Hydroelasticity of the kirchhoff rod: Buckling phenomena

We consider the nonlinear coupled hydroelastic problem of a general curved and twisted flexible slender structure (i.e. flexible riser, cable system, fish-farm net system, towed arrays, etc.) embedded in a nonuniform flow field such as the ocean environment; the flow direction is arbitrary, relative to the axis of the slender structure. The motion of the elastic structure is coupled with the hydrodynamic loads acting on the slender structure by the ambient flow field. An important input for such hydroelastic problems is the computation of the hydrodynamic loading per unit length experienced by the slender body. A rigorously derived improvement for the inertial loading per unit length over the commonly used Morison-type semi-empirical force (originally obtained for straight long structures in a uniform stream) is used. The structure is also allowed to undergo small (yet finite) deflections from its original reference central-line, due to a particular model of intrinsic elasticity governed by a corresponding nonlinear PDE, which corresponds to the well-known Kirchhoff rod elastic model. The system of coupled hydroelastic equations is investigated in order to derive analytically the influence of the hydrodynamic loading in a uniform stationary stream on the nonlinear stability of the straight rod. It is found that the presence of an ambient stationary stream decreases the critical parameters (critical twist) of the buckling phenomenon which is known to exist for the same rod when placed in a vacuum. Also revealed is a new type of stability loss, which is affected by viscous effects.