title: Shapes and speeds of steady forced premixed flames.
abstract: 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.
authors.affiliation: Institut Pprime, UPR No. 3346, CNRS, ENSMA, Université de Poitiers, 1 Rue Clément Ader, BP 40109, 86961 Futuroscope Cedex, Poitiers, France.
authors.forename: Guy
authors.initials: G
authors.lastname: Joulin
authors.affiliation: Aix-Marseille Université, IRPHE, UMR No. 7342, CNRS, Centrale-Marseille, Technopole de Château-Gombert, 49 Rue Joliot-Curie, 13384 Marseille Cedex 13, France.
authors.forename: Bruno
authors.initials: B
authors.lastname: Denet
mesh_terms: D008962:Models, Theoretical; D017711:Nonlinear Dynamics