Modeling and Analysis

The premixed flames experiment is a pattern-forming system with circular symmetry. Many distinct cellular patterns form as a result of symmetry-breaking bifurcations from the uniform flame front. These patterns in turn lose stability resulting in cell motions ranging from uniform rotation to chaotic dynamics.

Phenomenological Model: Numerical solution to a full nonlinear model is formidable due to singularities that arise because of circular geometry. However, a phenomenological model reproduces the behavior remarkably well and provides insight into the universal nature of the underlying bifurcations.

Karhunen-Loeve Analysis is used to reveal the primary modes leading to nonstationary patterns. The projection of the original data on the K-L modes reveal the nature of the bifurcations.