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A perturbative analysis is used to investigate the effect of rotation on theinstability of a steady accretion shock (SASI) in a simple toy-model, in viewof better understanding supernova explosions in which the collapsing corecontains angular momentum. A cylindrical geometry is chosen for the sake ofsimplicity. Even when the centrifugal force is very small, rotation can have astrong effect on the non axisymmetric modes of SASI by increasing the growthrate of the spiral modes rotating in the same direction as the steady flow.Counter-rotating spiral modes are significantly damped, while axisymmetricmodes are hardly affected by rotation. The growth rates of spiral modes have anearly linear dependence on the specific angular momentum of the flow. Thefundamental one-armed spiral mode (m=1) is favoured for small rotation rates,whereas stronger rotation rates favour the mode m=2. A WKB analysis of higherharmonics indicates that the efficiency of the advective-acoustic cyclesassociated to spiral modes is strongly affected by rotation in the same manneras low frequency modes, whereas the purely acoustic cycles are stable. Theseresults suggest that the linear phase of SASI in rotating core-collapsesupernovae naturally selects a spiral mode rotating in the same direction ofthe flow, as observed in the 3D numerical simulations of Blondin & Mezzacappa(2007). This emphasizes the need for a 3D approach of rotating core-collapse,before conclusions on the explosion mechanisms and pulsar kicks can be drawn.

Effect of Rotation on the Stability of a Stalled Cylindrical Shock and its Consequences for Core-Collapse Supernovae