title: Coupled continuous-time random walks for fluid stretching in two-dimensional heterogeneous media.
abstract: We study the relation between flow structure and fluid deformation in steady flows through two-dimensional heterogeneous media, which are characterized by a broad spectrum of stretching behaviors, ranging from sub- to superlinear. We analyze these behaviors from first principles, which uncovers intermittent shear events to be at the origin of subexponential stretching. We derive explicit expressions for Lagrangian deformation and demonstrate that stretching obeys a coupled continuous-time random walk, which for broad distributions of flow velocities becomes a Lévy walk. The derived model provides a direct link between the flow and deformation statistics, and a natural way to quantify the impact of intermittent shear events on the stretching behavior.
authors.affiliation: Spanish National Research Council (IDAEA-CSIC), 08034 Barcelona, Spain.
authors.forename: Marco
authors.initials: M
authors.lastname: Dentz
authors.affiliation: School of Engineering, RMIT University, 3000 Melbourne, Victoria, Australia.
authors.forename: Daniel R
authors.initials: DR
authors.lastname: Lester
authors.affiliation: Geosciences Rennes, UMR 6118, Université de Rennes 1, CNRS, Rennes, France.
authors.forename: Tanguy
authors.initials: T
authors.lastname: Le Borgne
authors.affiliation: Sonny Astani Department of Civil and Environmental Engineering, University of Southern California, 3620 South Vermont Avenue, KAP 224B, Los Angeles, California 90089, USA.
authors.forename: Felipe P J
authors.initials: FP
authors.lastname: de Barros