Local and global instability of fluid-conveying cantilever pipes

The flutter of a cantilever fluid-conveying pipe is one of the most generic problems of flow-induced vibrations. In its simplest model, linear stability is lost as the flow velocity is increased, at a threshold which depends on the mechanical parameters of the system. This is a global instability. An infinite pipe modeled with the same local equations experience local instability as soon as the fluid is put into motion. When an elastic foundation is present, cases of local stability with global instability, or, conversely, local instability with global stability are found. The purpose of this paper is to address the question of compatibility between local and global approaches. More specifically, when an elastic foundation is present, we give a criterion on traveling waves to allow a global instability to develop.