Regional Stability Analysis of Transitional Fluid Flows

TL;DR

This paper introduces a new method for regional stability analysis of transitional fluid flows, improving the bounds on maximum energy perturbations by exploiting nonlinear properties and ellipsoid axes in stability conditions.

Contribution

The paper presents a novel approach that enhances stability bounds for fluid flow models by utilizing lossless nonlinearities and ellipsoid axes as variables.

Findings

Increased maximum energy perturbation bounds by 29% for WKH shear flow.

Increased bounds by 38% for a reduced Couette flow model.

Method outperforms existing approaches in stability analysis.

Abstract

A method to bound the maximum energy perturbation for which regional stability of transitional fluid flow models can be guaranteed is introduced. The proposed method exploits the fact that the fluid model's nonlinearities are both lossless and locally bounded and uses the axes lengths of the ellipsoids for the trajectory set containment as variables in the stability conditions. Compared to existing approaches, the proposed method leads to an average increase in the maximum allowable energy perturbation of 29% for the Waleffe-KimHamilton (WKH) shear flow model and of 38% for the 9-state reduced model of Couette flow.