Controls on entrainment of a dense chemical layer by thermal plumes

Results from two-dimensional axisymmetric numerical models of a chemically dense layer entrained by thermal plumes, featuring a plume temperature structure fixed a priori as a Gaussian function and strongly temperature-dependent viscosity, show that the entrainment rate, Q, is controlled by the radius of the thermal plume, r(T), the ratio of excess chemical to thermal buoyancy, R-b, and viscosity contrast across the two layers, gamma. Fitting of the numerical results shows that Q similar to gamma(0.65) r(T)(3.90) R-b(-2.89 gamma 0.17). A smaller rT and/or a larger R-b results in a smaller entrainment rate, as expected. However, the dependence of Q on Rb is Much stronger than previously suggested if the fluid viscosity is strongly temperature dependent. The effects of gamma on Q depend on R-b because the scale of Q on R-b is dependent on gamma, and when R-b is around 1.8, the dependence of Q on gamma is weak. The results also show that the dependences of the radius, r(c), and the vertical velocity, V-zc, of the chemical plume on R-b are also much stronger than previously suggested if the fluid viscosity is strongly temperature dependent. Scaling the numerical results to the Earth's mantle suggests that the chemically dense layer in the mantle may survive through the age of the Earth with insignificant entrainment, e.g. in a mantle with a reference viscosity of 5 x 10(21) Pas and a reference density of 4000 kg/m(3), a thermal plume that has a radius of 80 km, a temperature of 600 K hotter and a viscosity of 100 times lower at the center of the plume than in the ambient mantle can only entrain less than 5% of the bottom chemical layer that is 300 km thick, 0.9% denser than the above mantle (R-b = 1.5) and spread over an area of size similar to 0.5D(2) (D = 2900 km, thickness of the mantle) through the age of the Earth. (C) 2008 Elsevier B.V. All rights reserved.