Are strongly tilted plume conduits gravitationally unstable?

We report on three dimensional numerical experiments designed to study the rise of an initially horizontal buoyant cylinder of fluid through a denser fluid at low Reynolds number. Two series of experiments are performed and analyzed as a function of the Péclet number and the viscosity ratio between the inner cylinder fluid and the outer ambient fluid. In the first series of numerical experiments, particle tracking methods are used to examine plumes at infinite Péclet number. These experiments show that the buoyant cylinder develops gravitational instabilities as it rises through the surrounding fluid. We compare the resulting wavelengths of instability with laboratory experiments of compositionally buoyant cylinders at very large Péclet numbers and with a theoretical stability analysis. In the second series of numerical experiments, the effect of diffusion is investigated, to determine whether there is a transition (at a sufficiently small Péclet number) to a regime of steady uniform rise without instability. From these experiments, we aim to understand whether mantle plume tails in the mantle can develop gravitational instabilities when they are sufficiently strongly tilted.