The instability of the shear layer separating from a bluff body

Abstract

Notwithstanding the fact that the instability of the separated shear layer in the cylinder wake has been extensively studied, there remains some uncertainty regarding not only the critical Reynolds number at which the instability manifests itself, but also the variation of its characteristic frequency with Reynolds number (Re). A large disparity exists in the literature in the precise value of the critical Reynolds number, with quoted values ranging from Re = 350 to Re = 3000. In the present paper, we demonstrate that the spanwise end conditions which control the primary mode of vortex shedding significantly affect the shear-layer instability. For parallel shedding conditions, shear-layer instability manifests itself at Re ≈ 1200, whereas for oblique shedding conditions it is inhibited until a significantly higher Re ≈ 2600, implying that even in the absence of a variation in free-stream turbulence level, the oblique angle of primary vortex shedding influences the onset of shear-layer instability, and contributes to the large disparity in quoted values of the critical Reynolds number. We confirm the existence of intermittency in shear-layer fluctuations and show that it is not related to the transverse motion of the shear layers past a fixed probe, as suggested previously. Such fluctuations are due to an intermittent streamwise movement of the transition point, or the location at which fluctuations develop rapidly in the shear layer.

Following the original suggestion of Bloor (1964), it has generally been assumed in previous studies that the shear-layer frequency (normalized by the primary vortex shedding frequency) scales with Re^1/2, although a careful examination of the actual data points from 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 relationship which is close to Re^1/2. A least-squares analysis which includes 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 shear layer, we predict a variation for the normalized shear-layer frequency of the form Re^0·7, which is in good agreement with the experimental measurements.