Canard explosions in turbulent thermo-fluid systems

TL;DR

This paper reports the experimental observation of a canard explosion in a turbulent thermo-fluid system, revealing a continuous transition with rapid amplitude increase via bursting, supported by a phenomenological slow-fast dynamics model.

Contribution

It presents the first experimental evidence of a canard explosion in turbulent reactive flows and introduces a phenomenological model to explain the observed bifurcation behavior.

Findings

Discovered a canard explosion in turbulent reactive flow systems.

Observed a continuous transition with rapid amplitude growth via bursting.

Developed a model explaining the slow-fast dynamics at the bifurcation.

Abstract

A sudden transition to a state of high amplitude limit cycle oscillations is catastrophic in a thermo-fluid system. Conventionally, upon varying the control parameter, a sudden transition is observed as an abrupt jump in the amplitude of the fluctuations in these systems. In contrast, we present an experimental discovery of a canard explosion in a turbulent reactive flow system where we observe a continuous bifurcation with a rapid rise in the amplitude of the fluctuations within a narrow range of control parameters. The observed transition is facilitated via a state of bursting, consisting of the epochs of large amplitude periodic oscillations amidst the epochs of low amplitude periodic oscillations. The amplitude of the bursts is higher than the amplitude of the bursts of intermittency state in a conventional gradual transition, as reported in turbulent reactive flow systems. During the bursting state, we observe that temperature fluctuations of exhaust gas vary at a slower time scale in correlation with the amplitude envelope of the bursts. We also present a phenomenological model for thermoacoustic systems to describe the observed canard explosion. Using the model, we explain that the large amplitude bursts occur due to the slow-fast dynamics at the bifurcation regime of the canard explosion.