Instabilities in the wake of an isolated cylindrical roughness element

Abstract

The instability mechanism behind a geometrically simple cylindrical roughness element continues to be a challenging topic in fluid mechanics. Considerable progress has been made in understanding the phenomena in recent years, but more research is needed to predict the temporal nature and spatial structure of the dominant instability in a given flow configuration. This is of particular interest, as these instabilities dictate the transition to turbulence and thus are significant for large-scale effects such as skin friction drag. A smoke-flow visualization study with a large variation of parameters, featuring a cylindrical roughness element connected to a linear traverse, has been performed. Results show good agreement with previous investigations and provide further insights into the stability properties, revealing several unexpected effects. For a low roughness aspect ratio $\eta$ , no global instability is detected even at the highest roughness Reynolds number $Re_{kk}$ , whereas a high aspect ratio indicates a delay in the onset of instability. From the acquired visualizations, we constructed the, so far, richest instability diagram of the wake behind an isolated roughness element in the $Re_{kk}\unicode{x2013}\eta$ space, sampled in the same measurement campaign. Furthermore, information regarding the dominant frequency in the wake can be extracted from the visualization images. Our results suggest a new scaling of the frequency as the velocity is increased. Finally, it is shown that the dominant frequency in a certain flow regime can be well predicted using a Strouhal number based on the cylinder diameter and the roughness velocity.