Model relating heat-flow values near, and vertical velocities of mass transport beneath, oceanic rises

The heat transport equation along the stagnation point streamline is solved by the method of matched asymptotic expansions as a first approximation of the temperature distribution directly beneath an oceanic rise. Far below the ocean bottom the temperature T(Z, e) is given by the temperature calculated for adiabatic (upward) displacement. In a narrow region near the surface, the thermal boundary layer, T(Z, e) rapidly adjusts through conductive heat flow to match the surface temperature. The linear coefficient of the series expansion of the vertical velocity distribution υ(Z) can be determined from the surface heat flow near the rise crest Qcrest. Under simplifying assumptions an estimate of the maximum value of υ(Z) can be obtained. Qcrest is primarily controlled by the thickness of, and temperature at the base of, the thermal boundary layer; at greater depth, a wide range of velocity and temperature distributions can exist without materially altering the thermal structure of the boundary layer. Within the limitations of the assumed model, provided that vertical velocities at depth are comparable to horizontal spreading velocities away from the rise, observed values of Qcrest are too low by at least several factors of 2. Low values of Qcrest can be rationalized as a time-dependent effect if igneous emplacement at the axis of spreading has been at a relatively low level for the past 0.5–1 m.y. The thickness of the thermal boundary layer is probably the primary constraint on the seismic depth of spreading centers and associated transform faults.