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Updated: Mar 12, 2026

Fabrication, Operation and Flow Visualization in Surface-acoustic-wave-driven Acoustic-counterflow Microfluidics
Published on: August 27, 2013
Streamwise decay of localized states in channel flow
Stefan Zammert1, Bruno Eckhardt2,3
1Laboratory for Aero and Hydrodynamics, TU Delft, 2628 CD Delft, The Netherlands.
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.
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