Coherent Structures in Flame Fronts

TL;DR

This paper investigates traveling wave solutions in a model of flame fronts, proving their existence and computing them within a framework that describes the interface between burnt and unburnt gases.

Contribution

It establishes the existence and provides computational methods for traveling wave solutions in a coordinate-free flame front model.

Findings

Existence of traveling wave solutions in the model.

Explicit computation of these wave solutions.

Framework applicable to periodic and unbounded settings.

Abstract

We study traveling waves in a coordinate-free model of flame fronts. The flame front is the interface between the burnt and unburnt phases of a gas undergoing combustion. The front therefore moves in a preferred direction, as the unburnt gas is consumed. In the horizontally periodic, vertically unbounded setting, we prove the existence of waves of permanent form which are traveling in the vertical direction. We also compute these waves. The analysis and computation use the framework of traveling waves in the arclength parameterization as previously developed by two of the authors and Wright.