ALBERT

Description: Models incorporating plate-like behavior, i.e., near uniform surface velocity and deformation concentrated at plate boundaries, into a convective system, heated by a mix of internal and basal heating and allowing for temperature dependent viscosity, were constructed and compared to similar models not possessing plate-like behavior. The simplified numerical models are used to explore how plate-like behavior in a convective system can effect the lower boundary layer from which thermal plumes form. A principal conclusion is that plate-like behavior can significantly increase the temperature drop across the lower thermal boundary layer. This temperature drop affects the morphology of plumes by determining the viscosity drop across the boundary layer. Model results suggest that plumes on planets possessing plate-like behavior, e.g., the Earth, may differ in morphologic type from plumes on planets not possessing plate-like behavior, e.g., Venus and Mars.

Description: Effective numerical treatment of multicomponent viscous flow problems involving the advection of sharp interfaces between materials of differing physical properties requires correction techniques to prevent spurious diffusion and dispersion. We develop a particular algorithm, based on modern shock-capture techniques, employing a two-step nonlinear method. The first step involves the global application of a high-order upwind scheme to a hyperbolic advection equation used to model the distribution of distinct material components in a flow field. The second step is corrective and involves the application of a global filter designed to remove dispersion errors that result from the advection of discontinuities (e.g., material interfaces) by high-order, minimally dissipative schemes. The filter introduces no additional diffusion error. Nonuniform viscosity across a material interface is allowed for by the implementation of a compositionally weighted-inverse interface viscosity scheme. The combined method approaches the optimal accuracy of modern shock-capture techniques with a minimal increase in computational time and memory. A key advantage of this method is its simplicity to incorporate into preexisting codes be they finite difference, element, or volume of two or three dimensions.

Description: It is proposed that subducting tectonic plates can affect the nature of thermal mantle plumes by determining the temperature drop across a plume source layer. The temperature drop affects source layer stability and the morphology of plumes emitted from it. Numerical models are presented to demonstrate how introduction of platelike behavior in a convecting temperature dependent medium, driven by a combination of internal and basal heating, can increase the temperature drop across the lower boundary layer. The temperature drop increases dramatically following introduction of platelike behavior due to formation of a cold temperature inversion above the lower boundary layer. This thermal inversion, induced by deposition of upper boundary layer material to the system base, decays in time, but the temperature drop across the lower boundary layer always remains considerably higher than in models lacking platelike behavior. On the basis of model-inferred boundary layer temperature drops and previous studies of plume dynamics, we argue that generally accepted notions as to the nature of mantle plumes on Earth may hinge on the presence of plates. The implication for Mars and Venus, planets apparently lacking plate tectonics, is that mantle plumes of these planets may differ morphologically from those of Earth. A corollary model-based argument is that as a result of slab-induced thermal inversions above the core mantle boundary the lower most mantle may be subadiabatic, on average (in space and time), if major plate reorganization timescales are less than those acquired to diffuse newly deposited slab material.

Description: We present results from convection models allowing for self-lubrication of downflows. Models impose a line source of chemically light, low viscosity material at the top of a convecting layer of temperature-dependent viscosity material. Low viscosity surface material serves as an analog to hydrated sediment/crust and the high viscosity upper portion of the convecting layer as an analog to mantle lithosphere. Slow near surface motion in the convecting layer entrains low viscosity material into zones of downflow, which has a lubricating effect. Once entrained lubricant is deeper than the cold high viscosity portion of the convecting layer, rapid upper boundary layer overturn occurs and system properties change (e.g., heat flux doubles). This marks transition to a lubricated state. Before and after transition, transport properties are dominantly determined by, respectively, the viscosity of mantle lithosphere and that of interior mantle. Lubricated and nonlubricated states appear as distinct regions in system output space suggesting that exchange between them is akin to a phase transition. That such exchange depends on a near surface lubricant implies that the geodynamics of planets lacking such lubricants may fundamentally differ from that of planets possessing them.