Buoyancy-driven flow beneath mid-ocean ridges: the role of chemical heterogeneity

In the classical model, mid-ocean ridges (MOR) sit above an asthenospheric corner flow that is symmetrical about a vertical plane aligned with the ridge axis. However, geophysical observations of MORs indicate strong asymmetry in melt production and upwelling across the axis (e.g., Melt Seismic Team, 1998, Rychert et al., 2020). In order to reproduce the observed asymmetry, models of plate-driven (passive) flow require unrealistically large forcing, such as rapid asthenospheric cross-axis flow (~30 cm/yr) at high asthenospheric viscosities (~10^21 Pa.s), or temperature anomalies of >100 K beneath the MELT region in the East Pacific Rise (Toomey et al, 2002). 

Buoyancy-driven flows are known to produce symmetry-breaking behaviour in fluid systems. A small contribution from buoyancy-driven (active) flow promotes asymmetry of upwelling and melting beneath MORs (Katz, 2010). Previously, buoyancy has been modelled as a consequence of the retained melt fraction, but depletion of the residue (and heterogeneity) should be involved at a similar level. 

Here, we present new 2-D mid-ocean ridge models that incorporate density variations within the partial-melt zone due to the low density of the liquid relative to the solid (porous buoyancy), and the Fe/Mg partitioning between melt and residue (compositional buoyancy). The model is built after Katz (2010) using a new finite difference staggered grid framework for solving partial differential equations (FD-PDE) for single-/two-phase flow magma dynamics (Pusok et al., 2020). The framework uses PETSc (Balay et al., 2020) and aims to separate the user input from the discretisation of governing equations, thus allowing for extensible development and a robust framework for testing. 

Results show that compositional buoyancy beneath the ridge is negative and can partially balance porous buoyancy. Despite this, models with both chemical and porous buoyancy are susceptible to asymmetric forcing. Asymmetrical upwelling in this context is obtained for forcing that is entirely plausible. A scaling analysis is performed to determine the relative importance of the contribution of compositional and porous buoyancy to upwelling, which is followed by predictions on the crustal thickness production and asymmetry beneath the ridge axis. 

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