The thesis aims to apply recent developments of methodology from the field of linear instability theory to the study of combustion instability. The flame instability here refers to the unsteady oscillations in the reacting flow field. The eigenmode analysis for the description of self-sustained oscillations, and input-output analysis for the charac...
Published in Journal of Engineering Mathematics
We present linear stability analysis of a pressure-driven flow in a fluid-layer overlaying porous media in the presence of a Couette component introduced by an upper impermeable wall. We model the flow dynamics in the porous media by the Brinkman equation and couple it with the Navier–Stokes equation for flows in the fluid-layer. The effect of the ...
Cette étude est consacrée aux instabilités linéaires des écoulements permanents et pulsés dans des canaux à parois déformables. Le modèle de paroi consiste en une plaque mince supportée par des ressorts et des amortisseurs. Le couplage fluide-structure prend en compte toutes les contraintes visqueuses et forces de pression. L’étude des écoulements ...
Published in Heliyon
Anisotropic porous layer; Ferrofluid; Internal heating; Linear instability; Thermal convection
Published in Nonlinear Dynamics
Identification and control of transient instabilities in high-dimensional dynamical systems remain a challenge because transient (non-normal) growth cannot be accurately captured by reduced-order modal analysis. Eigenvalue-based methods classify systems as stable or unstable on the sole basis of the asymptotic behavior of perturbations and therefor...
Published in Ocean Dynamics
The nonlinear dynamics of long-wave perturbations of the inviscid Kolmogorov flow, which models periodically varying in the horizontal direction oceanic currents, is studied. To describe this dynamics, the Galerkin method with basis functions representing the first three terms in the expansion of spatially periodic perturbations in the trigonometri...
Cette thèse présente quelques contributions à l'étude qualitative de solutions d'équations aux dérivées partielles non linéaires dans des modèles issus de l'optique et de la mécanique des fluides. Nous nous intéressons plus précisément à l'existence de solutions et à leur stabilité temporelle. Le Chapitre 1 est consacré à l'équation de Lugiato-Lefe...
This work investigates the flow in a symmetric channel with a sudden expansion and contraction, creating two facing cavities, a so called double cavity. Double cavity flow at moderate Reynolds numbers is studied experimentally, numerically and analytically, as the inflow velocity and the distance between the cavities are varied. The focus is put on...
Abstract We investigate the linear stability threshold of a dielectric liquid subjected to unipolar injection in a two-dimensional rectangular enclosure with rigid boundaries. A finite element formulation transforms the set of linear partial differential equations that governs the system into a set of algebraic equations. The resulting system poses...
Published in Journal of Mathematical Chemistry
Initial stages in the evolution of linear disturbances near a homogeneous equilibrium are considered for the standard Schnakenberg and modified Schnakenberg models. The focus is on a possibility of transient amplification of perturbations. It is shown that, depending on the coefficients in the governing equations, transient growth may appear in bot...
