Premixed flame shapes and polynomials
arXiv:1410.6037 · doi:10.1016/j.physd.2014.10.007
Abstract
The nonlinear nonlocal Michelson-Sivashinsky equation for isolated crests of unstable flames is studied, using pole-decompositions as starting point. Polynomials encoding the numerically computed 2N flame-slope poles, and auxiliary ones, are found to closely follow a Meixner Pollaczek recurrence; accurate steady crest shapes ensue for N>=3. Squeezed crests ruled by a discretized Burgers equation involve the same polynomials. Such explicit approximate shape still lack for finite-N pole-decomposed periodic flames, despite another empirical recurrence.
arXiv commentAccepted for publication in Physica D :Nonlinear Phenomena
References in corpus (10)
- The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue
- On-Shell Description of Stationary Flames
- Fast electrochemical doping due to front instability in organic semiconductors
- Unitary Random-Matrix Ensemble with Governable Level Confinement
- Flame front propagation V: Stability Analysis of Flame Fronts: Dynamical Systems Approach in the Complex Plane
- Detailed analysis of a pseudoresonant interaction between cellular flames and velocity turbulence
- The Sivashinsky equation for corrugated flames in the large-wrinkle limit
- Wrinkled flames and geometrical stretch
- Flame Wrinkles From the Zhdanov-Trubnikov Equation
- Resolvent methods for steady premixed flame shapes governed by the Zhdanov-Trubnikov equation