THE INSTABILITY OF THE SHEAR-LAYER SEPARATING FROM A BLUFF-BODY

Notwithstanding the fact that the instability of the separated shear l ayer in the cylinder wake has been extensively studied, there remains some uncertainty regarding not only the critical Reynolds number at wh ich the instability manifests itself, but also the variation of its ch aracteristic frequency with Reynolds number (Re). A large disparity ex ists in the literature in the precise value of the critical Reynolds n umber, with quoted values ranging from Re = 350 to Re = 3000. In the p resent paper, we demonstrate that the spanwise end conditions which co ntrol the primary mode of vortex shedding significantly affect the she ar-layer instability. For parallel shedding conditions, shear-layer in stability manifests itself at Re approximate to 1200, whereas for obli que shedding conditions it is inhibited until a significantly higher R e approximate to 2600, implying that even in the absence of a variatio n in free-stream turbulence level, the oblique angle of primary vortex shedding influences the onset of shear-layer instability, and contrib utes to the large disparity in quoted values of the critical Reynolds number. We confirm the existence of intermittency in shear-layer fluct uations and show that it is not related to the transverse motion of th e shear layers past a fixed probe, as suggested previously. Such fluct uations are due to an intermittent streamwise movement of the transiti on point, or the location at which fluctuations develop rapidly in the shear layer. Following the original suggestion of Bloor (1964), it ha s generally been assumed in previous studies that the shear-layer freq uency (normalized by the primary vortex shedding frequency) scales wit h Re-1/2, although a careful examination of the actual data points fro m these studies does not support such a variation. We have reanalysed all of the actual data points from previous investigations and include our own measurements, to find that none of these studies yields a rel ationship which is close to Re-1/2. A least-squares analysis which inc ludes all of the previously available data produces a variation of the form Re-0.67. Based on simple physical arguments that account for the variation of the characteristic velocity and length scales of the she ar layer, we predict a variation for the normalized shear-layer freque ncy of the form Re-0.7, which is in good agreement with the experiment al measurements.