The stability properties of the flow past an infinitely long circular cylinder are studied in the context of linear theory. An immersed-boundary technique is used to represent the cylinder surface on a Cartesian mesh. The characteristics of both direct and adjoint perturbation modes are studied and the regions of the flow more sensitive to momentum forcing and mass injection are identified. The analysis shows that the maximum of the perturbation envelope amplitude is reached far downstream of the separation bubble, where as the highest receptivity is attained in the near wake of the cylinder, close to the body surface. The large difference between the spatial structure of the two-dimensional direct and adjoint modes suggests that the instability mechanism cannot be identified from the study of either eigenfunctions separately. For this reason a structural stability analysis of the problem is used to analyse the process which gives rise to the self-sustained mode. In particular, the region of maximum coupling among the velocity components is localized by inspecting the spatial distribution of the product between the direct and adjoint modes. Results show that the instability mechanism is located in two lobes placed symmetrically across the separation bubble, confirming the qualitative results obtained through a locally plane- wave analysis. The relevance of this novel technique to the development of effective control strategies for vortex shedding behind bluff bodies is illustrated by comparing the theoretical predictions based on the structural perturbation analysis with the experimental data of Strykowski & Sreenivasan (J. Fluid Mech. vol. 218, 1990, p. 71)

The two-dimensional flow around a rotating circular cylinder is studied at Re = 100. The instability mechanisms for the first and second shedding modes are analysed. The region in the flow with a role of ‘wavemaker’ in the excitation of the global instability is identified by considering the structural sensitivity of the unstable mode. This approach is compared with the analysis of the perturbation kinetic energy production, a classic approach in linear stability analysis. Multiple steady-state solutions are found at high rotation rates, explaining the quenching of the second shedding mode. Turning points in phase space are associated with the movement of the flow stagnation point. In addition, a method to examine which structural variation of the base flow has the largest impact on the instability features is proposed. This has relevant implications for the passive control of instabilities. Finally, numerical simulations of the flow are performed to verify that the structural sensitivity analysis is able to provide correct indications on where to position passive control devices, e.g. small obstacles, in order to suppress the shedding modes.

The sensitivity of the three-dimensional secondary instability of a circular-cylinder wake to a structural perturbation of the associated linear equations is investigated. In particular, for a given flow condition, the region of maximum coupling between the velocity components is localized by using the most unstable Floquet mode and its adjoint mode. The variation of this region in time is also found by considering a structural perturbation which is impulsively applied in time at a given phase of the vortex-shedding process. The analysis is carried out for both mode A and mode B types of transition in the wake of a circular cylinder using a finite-difference code. The resulting regions identified as the core of the instability are in full agreement with the results reported in the literature and with the a posteriori checks documented here

The first bifurcation and the instability mechanisms of shear-thinning and shear-thickening fluids flowing past a circular cylinder are studied using linear theory and numerical simulations. Structural sensitivity analysis based on the idea of a ‘wavemaker’ is performed to identify the core of the instability. The shear-dependent viscosity is modelled by the Carreau model where the rheological parameters, i.e. the power-index and the material time constant, are chosen in the range 0.4

The two-dimensional stationary flow past a rotating cylinder is analyzed for both two and three-dimensional perturbations. The instability mechanisms for the high and low- frequency modes are analyzed and the complete neutral curve presented. It is shown that the first bifurcation in the case of the rotating cylinder occurs for stationary three- dimensional perturbations, confirming recent experiments. Interestingly, the critical Reynolds number at high rotation rates is lower than the one for the stationary circular cylinder. The spatial characteristics of the disturbance and a qualitative comparison with the re- sults obtained for linear flows suggest that the stationary unstable three-dimensional mode could be of a hyperbolic nature