** Abstract: **

###
Whittaker, R.J., Waters, S.L., Jensen, O.E., Boyle, J. & Heil,
M. (2010) The energetics of flow through a rapidly oscillating tube.
Part I: General theory. *Journal of Fluid Mechanics*
**648**, 83-121.

We examine the effect of prescribed wall-driven oscillations of a
flexible tube of arbitrary cross-section, through which a flow is
driven by prescribing either a steady flux at the downstream end, or a
steady pressure difference between the ends. A large-Womersley-number
large-Strouhal-number regime is considered, in which the oscillations
of the wall are small in amplitude, but sufficiently rapid to ensure
viscous effects are confined to a thin boundary layer. We derive
asymptotic expressions for the flow fields and evaluate the energy
budget. A general result for the conditions under which there is zero
net energy transfer from the flow to the wall is provided. This is
presented as a critical inverse Strouhal number (a dimensionless
measure of the background flow rate) which is expressed only in terms
of the tube geometry, the fluid properties, and the profile of the
prescribed wall oscillations. Our results identify an essential
component of a mechanism for self-excited oscillations in
three-dimensional collapsible tube flows, and enable us to assess how
geometric and flow properties affect the stability of the system.

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