It is generally accepted that melt extraction from the mantle at mid-ocean ridges (MORs) is concentrated in narrow regions of elevated melt fraction called channels. Two feedback mechanisms have been proposed to explain why these channels grow by linear instability: shear flow of partially molten mantle and reactive flow of the ascending magma. These two mechanisms have been studied extensively, in isolation from each other, through theory and laboratory experiments as well as field and geophysical observations. Here, we develop a consistent theory that accounts for both proposed mechanisms and allows us to weigh their relative contributions. We show that interaction of the two feedback mechanisms is insignificant and that the total linear growth rate of channels is well-approximated by summing their independent growth rates. Furthermore, we explain how their competition is governed by the orientation of channels with respect to gravity and mantle shear. By itself, analysis of the reaction-infiltration instability predicts the formation of tube-shaped channels. We show that with the addition of even a small amount of extension in the horizontal, the combined instability favours tabular channels, consistent with the observed morphology of dunite bodies in ophiolites. We apply the new theory to MORs by calculating the accumulated growth and rotation of channels along streamlines of the solid flow. We show that reactive flow is the dominant mechanism deep beneath the ridge axis, where the most unstable orientation of high-porosity channels is sub-vertical. Channels are then rotated by the solid flow away from the vertical. The contribution of the shear-driven instability is confined to the margins of the melting region. Within the limitations of our study, the shear-driven feedback is not responsible for significant melt focusing or for shallowly dipping seismic anisotropy [abridged].
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