The dynamics of plume-ridge interaction, 1: Ridge-centered plumes

We investigate the dynamics of mantle plumes rising beneath mid-ocean ridges. To clarify the physics of this process, we examine first a simple ‘lubrication theory’ model in which a point source (analogous to a plume ‘stem’) of volume flux Q located directly beneath the ridge releases buoyant fluid into a viscous corner flow driven by a velocity boundary condition u(x) = Utanh(x/d), where U is the half-spreading rate and the ‘gap width’ between the diverging plates is ∼ 5d. Numerical solutions of the differential equation governing the plume head thickness S(x, y) show how the width W of the plume head along the ridge depends on Q, U, d, and σ ≡ gΔϱ/48n, where Δϱ is the density deficit of the plume and η is the viscosity. In the geophysically relevant ‘narrow gap’ limit (Q/σ)1/4 ≫ d, W ∼ (Q/U)1/2IIb0.053, where IIb =Q/σU2 is the ‘buoyancy number’. Numerical solutions of a more realistic 3D convection model with strongly temperature and pressure-dependent viscosity obey a nearly identical scaling law, and show no evidence that W is increased by ‘upslope’ flow of plume material toward the ridge along the sloping base of the rheological lithosphere. To apply our model to Iceland, we incorporate into it a melting parameterization that allows prediction of the excess crustal thickness produced by melting in the plume head. This extended model shows that the observed depth anomalies along the Mid-Atlantic Ridge near Iceland cannot be explained by a hot (temperature contrast ΔT ∼ 250°C) and narrow (radius ∼ 60 km) ridge-centered plume. Instead, the anomalies are consistent with a much cooler and broader upwelling.