You are not currently logged in.
Access JSTOR through your library or other institution:
If You Use a Screen ReaderThis content is available through Read Online (Free) program, which relies on page scans. Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
The energetics of flow through a rapidly oscillating tube with slowly varying amplitude
Robert J. Whittaker, Matthias Heil and Sarah L. Waters
Philosophical Transactions: Mathematical, Physical and Engineering Sciences
Vol. 369, No. 1947, The mathematical challenges and modelling of hydroelasticity (28 July 2011), pp. 2989-3006
Published by: Royal Society
Stable URL: http://www.jstor.org/stable/23035843
Page Count: 18
You can always find the topics here!Topics: Kinetic energy, Energy budgets, Boundary conditions, Velocity, Energy, Mathematical growth, Inertia, Axial flow, Oscillation, Flux
Were these topics helpful?See something inaccurate? Let us know!
Select the topics that are inaccurate.
Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Preview not available
Motivated by the problem of self-excited oscillations in fluid-filled collapsible tubes, we examine the flow structure and energy budget of flow through an elastic-walled tube. Specifically, we consider the case in which a background axial flow is perturbed by prescribed small-amplitude high-frequency long-wavelength oscillations of the tube wall, with a slowly growing or decaying amplitude. We use a multiple-scale analysis to show that, at leading order, we recover the constant-amplitude equations derived by Whittaker et al. (Whittaker et al. 2010 J. Fluid Mech. 648, 83—121. (doi:10.1017/S0022112009992904)) with the effects of growth or decay entering only at first order. We also quantify the effects on the flow structure and energy budget. Finally, we discuss how our results are needed to understand and predict an instability that can lead to self-excited oscillations in collapsible-tube systems.
Philosophical Transactions: Mathematical, Physical and Engineering Sciences © 2011 Royal Society