A Convex Approach to Hydrodynamic Analysis

Abstract

We study stability and input-state analysis of three dimensional (3D) incompressible, viscous flows with invariance in one direction. By taking advantage of this invariance property, we propose a class of Lyapunov and storage functionals. We then consider exponential stability, induced L2-norms, and input-to-state stability (ISS). For streamwise constant flows, we formulate conditions based on matrix inequalities. We show that in the case of polynomial laminar flow profiles the matrix inequalities can be checked via convex optimization. The proposed method is illustrated by an example of rotating Couette flow.

Preliminary version submitted to 54rd IEEE Conference on Decision and Control, Dec. 15-18, 2015, Osaka, Japan

References in corpus (1)

• Global Stability Analysis of Fluid Flows using Sum-of-Squares

Cited by in corpus (2)

• A Framework for Input-Output Analysis of Wall-Bounded Shear Flows
• Optimization with affine homogeneous quadratic integral inequality constraints