The coupled effects of mantle mixing and a water-dependent viscosity on the surface ocean

Abstract

Water content plays a vital role in determining mantle rheology and thus mantle convection and plate tectonics. Most parameterised convection models predict that Earth initially underwent a period of rapid degassing and heating, followed by a slow and sustained period of regassing and cooling. However, these models assume water is instantaneously mixed and homogeneously distributed into the mantle. This is a limitation because the mixing time for water entering and leaving the mantle is a function of the Rayleigh number which varies dramatically with water content, temperature, and through time. Here we present an adapted parametrised model (Crowley et al., 2011) to include the coupled effects of the time scale of mixing with a water-dependent viscosity. We consider two mixing types: first, where the mixing time is constant throughout the model and second, where mixing time varies as a response to an evolving Rayleigh number. We find that, facilitated by the effects of water content in the melt region at mid-ocean ridges, a constant mixing time can induce long periods of degassing. The inclusion of a variable mixing time dependent on the Rayleigh number acts to limit the period of degassing and also results in more water being stored in the mantle and less at the surface than in both the constant and instantaneous mixing cases. Mixing time cannot be more than ∼2 billion years as large mixing times trap water in the mantle, leaving a dry surface. Even small changes in the surface ocean induced by mixing times on the order of 0.1 Gyrs can cause changes in the global-mean sea level on the order of 10's of metres. These changes in sea level could easily uncover topographic highs in the bathymetry, potentially aiding sub-aerial erosion a process thought to be important in early Earth evolution. Even in this relatively simple model, the inclusion of a mixing time between water entering and leaving the mantle creates a more dynamic water cycle.