Navier-stokes problems

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When cylindrical structures in ocean engineering and undersea technology are exposed to ocean currents and/or waves, they may experience structural vibrations. One of these instabilities involves vortex shedding, which can cause a serious threat to the integrity and fatigue life of structure. This program of research focuses on the unsteady flow around a horizontal cylindrical body in the absence or presence of a free surface which is a classical topic within hydrodynamics. In nature, a special type of fluid boundary which separates two fluids with different physical properties, for example water and the air in the Earth's atmosphere is known as a free surface. Representative structures having cylindrical geometry include towing cables, which may be inclined at an angle with respect to the free surface: in some cases they may be at a shallow angle with respect to the free surface, thereby approximating a horizontal orientation. Moreover, offshore platforms typically have horizontal, cylindrically shaped members. The knowledge of this kind of fluid motion has attracted considerable attention from many mechanical and civil engineers working in the offshore field, since the rapid expansion of the offshore industry in the 60s. Fluid motion causes forces to be exerted on structures immersed in them due to vortex shedding. Resonant oscillations caused by these forces may destroy riser pipes of an oil production system in the ocean. Thus, the proposed research studies are of considerable and practical importance in the stability and safety of engineering structures. The intent is to produce useful information about the relationship between physics of fluid motion of this type and the impact (drag and lift forces) of the fluid motion on the cylindrical body. The ultimate objective is, of course, the understanding, prediction, and prevention of vortex- or flow-induced vibrations. The present program of research requires the solution of the well known Navier-Stokes equations using applied mathematical analyzes, numerical simulations and comparisons with experimental observations whenever possible. Comparisons with experiments provides an estimate of the limits of our numerical simulations of very complex flows.