ME/CIMMS Lunchtime Seminar: Structural sensitivity of linear and nonlinear global modes

Paolo Luchini, Dipartimento di Ingegneria Meccanica, Universita di Salerno, Italia

In 2007 Giannetti & Luchini (JFM 581, 167) obtained a numerical confirmation of the presence of a "wavemaker" in the linear instability of  the cylinder wake, previously predicted by Pier on the basis of the asymptotic, quasi-parallel theory of global modes as formulated by Huerre & Monkewitz (1990). The tool enabling this result was the "structural sensitivity" of the global mode, i.e., the functional derivative of its frequency with respect to an external local feedback from velocity to force, seen as a function of the point in space where feedback is applied.  This sensitivity can be computed numerically from direct and adjoint global modes without any assumption of local quasi-parallelism.
                                                                
The concept of structural sensitivity makes perfect sense for nonlinear as  well as linear oscillations. More recent work has led us to computing the   structural sensitivity of the finite-amplitude periodic cycle of the cylinder wake and of its secondary instability. A general overview of the   calculation and uses of structural sensitivity in this context will be the  topic of the seminar.

http://www.cds.caltech.edu/research/related/related.php?id='621'