Exact geometric theory for flexible,fluid-conducting tubes

Instability of flexible tubes conducting fluid, or “garden hose instability”, is a phenomenon both familiar from everyday life and important for applications, which has been actively studied. However, previous works did not consider one of the most crucial physical effects — the dynamical change of the cross-section. We show how to consistently address this issue by coupling the geometrically exact rod dynamics with the fluid motion via the use of a constrained Hamilton's variational principle. We find strong effect of this dynamics on stability, and derive a variety of exact nonlinear solutions of traveling-wave type.