Stability of flow around a rotating, semi-infinite cylinder placed in an axial stream is investigated. Assuming large Reynolds number, the basic flow is computed numerically as described by Derebail Muralidhar et al. [Proc. R. Soc. London, Ser. A 472, 20150850 (2016)], while numerical solution of the local stability equations allows calculation of the modal growth rates and hence determination of flow stability or instability. The problem has three nondimensional parameters: the Reynolds number $\mathrm{Re}$, the rotation rate $S$, and the axial location $Z$. Small amounts of rotation are found to strongly affect flow stability. This is the result of a nearly neutral mode of the nonrotating cylinder which controls stability at small $S$. Even small rotation can produce a sufficient perturbation that the mode goes from decaying to growing, with obvious consequences for stability. Without rotation, the flow is stable below a Reynolds number of about 1060 and also beyond a threshold $Z$. With rotation, no matter how small, instability is no longer constrained by a minimum $\mathrm{Re}$ nor a maximum $Z$. In particular, the critical Reynolds number goes to zero as $Z\to \infty$, so the flow is always unstable at large enough axial distances from the nose. As $Z$ is increased, the flow goes from stability at small $Z$ to instability at large $Z$. If the critical Reynolds number is a monotonic decreasing function of $Z$, as it is for $S$ between about 0.0045 and 5, there is a single boundary in $Z$, which separates the stable from the unstable part of the flow. On the other hand, when the critical Reynolds number is nonmonotonic, there can, depending on the choice of $\mathrm{Re}$, be several such boundaries and flow stability switches more than once as $Z$ is increased. Detailed results showing the critical Reynolds number as a function of $Z$ for different rotation rates are given. We also obtain an asymptotic expansion of the critical Reynolds number at large $Z$ and use perturbation theory to further quantify the behavior at small $S$.

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• Boundary layer receptivity, stability & separation
• Boundary layers
• Flow instability