The flow around circular cylinders has been studied by aeronautical engineers almost since powered flight began. There are numerous applications that can be cited, and the problems that have been examined closely range from the forces on the bracing wires and struts of early biplanes to the wind loading of space rockets on the launch pad Although a circular cylinder is geometrically extremely simple, its associated flow field is very complex and can be viewed as an extensive series of transitions between different flow states. In recent years it has become a focus for work in computational fluid dynamics and is often employed as a test case for various numerical approaches However, the circular cylinder still holds a number of secrets, as will be demonstrated by reference to problems in marine technology.

The circular cross-section tube is a key element in offshore structures, where it may be exposed to a steady current flow or to waves. In many locations it may also experience a flow environment which is a combination of waves, with a directional spread, and a current. An important phenomenon observed in a steady water flow, but not found in air flow, is that a flexible circular cylinder may experience in-line oscillations due to the motion-m, regular shedding of synmetric vortices. This was first documented by Wootton et al (1969) and occurs when the structural damping is small and when the ratio of the mass of the cylinder to the mass of the fluid displaced is also small However, most of the research into circular cylinders in water flow, and the majority of the new results, relate to interaction with free surface waves When the wavelength, ¿, is less than or comparable to the diameter, D, of the cylinder, the loading can be estimated from diffraction theory, assuming the flow to be rotational Sarpkaya and Isaacson (1981) state that wave diffraction is important when D/¿1 > 02 This chapter, however, will consider the case where the wavelength is larger than the cylinder diameter and where the effects of fluid viscosity, leading to flow separation and vortex shedding, are important A critical question then is how do the various flow regimes and transitions observed in steady flow apply to a circular cylinder in waves?

FLOW REGIMES IN STEADY FLOW

Over the range of Reynolds number between 104 and l07 several important changes occur in the flow field, and it is known that these changes can be explained in terms of variations in the boundary layer development Figure 1, reproduced from Schewe (1983), shows drag coefficient plotted against Reynolds number At Reynolds numbers of the order of 105 the boundary layer at separation is laminar, and transition occurs within the free shear layers prior to their rolling up into the vortices that form the vortex street wake This regime is known as the sub-critical since it precedes the Reynolds number at which the drag coefficient falls rapidly.

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