On the Periodicity of Atmospheric von K\'{a}rm\'{a}n Vortex Streets

For over one hundred years, a similarity relationship between Strouhal number ($Sr$), a non-dimensional metric for vortex shedding frequency ($N$), and Reynolds number ($Re$) has been aggressively pursued in the context of von K\'{a}rm\'{a}n vortex streets (VKVSs). In this study, we document the $Sr-Re$ relationship of atmospheric VKVSs (i.e., in the extremely high $Re$ regime) in order to gain new insight into a regime of the similarity theory which has never before been investigated. Through quasi-idealized numerical simulations of realistic atmospheric VKVS events, we observe a range of $Re$ in which mesoscale VKVSs are clearly present yet $Sr$ remains in a steady range of 0.15 - 0.22 (irrespective of $Re$). This relationship resembles what has been observed for VKVSs in the much lower $10^2 < Re < 10^4$ regime suggesting eddy viscosity as a proxy for molecular viscosity with regards to $Sr-Re$ similarity theory at high-$Re$. In addition, we find the dominant length scale dictating the $Sr-Re$ relationship in the atmosphere to be the cross-stream mountain diameter, specifically at the height of the boundary layer thermal inversion.