearly stable throughout the periodic cycle, a very surprising result within the fluid dynamics community.
Time permitting I will discuss a simple numerical scheme for reducing computation time in very large fluid (and other PDE) simulatlations by about a factor of two with minimal programming effort.