Joulin Guy, Denet Bruno
Institut Pprime, UPR No. 3346, CNRS, ENSMA, Université de Poitiers, 1 Rue Clément Ader, BP 40109, 86961 Futuroscope Cedex, Poitiers, France.
Aix-Marseille Université, IRPHE, UMR No. 7342, CNRS, Centrale-Marseille, Technopole de Château-Gombert, 49 Rue Joliot-Curie, 13384 Marseille Cedex 13, France.
Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Jun;89(6):063001. doi: 10.1103/PhysRevE.89.063001. Epub 2014 Jun 2.
Steady premixed flames subjected to space-periodic steady forcing are studied via inhomogeneous Michelson-Sivashinsky (MS) and then Burgers equations. For both, the flame slope is posited to comprise contributions from complex poles to locate, and from a base-slope profile chosen in three classes (pairs of cotangents, single-sine functions or sums thereof). Base-slope-dependent equations for the pole locations, along with formal expressions for the wrinkling-induced flame-speed increment and the forcing function, are obtained on excluding movable singularities from the latter. Besides exact few-pole cases, integral equations that rule the pole density for large wrinkles are solved analytically. Closed-form flame-slope and forcing-function profiles ensue, along with flame-speed increment vs forcing-intensity curves; numerical checks are provided. The Darrieus-Landau instability mechanism allows MS flame speeds to initially grow with forcing intensity much faster than those of identically forced Burgers fronts; only the fractional difference in speed increments slowly decays at intense forcing, which numerical (spectral) timewise integrations also confirm. Generalizations and open problems are evoked.
通过非齐次的迈克尔逊 - 西瓦什金斯基（MS）方程，然后是伯格斯方程，研究了受到空间周期稳态强迫的稳态预混火焰。对于这两种方程，火焰斜率被假定为由待定位的复极点以及从三类（双余切对、单正弦函数或它们的和）中选择的基斜率分布所构成。通过从后者中排除可移动奇点，得到了极点位置的基斜率相关方程，以及由褶皱引起的火焰速度增量和强迫函数的形式表达式。除了精确的少极点情况外，还对控制大褶皱极点密度的积分方程进行了解析求解。由此得出了封闭形式的火焰斜率和强迫函数分布，以及火焰速度增量与强迫强度曲线；并提供了数值验证。达里厄斯 - 朗道不稳定性机制使得MS火焰速度在初始阶段随强迫强度的增长比相同强迫的伯格斯前沿快得多；只有在强强迫下速度增量的分数差异才会缓慢衰减，这也得到了数值（谱）时间积分的证实。文中还提到了推广和未解决的问题。
