A. Mark Jellinek and Michael Manga
Department of Earth and Planetary Science, University of California, Berkeley, USA
\parindent 0pt {\it Summary} Analog fluid mechanical experiments show that the presence of a dense, low viscosity compositional boundary layer at the base of the Earthıs mantle induces lateral variations in temperature and viscosity that, in turn, determine the location and dynamics of mantle plumes. In detail, the presence of a dense layer causes mantle plumes to become fixed in space. Moreover, the entrainment of low viscosity fluid from the dense layer enables plumes to persist for hundreds of millions of years and influences their composition. Our results may resolve a basic conundrum in mantle dynamics that hotspots remain approximately fixed in space relative to each other for time scales much larger than the time for a plume to rise through the depth of the mantle. This finding is consistent with an observed correlation between the locations of Pacific hotspots and sightings of a dense layer at the base of the mantle.\\ {\it Introduction and motivation} Several outstanding questions remain about hotspots and their associated mantle plumes: \begin{itemize} \item Why are hotspots approximately fixed in space relative to one another? \item Why do hotspots persist for time scales much longer than the time for a mantle plume to rise through the mantle? \item What governs the location and spacing of mantle plumes? \end{itemize} Seismological observations obtained over the last few decades provide convincing evidence that the lower few hundred kilometers of the mantle consists of superposed thermal and (dense) compositional boundary layers that are laterally heterogeneous. Mantle flow into ascending plumes can potentially deform the dense layer, leading, in turn, to its gradual entrainment. Here, we present the results of new analog experiments aimed at understanding the extent to which the deformation of, and entrainment from, a dense compositional boundary layer can govern the location and dynamics of mantle plumes and explain the relative fixity of hotspots. Our experiments extends previous experimental (e.g., 1-3) and numerical studies (e.g., 4-5) to the case in which the lower layer is much less viscous than the overlying fluid.\\ {\it Approach: Laboratory experiments and scaling analyses} Because of the computational challenge of resolving small (kilometer) length scales while tracking viscosity and density interfaces, we adopt an experimental approach. Our goals are to: \begin{itemize} \item Characterize the nature of the interaction between convection due to core-cooling and an underlying dense layer. \item Identify conditions leading to long-lived, spatially fixed plumes. \item Use experimental results to extend existing scaling theories (e.g., 2, 6-8) to understand the composition, spacing and lifetime of mantle plumes. \end{itemize} 27 convection experiments without a dense layer are first performed to establish a control. 19 additional experiments with a dense layer are designed specifically to understand the interaction between plumes and an underlying dense layer of equal or lower viscosity. Heat flux probes, thermocouples, and time-lapse video are used to characterize the observed flows quantitatively. Working fluids are polybutene oils for the mantle. A variety of more dense, less viscous and miscible vegetable oils are used for the dense layer. We find that four dimensionless parameters are required to characterize our experiments and scale the results to the Earth: 1) the Rayleigh number, Ra, 2) the viscosity ratio due to intrinsic compositional differences, $\lambda_d$, 3) the viscosity ratio due to temperature variations, $\lambda_h$ and 4) the ratio B of the stabilizing compositional buoyancy of the dense layer to the destabilizing thermal buoyancy of the overlying thermal boundary layer.\\ {\it Results: Fixity and longevity of mantle plumes} The dense layer is deformed by the flow of thermal boundary layer fluid into ascending plumes, leading to two important effects: \begin{itemize} \item The dynamic coupling between topography and motions driven by lateral temperature variations stabilize the pattern of flow. Plumes become fixed when hot, buoyant fluid is able to ascend along the sloping interface with the low viscosity vegetable oil more easily than it can rise vertically into the overlying polybutene oil. We find that smaller relief on the dense layer is needed to stabilize the flow when the viscosity ratio $\lambda_d$ is large. \item The entrainment of dense, low viscosity fluid establishes structurally robust cylindrical conduits that persist for time scales much longer than the time for plumes to rise. \end{itemize} {\it Applications to the Earth} For Ra, $\lambda_d$ and B suitable to the Earth's mantle scaling analyses suggest that entrained tendrils of dense layer will be 5-10 km thick, erosion rates will be $10^{-2}$ to $10^{-3}$ km/Myr and plume spacing will be order 1000 km. A 100-300 km thick dense layer could thus persist over the age of the Earth.\\ {\footnotesize {\bf References}: 1. Olson, P., and Kincaid, C. (1991) {\it J. Geophys. Res.} {\bf 96}, 4347-4354; 2. Davaille, A. (1999) {\it Nature} {\bf 402}, 756-760; 3. Gonnermann, H., Manga, M. and Jellinek, A.M. (2002) {\it Geophys. Res. Lett.} {\bf 29}, 10.1029/2002GL01485; 4. Montague, N.L., Kellogg, L.H. (2000) {\it J. Geophys. Res.} {\bf 105}, 11101-11114; 5. Tackley, P.J. (in press) {\it G$^3$}; 6. Sleep, N.H. (1988) {\it Geophys. J. Int.} {\bf 95}, 437-447; 7. Olson, P., Schubert, G. and Anderson, C. (1993) {\it J. Geophys. Res.} {\bf 98}, 6829-6844; 8. Davaille, A. (1999) {\it J. Fluid Mech.} {\bf 379}, 223-253.}