A convex approach to hydrodynamic analysis

We study stability and input-to-state properties of incompressible, viscous flows with perturbations that are constant in one of the directions. By taking advantage of this flow structure, we propose a class of Lyapunov and storage functionals and consider exponential stability, induced ℒ²-norms, and input-to-state stability (ISS). For streamwise constant perturbations, we formulate conditions based on matrix inequalities. We show that in the case of polynomial base flow profiles the matrix inequalities can be verified by convex optimization. The proposed method is illustrated by an example of rotating Couette flow.