title: Fluid dynamic instabilities: theory and application to pattern forming in complex media.
abstract: In this review article, we exemplify the use of stability analysis tools to rationalize pattern formation in complex media. Specifically, we focus on fluid flows, and show how the destabilization of their interface sets the blueprint of the patterns they eventually form. We review the potential use and limitations of the theoretical methods at the end, in terms of their applications to practical settings, e.g. as guidelines to design and fabricate structures while harnessing instabilities.This article is part of the themed issue 'Patterning through instabilities in complex media: theory and applications'.
authors.affiliation: Laboratory of Fluid Mechanics and Instabilities, Ecole Polytechnique Federale de Lausanne, Lausanne 1015, Switzerland francois.gallaire@epfl.ch.
authors.forename: François
authors.identifier: http://orcid.org/0000-0002-3029-1457
authors.initials: F
authors.lastname: Gallaire
authors.affiliation: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA.
authors.forename: P-T
authors.initials: PT
authors.lastname: Brun
keywords: free interface; instabilities; pattern