title: Streamwise decay of localized states in channel flow.
abstract: Channel flow, the pressure driven flow between parallel plates, has exact coherent structures that show various degrees of localization. For states which are localized in streamwise direction but extended in spanwise direction, we show that they are exponentially localized, with decay constants that are different on the upstream and downstream sides. We extend the analysis of Brand and Gibson [J. Fluid Mech. 750, R1 (2014)]JFLSA70022-112010.1017/jfm.2014.285 for stationary states to the case of advected structures that is needed here, and derive expressions for the decay in terms of eigenvalues and eigenfunctions of certain second order differential equations. The results are in very good agreement with observations on exact coherent structures of different transversal wavelengths.
authors.affiliation: Laboratory for Aero and Hydrodynamics, TU Delft, 2628 CD Delft, The Netherlands.
authors.forename: Stefan
authors.initials: S
authors.lastname: Zammert
authors.affiliation: Fachbereich Physik, Philipps-Universität Marburg, D-35032 Marburg, Germany.|JM Burgerscentrum, TU Delft, 2628 CD Delft, The Netherlands.
authors.forename: Bruno
authors.initials: B
authors.lastname: Eckhardt