A model for limit-cycle switching in open cavity flow

TL;DR

This paper introduces a reduced mathematical model for open cavity flow that captures complex dynamics like limit-cycle switching and bifurcations, providing insights into flow stability and transitions.

Contribution

It develops a novel reduced model using center manifold theory that explains limit-cycle switching and stability exchanges in open cavity flow.

Findings

Model captures key flow dynamics including unstable quasi-periodic states.

Explains limit-cycle stability exchange via cross-coupling in amplitude equations.

Demonstrates bifurcation behavior consistent with observed flow phenomena.

Abstract

A reduced mathematical model for the flow in an open cavity is presented. The reduction is based on the center manifold theory applied to a perturbation of the original system which allows for a codimension two bifurcation point. The model exhibits many of the key characteristics observed in the flow dynamics including unstable quasi-periodic edge states as well as switching of limit cycles with parameter variations. An explanation for the exchange of stabilities of the limit-cycles is presented based on the cross-coupling terms of the two amplitude equations.