Structural sensitivity of linear and nonlinear global modes

The concept of "structural sensitivity" of a global mode is introduced and used to study the formation of the classical Kármá nvortex street in the wake of a circular cylinder. By evaluating the functional derivative of the global mode frequency with respect to an external local feedback from velocity to force, we show how to locate the "wavemaker" of the asymptotic theory, i.e.the point in space where the instability originates and from which propagates as a wave in all direction. This can be done by exploiting the properties of the numerically computed direct and adjoint global eigenfunctions, without any assumptions on the quasi-parallelism of the flow. This new approach is presented both in the context of linear as well nonlinear oscillations. Finally, recent results obtained by the application of the structural sensitivity concept to the study of the secondary instability of the cylinder wake are shown and discussed.