Response of the Shear Layers Separating from a Circular Cylinder to Small-Amplitude Rotational Oscillation.

The response of the shear layers separating from a circular cylinder subject to small amplitude rotational oscillation has been investigated experimentally in water for the Reynolds number (Re) range from 250 to 1200. Amplitude and phase measurements of resulting velocity fluctuations were obtained using a hot film anemometer connected to a lock-in analyzer, placed in the shear layers 1 to 1.5 diameters downstream from separation. Oscillations on the order of 1 to 5^circ (corresponding to cylinder peripheral speeds of 1 to 3 percent of the free stream) are shown to force both the Strouhal (or Karman) vortex shedding, and, for Re greater than 500, a secondary mode of 'shear layer vortices,' associated with the instability of the separated shear layers. Velocity oscillations in the shear layers were found to be roughly linear with forcing amplitude, for both the Strouhal and shear layer regimes. Phase measurements show a rapid phase change with forcing frequency near the Strouhal frequency, associated with the first formed Strouhal vortex 'changing sides' with respect to the cylinder motion, and forming closer to the cylinder. In the range of the shear layer instability, measurements show that the oscillations are for the most part convected at the mean shear layer speed. Frequencies associated with maximum response in the shear layer regime are shown to be compatible with those of maximum amplification rate predicted by others for free shear layers. Response of the shear layers is also shown to be compatible with linear instability theory and suggests the oscillations act as idealized perturbations to the main flow. Observations of both the forced and unforced wake suggest the shear layers become independently unstable at a Reynolds number of 500, clarifying a lower Reynolds number limit that has been otherwise obscure. Observations also indicate that the oscillations in the shear layers may occur asymmetrically, in distinction to the symmetric mode reported in the literature.