Centrifugal instability of Stokes layers in crossflow: the case of a forced cylinder wake

Abstract

The wake flow around a circular cylinder at Re ≈100 performing rotatory oscillations has been thoroughly discussed in the literature, mostly focusing on the modifications to the natural Bénard–von Kármán 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, because the secondary instabilities bringing a three-dimensional structure to the cylinder wake flow occur only at higher Reynolds numbers. In this 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 by the present authors.