Mode selection in concentric jets. The steady-steady 1:2 resonant mode interaction with O(2) symmetry

TL;DR

This paper thoroughly analyzes the flow dynamics of two concentric jets at low Reynolds numbers, revealing complex bifurcations, mode interactions, and stable heteroclinic cycles through stability analysis.

Contribution

It provides a detailed characterization of mode interactions and bifurcations in concentric jets, including the identification of resonant modes with O(2) symmetry.

Findings

Identification of critical Reynolds numbers for flow bifurcations

Discovery of traveling waves from steady state interactions

Existence of asymptotically stable heteroclinic cycles

Abstract

In this article, a thorough characterization of the configuration composed by two concentric jets at a low Reynolds number is presented. The analysis comprises a layout with a wide range for the velocity ratio between the inner and outer jets, defined within the interval [0, 2], and also details the influence of the distance between jets, where the wall thicknesses separating the two jets is [0.5, 4]. Global linear stability analysis identifies the most significant modes driving the changes in the flow dynamics. The neutral lines revealing the critical Reynolds number connected to the presence of the main (steady and unsteady) flow bifurcations, which are presented by global azimuthal modes, show the high complexity of the problem under study, where hysteresis and other types of complex cycles are pointed out. Finally, the mode interaction is analysed, highlighting the presence of travelling waves emerging from the interaction of steady states, and the existence of robust heteroclinic cycles that are asymptotically stable. The high level of detail in the results presented, makes this work as a reference for future research development in the field of concentric jets.