Abstract:
The method of feedback control on the stability of vortices is studied for an inviscid incompressible base flow subjected to an axisymmetric disturbance in a circular pipe with non-periodic boundary conditions. The investigation first focuses on the linear asymptotic equation with the control parameter applied. This is done to investigate the dynamics of the first growth rate branch curve because of the ease to apply constraints and the reduced complexity (allowing for analytical solutions) of the linear asymptotic equation. Numerical analysis indicates that the asymptotic equation is controllable, prompting the investigation of the same control mechanism applied to the linear WR equation. Since the asymptotic equation is only accurate to swirls up to and near the first growth rate branch, investigation focuses on whether the global equation is controllable and the effectiveness of said control mechanism. While this technique is only based on the specific solid body rotation flow (for its weakly non-linearity), investigation will pave way for improving the control mechanism and better understanding the dynamics of vortex stability of non-linear vortex flows.