Linear Stability of Fluid Flows and its Applications (Topology optimization theory and applications toward wide fields of natural sciences)

Abstract

First, mathematical formulation of linear stability analysis in fluid mechanics is given. Next, several examples in which the linear stability analysis was successfully applied are presented. Then, bifurcation diagrams are shown, and the basic equations by which fluid motions are calculated for specific boundary conditions are explained. Finally, numerical methods to obtain quasi‐analytic solutions in high accuracy are addressed, on which the perturbation is superimposed and thus the linear stability analysis can be applied, in the case that an exact solution is difficult to obtain.