As a fluid particle flows toward the leading edge of a cylinder, the pressure in the fluid particle rises from the free stream pressure to stagnation pressure. The high fluid pressure near the leading edge impels flow about the cylinder as boundary layer develop about both sides. However, the high pressure is not sufficient to force the flow about the back of the cylinder at high Reynolds numbers. Near the widest section of the cylinder, the boundary layers separate from each side of the cylinder surface and form two shear layers that trail aft in the flow and bound the wake. Since the innermost portion of the shear layers, which is in contact with the cylinder, moves much more slowly than the outermost portion of the shear layers, which is in contact with the free flow, the shear layers roll into near wake, where they fold on each other and coalesce into discrete swirling vortices (Perry et al,. 1982; Williamson and Roshko, 1988). A regular pattern of vortices, called a vortex street, trails aft in the wake. The vortices interact with the cylinder and they are the source of the effects called vortex-induced vibration.
Vortex pairs will be shed a frequency fv given by the Strouhal number: fv=SU/D, in which: U = flow velocity, D = cylinder diameter, S = Strouhal number. This creates an oscillatory lift force FL at the frequency fv. The shedding of vorticed will cause cylinder vibrations, and the motion of the cylinder will influence the shedding.
The reduced velocity and the inverse Strouhal number are closely related:
For fv= fn we have that Ured and 1/S are the same. Then if the flow velocity is gradually increased VIV will start. But it turns out that if the velocity is gradually increased the vortex shedding frequency will stay constant, so that it matches the natural frequency of the cylinder over a range of velocities. This is often referred to as ‘lock-in’ or ‘lock-on’ and is characteristic of VIV.
lock-in in water: The vibrating frequency will increase through the lock-in range, presumably due to changes in the added fluid mass, and vibrations will occur over a wider velocity range. This means that now 2 different definitions for reduced velocity can be used: The first is based on the frequency at which the vibrations are actually occurring, Ured,true, the second involves a reference natural frequency, e.g. the natural frequency in still water, yielding Ured,nom and that the velocity in each test is divided by the constant (fn0D). Alternatively in each test one would use the frequency at which the vibrations were actually occurring, obtaining a narrower lock-in range.
Parameters are used to predict VIV amplitudes, the combined stability parameter:
Source: Blevins R D 1994, Flow-Induced Vibration; Lecture Notes specialization in course: FIV by Prof. Geir Moe
