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We analyze theoretically and experimentally the wake behind a horizontalcylinder of diameter $d$ horizontally translated at constant velocity $U$ in afluid rotating about the vertical axis at a rate $\Omega$. Using particle imagevelocimetry measurements in the rotating frame, we show that the wake isstabilized by rotation for Reynolds number ${\rm Re}=Ud/\nu$ much larger thanin a non-rotating fluid. Over the explored range of parameters, the limit ofstability is ${\rm Re} \simeq (275 \pm 25) / {\rm Ro}$, with ${\rmRo}=U/2\Omega d$ the Rossby number, indicating that the stabilizing process isgoverned by the Ekman pumping in the boundary layer. At low Rossby number, thewake takes the form of a stationary pattern of inertial waves, similar to thewake of surface gravity waves behind a ship. We compare this steady wakepattern to a model, originally developed by [Johnson, J. Fluid Mech. 120, 359(1982)], assuming a free-slip boundary condition and a weak streamwiseperturbation. Our measurements show a quantitative agreement with this modelfor ${\rm Ro}\lesssim 0.3$. At larger Rossby number, the phase pattern of thewake is close to the prediction for an infinitely small line object. However,the wake amplitude and phase origin are not correctly described by theweak-streamwise-perturbation model, calling for an alternative model for theboundary condition at moderate rotation rate.

Wake of inertial waves of a horizontal cylinder in horizontal translation