Collapsible tube flow
= Collapsible tube flow
A one-dimensional collapsible tube model couples area $\alpha$, mean axial <velocity> $u$ and internal <pressure> $p$: $\alpha_t+(\alpha u)_x=0$ and $u_t+uu_x=-p_x-R(\alpha)u$. A wall relation specifies internal minus external <pressure> as a function of area. Decreasing area generally increases the friction coefficient $R$, while positive wall stiffness gives real small-amplitude <wave speed>.