The Sivashinsky equation for corrugated flames in the large-wrinkle limit

Abstract

Sivashinsky's (1977) nonlinear integro-differential equation for the shape of corrugated 1-dimensional flames is ultimately reducible to a 2N-body problem, involving the 2N complex poles of the flame slope. Thual, Frisch & Henon (1985) derived singular linear integral equations for the pole density in the limit of large steady wrinkles $(N\gg 1)$, which they solved exactly for monocoalesced periodic fronts of highest amplitude of wrinkling and approximately otherwise. Here we solve those analytically for isolated crests, next for monocoalesced then bicoalesced periodic flame patterns, whatever the (large-) amplitudes involved. We compare the analytically predicted pole densities and flame shapes to numerical results deduced from the pole-decomposition approach. Good agreement is obtained, even for moderately large Ns. The results are extended to give hints as to the dynamics of supplementary poles. Open problems are evoked.

References in corpus (5)

• Kicked Burgers Turbulence
• On-Shell Description of Stationary Flames
• Stationary solutions and Neumann boundary conditions in the Sivashinsky equation
• Flame front propagation V: Stability Analysis of Flame Fronts: Dynamical Systems Approach in the Complex Plane
• Sivashinsky equation in a rectangular domain

Cited by in corpus (6)

• Potential-flow models for channelled two-dimensional premixed flames around near-circular obstacles
• 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
• Shapes and speeds of forced premixed flames
• Premixed flame shapes and polynomials