RESEARCH ARTICLE Power-Spectral density estimate of the Bloor-Gerrard instability in flows around circular cylinders

Abstract There have been differences in the literature concerning the power law relationship between the Bloor-Gerrard instability frequency of the separated shear layer from the circular cylinder, the Bénard-von Kármán vortex shedding frequency and the Reynolds number. Most pre-vious experiments have shown a significant degree of scatter in the measurement of the development of the shear layer vortices. Shear layers are known to be sensitive to external influences, which can provide a by-pass transition to saturated growth, thereby camouflaging the fastest growing linear modes. Here, the spatial amplification rates of the shear layer instabilities are calculated using power-spectral density estimates, allowing the fastest growing modes rather than necessarily the largest structures to be determined. This method is found to be robust in deter-mining the fastest growing modes, producing results con-sistent with the low scatter results of previous experiments.