Related papers: Rakib-Sivashinsky and Michelson-Sivashinsky Equati…
We revisit the Near Equidiffusional Flames (NEF) model introduced by Matkowsky and Sivashinsky in 1979 and consider a simplified, quasi-steady version of it. This simplification allows, near the planar front, an explicit derivation of the…
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…
The (Michelson) Sivashinsky equation of premixed flames is studied in a rectangular domain in two dimensions. A huge number of 2D stationary solutions are trivially obtained by addition of two 1D solutions. With Neumann boundary conditions,…
The non linear description of laminar premixed flames has been very successful, because of the existence of model equations describing the dynamics of these flames. The Michelson Sivashinsky equation is the most well known of these…
The problem of non-perturbative description of stationary flames with arbitrary gas expansion is considered. On the basis of the Thomson circulation theorem an implicit integral of the flow equations is constructed. With the help of this…
We study the stability and dynamics of traveling-front solutions of a modified Kuramoto--Sivashinsky equation arising in the modeling of nanoscale ripple patterns that form when a nominally flat solid surface is bombarded with a broad ion…
New stationary solutions of the (Michelson) Sivashinsky equation of premixed flames are obtained numerically in this paper. Some of these solutions, of the bicoalescent type recently described by Guidi and Marchetti, are stable with Neumann…
The Michelson Sivashinsky equation, which models the non linear dynamics of premixed flames, has been recently extended to describe oblique flames. This approach was extremely successful to describe the behavior on one side of the flame,…
A theory of flame propagation in curved channels is developed within the framework of the on-shell description of premixed flames. Employing the Green function appropriate to the given channel geometry, an implicit integral representation…
The nonlinear nonlocal Michelson-Sivashinsky equation for isolated crests of unstable flames is studied, using pole-decompositions as starting point. Polynomials encoding the numerically computed 2N flame-slope poles, and auxiliary ones,…
Steady propagation of premixed flames in straight channels is studied numerically using the on-shell approach. A first numerical algorithm for solving the system of nonlinear integro-differential on-shell equations is presented. It is based…
This work is dedicated to the analysis of the delicate details of the effect of upstream velocity fluctuations on the flame propagation speed. The investigation was carried out using the Sivashinsky model of cellularisation of…
The problem of non-perturbative description of unsteady premixed flames with arbitrary gas expansion is solved in the two-dimensional case. Considering the flame as a surface of discontinuity with arbitrary local burning rate and gas…
We consider flame front propagation in channel geometries. The steady state solution in this problem is space dependent, and therefore the linear stability analysis is described by a partial integro-differential equation with a space…
The stability of a thick planar premixed flame, propagating steadily in a direction transverse to that of unidirectional shear flow, is studied. A linear stability analysis is carried out in the asymptotic limit of infinitely large…
A nonlinear equation describing curved stationary flames with arbitrary gas expansion $\theta = \rho_{{\rm fuel}}/\rho_{{\rm burnt}}$, subject to the Landau-Darrieus instability, is obtained in a closed form without an assumption of weak…
In this work we estimate rates of the linear transient growth of the perturbations of cellular flames governed by the Sivashinsky equation. The possibility and significance of such a growth was indicated ear- lier in both computational and…
Nonlinear non-stationary equation describing evolution of weakly curved premixed flames with arbitrary gas expansion, subject to the Landau-Darrieus instability, is derived. The new equation respects all the conservation laws to be…
The problem of premixed flame propagation in wide horizontal tubes is revisited. Employing the on-shell description of flames with arbitrary gas expansion, a nonlinear second-order differential equation for the front position of steady…
We first briefly recall the basic mechanisms controlling the hydrodynamic and thermo-diffusive stability of planar laminar premixed flames, and give the state of the theoretical analysis. We then describe some novel experiments to observe…