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arXiv · 1204.6565

Flame Wrinkles From the Zhdanov-Trubnikov Equation

Guy Joulin·Bruno Denet
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Abstract

The Zhdanov-Trubnikov equation describing wrinkled premixed flames is studied, using pole-decompositions as starting points. Its one-parameter (-1< c <1) nonlinearity generalizes the Michelson-Sivashinsky equation (c=0) to a stronger Darrieus-Landau instability. The shapes of steady flame crests (or periodic cells) are deduced from Laguerre (or Jacobi) polynomials when c = -1, which numerical resolutions confirm. Large wrinkles are analysed via a pole density: adapting results of Dunkl relates their shapes to the generating function of Meixner-Pollaczek polynomials, which numerical results confirm for 1 0 (over-stabilization) such analytical solutions can yield accurate flame shapes for 0< c <0.6. Open problems are invoked.

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Guy Joulin, Bruno Denet. 2012-04-30. Flame Wrinkles From the Zhdanov-Trubnikov Equation. https://doi.org/10.1016/j.physleta.2012.03.062

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