Adjoint Equations in Stability Analysis: Supplemental Video 2

A supplemental video from the 2014 review by Paolo Luchini and Alessandro Bottaro, "Adjoint Equations in Stability Analysis," from the Annual Review of Fluid Mechanics. 

Structural sensitivity map of the secondary instability of the cylinder wake mode A (Re = 190), calculated as in Giannetti et al. (2010a). The structural sensitivity of this mode is a function of two spatial coordinates and a periodic function of time, just as its base flow is. The sensitivity peak marks the location of the wave maker and its motion during the oscillation period, showing that this structural sensitivity is even more localized (at each instant of time) than the sensitivity of the primary instability (Figure 6 of the article). The three material closed orbits of the primary instability are superimposed on the sensitivity map.