大褶皱极限下波纹火焰的Sivashinsky方程
The Sivashinsky equation for corrugated flames in the large-wrinkle limit
摘要：
Sivashinsky（1977）的一维波纹火焰形状的非线性积分微分方程最终可简化为2N体问题，涉及火焰斜率的2N个复极点。Thual，Frisch & Henon（1985）导出了大稳定褶皱$(N \gg 1)$极限下极点密度的奇异线性积分方程，他们对最大振幅褶皱的单聚周期性波前精确求解，对其他情况近似求解。在这里，我们解决了孤立的波峰，接下来的monocalesced然后bicoalesced周期性火焰模式，无论（大）振幅。我们比较分析预测的极密度和火焰形状的数值结果推导出的极分解方法。即使对于中等大的Ns，也能得到很好的一致性。结果被扩展到给提示，作为补充极点的动态。公开的问题被提出来。
英文摘要：
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.
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