Premixed-flame shapes and polynomials

Bruno Denet (1) , Guy Joulin (2)

1 IRPHE - Institut de Recherche sur les Phénomènes Hors Equilibre
2 PPrime [Poitiers] - Institut Pprime [UPR 3346]

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.

Mots clés: Flame shapes; Nonlinear Nonlocal Equation; Poles; Polynomials; Recurrence

Domaines: Formation de Structures et Solitons [nlin.PS]; Mécanique des fluides [physics.class-ph]; Milieux fluides et réactifs

Bruno Denet, Guy Joulin. Premixed-flame shapes and polynomials. Physica D: Nonlinear Phenomena, 2015, 292, pp.46 - 50. ⟨10.1016/j.physd.2014.10.007⟩. ⟨hal-01084853⟩