The nonlinear dynamics of elastic tubes conveying a fluid

The Kirchhoff equations for elastic tubes are modified to include the effect of fluid flow. Using the techniques of linear and nonlinear analysis specially developed for the Kirchhoff equations, the effect of the fluid flow on the basic twist-to-writhe instability is investigated. The results suggest an intriguing modification of the bifurcation threshold due to the flow. Beyond threshold the buckled tube acquires a slight curvature which modifies the flow rate and results in a correction to nonlinearity of the amplitude equation governing the deformation dynamics.