Effect of slab rheology on mass transport across a phase transition boundary

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Abstract
In this study we explore the impact of a strongly temperature‐dependent viscosity on convective flow in the presense of an endothermic phase transition. Temperature‐dependent viscosity strengthens the upper thermal boundary layer and its associated downwellings (slabs). Three temperature‐dependent rheologies ranging from weakly to strongly temperature‐dependent, as well as a constant viscosity are considered in a two‐dimensional Cartesian model. All other properties of the flow and phase transition are held constant. The slab is located in the center of the computational grid to avoid the direct influence of a sidewall on the downgoing flow. We find that when holding the volume averaged Rayleigh number constant, the strength of the downwelling does not noticeably affect its ability to penetrate the phase transition as observed by the isotherms. Stronger downwellings, however, do maintain a more coherent, narrow, slablike shape and significantly increase the vertical mass flux compared to weaker downwellings which tend to build up in a large pool of cold material above the phase transition. Compared to the strong slabs, there is widespread deformation of the cold downwelling material above the phase transition. This effect is most noticeable at large negative values of the Clapeyron slope, when the constant viscosity models are strongly layered. In contrast, we find that whether the slab descends along the side of the box or in the middle of the box has a significant influence on the ability of the slab to penetrate the phase boundary as observed by the isotherms, but the variation in the mass flux diagnostic is minor. We conclude that neither slab penetration nor mass flux diagnostics is a sufficient indicator of long‐term mixing of material between the upper and lower mantle.