On the Hamiltonian structure and three-dimensional instabilities of rotating liquid bridges

We consider a rotating inviscid liquid drop trapped between two parallel plates. The liquid-air interface is a free surface and the boundaries of the wetted regions in the plates are also free. We assume that the two contact angles at the plates are equal. We present drop shapes that generalize the catenoids, nodoids and unduloids in the presence of rotation. We describe profile curves of these drops and investigate their stability to three-dimensional perturbations. The instabilities are associated with degeneracies of eigenvalues of the corresponding Hamiltonian linear stability problem. We observe that these instabilities are present even in the case when the analogue of the Rayleigh criterion for two-dimensional stability is satisfied.