Nonlinear stability analysis of transitional flows using quadratic constraints
Aniketh Kalur, Peter Seiler, Maziar S. Hemati
Abstract
The dynamics of incompressible flows are governed by an interaction between non-normal linear dynamics and a static nonlinearity. We propose a framework for stability analysis that considers the linear dynamics subject to constraints that reflect the fact that the nonlinearity is quadratic and energy conserving. The approach can be used to conduct global, local, and non-modal stability analyses and to uncover dominant nonlinear flow interactions that drive these instabilities.
Topics & Concepts
Nonlinear systemQuadratic equationMathematicsLyapunov functionApplied mathematicsInstabilityStability (learning theory)Perturbation (astronomy)Control theory (sociology)PhysicsComputer scienceMechanicsControl (management)Quantum mechanicsMachine learningArtificial intelligenceGeometryFluid Dynamics and Turbulent FlowsModel Reduction and Neural NetworksAdvanced Thermodynamics and Statistical Mechanics