Hydrodynamic torque on a slender cylinder rotating perpendicularly to its symmetry axis

Using fully-resolved simulations, we investigate the torque experienced by a finite-length circular cylinder rotating steadily perpendicularly to its symmetry axis. The aspect ratio $\chi$, i.e. of length diameter, is varied from 1 15. In creeping-flow regime, employ slender-body theory derive expression up order 4 with respect small parameter $1/\ln(2\chi)$. Numerical results agree well corresponding predictions for $\chi\gtrsim3$. We introduce an \textit{ad hoc} modification in theoretical prediction fit numerical obtained shorter cylinders, and second account increase resulting finite inertial effects. strongly regimes, prominent wake pattern made two pairs counter-rotating vortices takes place. Nevertheless flow remains stationary exhibits distinct symmetries, one which implies that contributions arising ends are identical. build separate empirical formulas pressure viscous stress provided lateral surface ends. show that, each contribution, dominant scaling law may be inferred simple physical arguments. This approach eventually formula rotation-induced valid throughout range regimes ratios considered simulations.