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Article overview
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Flame Wrinkles From the Zhdanov-Trubnikov Equation | Guy Joulin
; Bruno Denet
; | Date: |
30 Apr 2012 | 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<c<0 (reduced stabilization). Although locally ill-behaved if c>0
(over-stabilization) such analytical solutions can yield accurate flame shapes
for 0< c <0.6. Open problems are invoked. | Source: | arXiv, 1204.6565 | Services: | Forum | Review | PDF | Favorites |
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