On the rise of strongly tilted mantle plume tails

The rise of an initially horizontal, buoyant cylinder of fluid through a denser fluid at low Reynolds number is used to look at the ascent of strongly tilted mantle plumes through the mantle. Such ascents are characterized by (1) the growth of instabilities and (2) the development of a thermal wake downstream. Three-dimensional numerical experiments were carried out to examine these features. An hybrid particle-in-cell finite element method was used to look at the rise of non-diffusing cylinders and, a standard finite element method was used to look at the diffusing case. First the experiments show that the timescale of the fastest growing instability vary with the Rayleigh number and the viscosity ratio. In particular the growth rate decreases as the Rayleigh number decreases, in agreement with our analysis of the laboratory experiments of Kerr et al. (2008). Second the experiments show that the length of the thermal wake increases with the Rayleigh number but the change in viscosity has almost no influence on the wake length. Applied to strongly tilted mantle plumes we conclude that such plumes cannot be unstable given the plume timescales. We also discuss the application of this conclusion to weakly tilted plumes. Besides, this study allows to predict that mantle plumes are unlikely to have developed a significant thermal wake by the time they reach the surface. Finally, the resolution that is required to allow for the growth of mantle plume tails by combined diffusion and thermal entrainment is shown to represent a challenge for the large scale mantle convection simulations