  The wake flow around a circular cylinder at $Re\approx100$ performing
rotatory oscillations has been thoroughly discussed in the literature, mostly
focusing on the modifications to the natural B\'enard-von K\'arm\'an vortex
street that result from the forced shedding modes locked to the rotatory
oscillation frequency. The usual experimental and theoretical frameworks at
these Reynolds numbers are quasi-two-dimensional, since the secondary
instabilities bringing a three-dimensional structure to the cylinder wake flow
occur only at higher Reynolds numbers. In the present paper we show that a
three-dimensional structure can appear below the usual three-dimensionalization
threshold, when forcing with frequencies lower than the natural vortex shedding
frequency, at high amplitudes, as a result of a previously unreported
mechanism: a pulsed centrifugal instability of the oscillating Stokes layer at
the wall of the cylinder. The present numerical investigation lets us in this
way propose a physical explanation for the turbulence-like features reported in
the recent experimental study of D'Adamo et al. (2011).
