Advanced Techniques for Investigating Structures in Computational Fluid Dynamics

The problems of incompressible fluid flow past a cylinder in free flow and past a cylinder near a moving wall in two dimensions are studied numerically. Here the velocity and pressure fields are obtained using a spectral element method based solver. The study is performed for Reynolds numbers in the low end of the periodic shedding regime and is mainly concerned with analysing vortex structures existing behind the cylinder, with main focus on the vortices surviving downstream. A vortex is defined uniquely as an extremum in vorticity and this definition is used to implement an algorithm for identifying and tracing vortices. A way of assuring that periodicity in the numerical solution has been reached using the tracing method is presented. The Reynolds number, time and ratio of cylinder diameter to distance from the wall are identified as the only independent parameters of the problems. Dynamical systems theory is used to analyse changes in the vortex structures as the independent parameters are varied. Here, two types of bifurcations are identified and characterised using existing theory. Also, all different structures for vorticity extrema and saddle-points observed in the considere