Abstract
A general framework based on the extended Hamilton’s principle for external viscous flows is presented. The indicated method is shown to yield the correct governing equations and boundary conditions when applied to the problem (herein called the “model problem”) of vortex-induced oscillations of an elastically-mounted rigid circular cylinder with a transverse degree-of-freedom. The vortex shedding is assumed to be sufficiently correlated along the span of the cylinder that the flow can be taken as nominally two-dimensional. The incoming flow is assumed to be incompressible, steady, and uniform. The continuity equation results directly from the global mass balance law, thus avoiding its introduction via a Lagrange multiplier. The true strength of this framework lies in the fact that it represents a physically sound basis from which reduced-order models can be obtained. Some preliminary work on this reduced-order modeling applied to the model problem is described.