2:15 PM - 2:30 PM
[MIS15-09] Singular-Value Analyses of Perturbations on a Cylindrical Vortex Sheet
Keywords:singular-value analysis, cylindrical vortex sheet, multiple vortex
Here, it is necessary to carry out a singular-value analysis, not an eigenvalue analysis, to detect a possible perturbation which grows most rapidly during a given finite target time. This is because such an optimally-excited perturbation is, even if the equation is linear, not necessarily the most unstable eigen mode due to a non-normality of the governing equation. In this study, therefore, a singular-value analysis is carried out instead of an eigenvalue analysis. Three norms (i.e. L2 norm, energy norm, and Sobolev norm) are adopted as indices to measure the growth of perturbations, and then analytical forms of singular-values are derived for each norm. As a result of the analyses, it is revealed that non-normal growth of the perturbations is seen in all parameter space, where the amplitude of perturbations under L2 norm is generally largest and that under energy norm is the minimum.