The stability of two-dimensional cylinder wakes in the presence of a wavy ground

A local and global linear stability analysis was conducted for flow past a circular cylinder in the presence of wavy ground. The relative position of the cylinder with respect to the wavy ground was varied for four different cases. The global stability computations were performed using Nektar++, which utilized spectral/hp element methods. The baseflow for each case was obtained by increasing the Reynolds number (Re) until the lift coefficient varied through time by less than 10^-6. Stability analysis was then performed on the baseflow. The results of the simulations indicated an increase in the critical Re when compared to the basic flow past cylinder (Critical Re = 45). A critical value of approximately Re = 65 was found for cases 1-3, and a value of approximately Re = 200 was found for case 4. The various cases were also simulated at Re = 200, which showed boundary layer effects from the wavy ground and vorticity generation from the peaks of the wavy ground that convected into the cylinder wake. Skewed trajectories of vortices shed from the cylinder were also observed for cases 1-3 at Re = 200. The eigenmodes for cases 1-3 skewed upward as they traveled downstream, and the vortex shedding mode, which is most dominant for basic flow past a cylinder, got suppressed for cases 1-4.