ON THE HAMILTONIAN-STRUCTURE AND 3-DIMENSIONAL INSTABILITIES OF ROTATING LIQUID BRIDGES

We consider a rotating inviscid liquid drop trapped between two parall el plates. The liquid-air interface is a free surface and the boundari es of the wetted regions in the plates are also free. We assume that t he two contact angles at the plates are equal. We present drop shapes that generalize the catenoids, nodoids and unduloids in the presence o f 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 H amiltonian linear stability problem. We observe that these instabiliti es are present even in the case when the analogue of the Rayleigh crit erion for two-dimensional stability is satisfied. (C) 1999 The Japan S ociety of Fluid Mechanics and Elsevier Science B.V. All rights reserve d.