Universal dynamics in the onset of a Hagen-Poiseuille flow

Asger Mortensen, Henrik Bruus

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    Abstract

    The dynamics in the onset of a Hagen-Poiseuille flow of an incompressible liquid in a channel of circular cross section is well-studied theoretically. We use an eigenfunction expansion in a Hilbert space formalism to generalize the results to channels of an arbitrary cross section. We find that the steady state is reached after a characteristic time scale tau=(A/P)(2)(1/nu), where A and P are the cross-sectional area and perimeter, respectively, and nu is the kinematic viscosity of the liquid. For the initial dynamics of the flow rate Q for t
    Original languageEnglish
    JournalPhysical Review E
    Volume74
    Issue number1
    Pages (from-to)017301
    ISSN2470-0045
    DOIs
    Publication statusPublished - 2006

    Bibliographical note

    Copyright 2006 American Physical Society

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