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It is shown that incompressible cylindrical shells rotating in an external potential and having constant angular momentum distributions can be unstable with respect to non-axisymmetric perturbations. The instability occurs on dynamical time-scales and is due to the interaction of two free boundaries. The growth rates depending on the azimuthal wavenumber and the thickness of the shell are given in analytical form.
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Blaes et al. (1986) studied this question.
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