Two-dimensional numerical models of open-top hydrothermal convection at high Rayleigh and Nusselt numbers: Implications for mid-ocean ridge hydrothermal circulation

[1] Mid-ocean ridges host vigorous hydrothermal systems that remove large quantities of heat from the oceanic crust. Inferred Nusselt numbers (Nu), which are the ratios of the total heat flux to the heat flux that would be transported by conduction alone, range from 8 to several hundred. Such vigorous convection is not fully described by most numerical models of hydrothermal circulation. A major difficulty arises at high Nu from the numerical solution of the temperature equation. To avoid classical numerical artifacts such as nonphysical oscillatory behavior and artificial diffusion, we implement the Multidimensional Positive Definite Advection Transport Algorithm (MPDATA) technique, which solves the temperature equation using an iterated upwind corrected scheme. We first validate the method by comparing results for models with uniform fluid properties in closed- and open-top systems to existing solutions with Nu <= similar to 20. We then incorporate realistic fluid properties and run models for Nu up to 50 - 60. Solutions are characterized by an unstable bottom thermal boundary layer where thermal instabilities arise locally. The pattern of heat extraction is periodic to chaotic. At any Nu > similar to 13 the venting temperatures in a given plume are chaotic and oscillate from similar to 350 degrees to 450 degrees C. Individual plumes can temporarily stop short of the surface for intervals ranging from tens to hundreds of years at times when other plumes vent with an increased flow rate. The solutions also display significant recirculation, and as a result large areas of downflow are relatively warm with temperatures commonly exceeding 150 degrees C at middepths. Our results have important implications for mid-ocean ridge hydrothermal systems and suggest the following: (1) The reaction zones of mid-ocean ridge hydrothermal systems are enlarged by thermal instabilities that migrate laterally toward upflow zones. This will substantially increase the volume of rock involved in chemical reactions compared to steady state configurations. (2) Hydrothermal discharge can stop temporarily as zones of venting are dynamically replaced by zones of seawater recharge. (3) Anhydrite precipitation occurring at temperatures exceeding similar to 150 degrees C will likely occur throughout a large portion of recharge zone and will not necessarily clog downflow pathways as efficiently as has been recently inferred.