Diapirism in the earth's mantle: Experiments on the motion of a hot sphere in a fluid with temperature-dependent viscosity

The ascent of magma diapirs through the earth's mantle is modelled experimentally by the motion of a hot metal sphere through a fluid whose viscosity varies strongly with temperature. The dimensionless drag on the sphere (drag number D) and the heat transfer from it (Nusselt number Nu) are found as functions of the dimensionless velocity of the sphere (Peclet number Pe) and the viscosity contrast μ_∞/μ₀ = 10^γ, where μ_∞ and μ₀ are the viscosities of the fluid far from the sphere and at its surface. The drag D = D(Pe, γ) has two limits. For large Pe and small γ (“Stokes” limit), the drag approaches the Stokes' Law result. For small Pe and large γ (“lubrication” limit), the drag is orders of magnitude less than that predicted by Stokes' Law. Nu is a function of Pe alone. For reasonable values of the diapir radius and the viscosity contrast, the dimensionless scale height Pe/3 Nu may exceed a critical value, resulting in progressive melting during ascent. This suggests that diapirs may ascend great distances through the mantle while remaining largely molten. Lamont-Doherty Geological Observatory Contribution No. 3414.