  This work studies the three-dimensional flow dynamics around a rotating
circular cylinder of finite length, whose axis is positioned perpendicular to
the streamwise direction. Direct numerical simulations and global stability
analyses are performed within a parameter range of Reynolds number
$Re=DU_\infty/\nu<500$ (based on cylinder diameter $D$, uniform incoming flow
velocity $U_\infty$), length-to-diameter ratio $AR=L/D\leq2$ and dimensionless
rotation rate $\alpha=D\Omega/2U_\infty\leq2$ (where $\Omega$ is rotation
rate). By solving Nav\-ier--Sto\-kes equations, we investigated the wake
patterns and explored the phase diagrams of the lift and drag coefficients. For
a cylinder with $AR=1$, we found that when the rotation effect is weak
($0\leq\alpha\lesssim0.3$), the wake pattern is similar to the unsteady wake
past the non-rotating finite-length cylinder, but with a new linear unstable
mode competing to dominate the saturation state of the wake. The flow becomes
stable for $0.3\lesssim\alpha\lesssim0.9$ when $Re<360$. When the rotation
effect is strong ($\alpha\gtrsim0.9$), new low-frequency wake patterns with
stronger oscillations emerge. Furthermore, the stability analyses based on the
time-averaged flows and on the steady solutions demonstrate the existence of
multiple unstable modes undergoing Hopf bifurcation, greatly influenced by the
rotation effect. The shapes of these global eigenmodes are presented and
compared, as well as their structural sensitivity, visualising the flow region
important for the disturbance development with rotation. This research
contributes to our understanding of the complex bluff-body wake dynamics past
this critical configuration.

Fluid Dynamics