The Mechanics of Elastic-Walled Tubes Seminar

I shall talk about two related pieces of work concerning elastic-walled tubes, motivated by flows in biological systems.

The first concerns a long-wavelength, high-frequency instability in a fluid-filled elastic tube with an imposed mean flow. I shall describe asymptotic models for the fluid flow and the wall mechanics (a ""tube law""), and how these can be combined to predict the normal modes of the system and their growth rates.

The second concerns an asymptotic description of a boundary layer that occurs near the ends of an elastic-walled tube which is buckled in the middle but clamped to rigid supports at the ends. When the tube wall is very thin, the boundary layer modifies the tube-end boundary conditions of the ""tube law"" developed above, in order to account for shear effects near the ends.

In both cases, the asymptotic results compare favourably with numerical simulations conducted by Matthias Heil using the Oomph-lib framework.