  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].
