Local stability analysis along Lagrangian paths

We study the stability of a hydrodynamical flow by analysing the evolution of perturbations as advected along Lagrangian trajectories. This approach unifies and generalizes previous treatments of elliptical and centrifugal instabilities. To determine the role of viscosity and boundary conditions, we analyse the case of Couette flow between rotating cylinders. It is then applied to ABC flows with chaotic stream lines. A scaling relation between the Eulerian growth rate of perturbations, a Lagrangian growth rate determined from trajectories and the Reynolds number is derived and verified.