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Modal decomposition of hopping states in cellular flames
Antonio Palacios1, Michael Gorman, Gemunu H. Gunaratne
1Department of Mathematics, San Diego State University, San Diego, California 92812.
Chaos (Woodbury, N.Y.)
|June 5, 2003
Summary
Cellular flames exhibit a unique "hopping state" where cells in a ring shift position. Karhunen-Loeve decomposition reveals this spatiotemporal dynamic, arising from secondary bifurcations of traveling waves.
Area of Science:
- Fluid dynamics
- Combustion science
- Nonlinear dynamics
Background:
- Cellular flames display ordered states with concentric rings of luminous cells.
- A unique spatiotemporal dynamic, the "hopping state," involves sequential angular repositioning of individual cells within a ring.
- Understanding these dynamics is crucial for flame behavior analysis.
Purpose of the Study:
- To analyze the spatiotemporal dynamics of the
- hopping state
- in cellular flames using Karhunen-Loeve (KL) decomposition.
Main Methods:
- Application of KL decomposition to video images of cellular flames.
- Analysis of spatial and temporal characteristics of the hopping motion.
- Deduction of normal form equations based on experimental symmetries.
Main Results:
- KL decomposition successfully separated spatial and temporal features of the hopping motion.
- Normal form equations were derived, describing the formation of hopping states.
- Hopping states were identified as mixed-mode solutions resulting from secondary bifurcations.
Conclusions:
- The hopping state in cellular flames originates from secondary bifurcations of traveling waves.
- The study provides a mathematical framework for understanding this complex flame behavior.
- KL decomposition is an effective tool for analyzing spatiotemporal dynamics in combustion systems.