** Abstract: **

###
Whittaker, R.J., Heil, M., Boyle, J., Jensen, O.E., & Waters, S.L.
(2010) The energetics of flow through a rapidly oscillating tube.
Part II: Application to an elliptical tube.
*Journal of Fluid Mechanics* **648**, 123-153.

In Part I of this work, we derived general asymptotic results for the
three-dimensional flow-field and energy fluxes for flow within a tube
whose walls perform prescribed small-amplitude periodic oscillations
of high frequency and large axial wavelength. In this paper, we
illustrate how these results can be applied to the case of flow
through a finite-length axially non-uniform tube of elliptical
cross-section --- a model of flow in a Starling resistor. The results
of numerical simulations for three model problems (an axially uniform
tube under pressure--flux and pressure--pressure boundary conditions,
and an axially non-uniform tube with prescribed flux) are compared
with the theoretical predictions made in Part I, each showing
excellent agreement. When upstream and downstream pressures are
prescribed, we show how the mean flux adjusts slowly under the action
of Reynolds stresses using a multiple scale analysis. We test the
asymptotic expressions obtained for the mean energy transfer *E* from
the flow to the wall over a period of the motion. In particular, the
critical point at which *E=0* is predicted accurately: this point
corresponds to energetically neutral oscillations, the condition for
which is relevant to the onset of global instability in the Starling
resistor.

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