On the Hamiltonian Structure and Three-dimensional
Instabilities of Rotating Liquid Bridges
Kruse, H. P., A. Mahalov and J. E. Marsden
Fluid Dyn. Research, 24, 37-59
Abstract:
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.