A gravity current model of cooling mantle plume heads with temperature-dependent buoyancy and viscosity
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Gravity currents are a ubiquitous fluid dynamical phenomenon which involve the horizontal spreading of fluid masses under their own weight or buoyancy. A theoretical model is developed to account for the effects of bulk cooling on the dynamics and morphology of geological gravity currents, with particular focus on mantle plume heads spreading beneath the lithosphere. As many geological gravity currents (e.g., plume heads and lava flows) spread, they cool and thereby become more viscous and dense. All gravity currents initially spread at the same rate as the isothermal currents predicted by Huppert . However, currents with temperature-dependent viscosity and/or buoyancy eventually go to a much slower spreading rate than the isothermal currents. Moreover, unlike the isothermal gravity currents, cooling variable-viscosity and/or variable-buoyancy currents do not conserve shape as they spread. Both constant volume and constant volume flux currents with strongly temperature dependent viscosity develop steep-sided flat-topped, plateau shapes which become more rounded once the currents lose most of their heat. Currents with temperature-dependent buoyancy develop inflections or even extensive swelling at their flow fronts. The surface expression of the edge-steepening effect in mantle plume heads is likely to be filtered by lithospheric flexure but may contribute to the flattened plateau shape inferred by Wessel  for the Hawaiian swell. The frontal inflation effect due to variable buoyancy may contribute to the dual-lobe structure of the Hawaiian swell gravity anomaly and suggests an alternate physical mechanism for forming the torus- or horseshoe-shaped geochemical patterns in the Galapagos and the Marquesas hotspots. Perhaps most significantly, the gravity current model also predicts the thermal (i.e., degree-of-melting) pattern for Galapagos and Marquesas hotspots more readily than the traditional entrainment models.