Document Type

Article

Publication Date

6-18-2014

Publication Source

Chaos

Volume

24

Inclusive pages

023135-1 : 02135-9

DOI

http://dx.doi.org/10.1063/1.4883500

Publisher

American Institute of Physics

Peer Reviewed

yes

Abstract

We study steady thin reaction fronts described by the Kuramoto-Sivashinsky equation that separates fluids of different densities. This system may lead to hydrodynamic instabilities as buoyancy forces interact with the propagating fronts in a two-dimensional slab. We use Darcy’s law to describe the fluid motion in this geometry. Steady front profiles can be flat, axisymmetric, or nonaxisymmetric, depending on the slab width, the density gradient, and fluid viscosity. Unstable flat fronts can be stabilized having a density gradient with the less dense fluid on top of a denser fluid. We find the steady front solutions from the nonlinear equations executing a linear stability analysis to determine their stability. We show regions of bistability where stable nonaxisymmetric and axisymmetric fronts can coexist. We also consider the stability of steady solutions in large domains, which can be constructed by dividing the domain into smaller parts or cells.

Keywords

Pattern formation, Hydrodynamic Instabilities

Disciplines

Fluid Dynamics | Physics

Share

COinS
 
 

Link to Original Published Item

http://dx.doi.org/10.1063/1.4883500