Structural sensitivity of the finite-amplitude vortex shedding behind a circular cylinder

In this paper we study the structural sensitivity of the nonlinear periodic oscillation arising in the wake of a circular cylinder for Re47. The sensibility of the periodic state to a spatially localised feedback from velocity to force is analysed by performing a structural stability analysis of the problem. The sensitivity of the vortex shedding frequency is analysed by evaluating the adjoint eigenvectors of the Floquet transition operator. The product of the resulting neutral mode with the nonlinear periodic state is then used to localise the instability core. The results obtained with this new approach are then compared with those derived by Giannetti & Luchini [8]. An excellent agreement is found comparing the present results with the experimental data of Strykowski & Sreenivasan [7]. © 2009 Springer Science+Business Media B.V.