The effect of shearing on the buoyant migration of melt in compacting-dissolution channels

Melt migration in the mantle by porous flow through compacting, high porosity dissolution channels may occur in a variety of settings including both the upwelling mantle beneath spreading centers and the flowing mantle wedge at convergent plate boundaries. Such channels may form by a positive feedback between dissolution and melt percolation. Previous studies [1, 2] have considered the compacting-dissolution channels in the presence of a uniform upwelling mantle flow. In this study the analysis of mantle flow beneath the plate boundaries was extended by introducing a horizontal shearing component. A numerical experiment was formulated using the finite element software deal.II [3] applying a high order Discontinuous Galerkin (DG) method to examine melt flow in a deforming, porous matrix. The conditions are similar to those in [2] except the addition of a prescribed horizontal shear component in the solid matrix. Melt migration occurs within a rectangular domain subject to horizontal periodic boundary conditions. Initially a Gaussian perturbation in the porosity at the base extends vertically through the domain defining a melt channel. By varying the shear and upwelling rates, the porosity and matrix dissolution were examined to determine the behavior of the channel and melt flow. Models of buoyant melt transport through dissolution channels in upwelling mantle sheared on horizontal planes show that shearing deformation introduces several effects that could have important consequences for melt migration. Shearing tends to rotate dissolution channels away from the vertical thus reducing the component of buoyancy acting along the channels and decreasing the stability of the channel. The channels remain more vertical than would be expected if they followed the matrix flow, as determined by the dissolution. Channels thus migrate horizontally relative to the mantle matrix and melt flows horizontally through dissolution channels. Evolution of the channels depends on the ratio of upwelling to shearing rates. A compacting region of reduced porosity develops on the downstream side of a channel. This region advects with the velocity of the matrix. Melt collecting beneath the compacting region generates new tilted melt channels. In the absence of horizontal shear melt rising vertically in the melt channel remains within mantle matrix in the channel. However, horizontal shearing destroys this isolation by causing melt to flow horizontally relative to the matrix. As upwelling rate decreases, and hence the compaction, there is less relative motion between the melt and matrix and the channel behavior agrees more with the theoretical relationship. This behavior may have important geochemical implications for the transport of chemically heterogeneous melts in the deforming mantle. Melt rising in sheared mantle columns may not retain the high pressure signature frequently invoked to explain mid-ocean ridge basalt chemistry if local chemical equilibrium is maintained. [1]. Spiegelman et al. (2001) JGR, 106, 2061-2077. [2]. Schiemenz et al. (2011) Geophys. J. Int. 186, 641-664. [3]. Bangerth et al. (2007) ACM Trans. Math. Software 33, doi: 10.1145/1268776.1268779.