Advanced instability methods using spectral/hp discretisations and their applications to complex geometries

Controlling wakes of flows past bluff bodies is a fundamental problem in a wide range of engineering applications. In the present work, we investigate such problems theoretically and numerically using linear stability analysis. We initially consider a flow past a cylinder in a fully developed vortex shedding regime, and we apply sufficiently high spanwise forcing on the surface of the cylinder to stabilise the near-wake. The effects on the aerodynamic forces, the wake topology and the dynamics of the vorticity are investigated using spanwise sinusoidal and Gaussian forcing. Stability analysis of the linearised Navier-Stokes equations is then performed on the fully three-dimensional flow to investigate the role of the spanwise modulation on the absolute instability associated with the von-Kármán street. The three-dimensional global modes allows us to detect the regions where the instability acts, and the interactions of the perturbations with the base flow shed light on the most relevant mechanism for the wake stabilisation. Additional relevant information on the design of an efficient control device are provided by receptivity analysis and the structural sensitivities. A similar approach is used to study the stability of a flow through a compressor passage at a Re = 138, 500. Due to the complexity of both the geometry and dynamics of the flow, a phase-averaging technique is used to generate a globally periodic basic flow, extracting only the organised structures and neglecting all the background unsteadiness. This approach allows us to perform Floquet and transient growth analyses to detect the structure of the global modes and the presence of convective instabilities.