Plumes,subaxial pipe flow,and topography along the Mid-Oceanic Ridge

If plate thickness depends on crustal age, the region of extensive partial melting below the spreading axis will be wider around fast-spreading ridges. The melt region creates a subaxial conduit channeling partial melts away from ridge-centered hot spots. The channel is here modeled by an elliptical pipe of semiminor (vertical) axis 2 × 10⁶ cm (20 km) and semimajor (horizontal) axis KS, where S is spreading half-rate (cgs) and K is a constant of magnitude 10¹⁴ to 10¹⁵ seconds. This simple analytical model is used to explain the observation that maximum hot spot elevations on the Mid-Oceanic Ridge fall dramatically with increasing spreading rate (there are no Icelands or Afars on the East Pacific Rise!). A hot spot under a fast-spreading ridge has a broad pipe in which to discharge its partial melts; hence, only a slight topographic gradient and a low elevation is needed to discharge the mass flux rising out of the deeper mantle at the hot spot center. A second factor is that partial melts are “used up” faster in the accretion process on fast-spreading ridges. In the simple analytical model, both factors operating together explain the rapid fall of hot spot heights with increasing spreading half-rate. This result indirectly helps confirm the idea of horizontal pipe flow below the Mid-Oceanic Ridge.A theoretical topographic profile through a hot spot on the Mid-Oceanic Ridge is derived from the assumption that the pressure — i.e., topographic — gradient at a distance x from the hot spot is sufficient to supply all the accreting lithosphere downstream of x, out to x_n, the limit of topographic hot spot influence. The predicted profile is quadratic in x and concave upward, and resembles several observed profiles where neighboring hot spots are not so close as to confuse the profiles. Some observed profiles are more nearly linear or even convex upward. This could be explained, for example, by downstream increases in viscosity or decreases in pipe dimensions.A hot spot on a ridge spreading at much less than 1 cm/yr half-rate would produce an enormous elevation of the ridge axis, according to our model, because the pipe would be very narrow. Such a large topographic high would create a large gravity potential which would cause the plates to move apart faster, thereby widening the pipe, and reducing the topographic high. The system of ridges and hot spots may thus be self-regulating with respect to plate speeds; this could explain why spreading half-rates on the Mid-Oceanic Ridge are in many areas as low as 1.0 cm/yr but very rarely as low as 0.5 cm/yr.