A similarity solution has been developed for vertical, steady-state mantle plume conduits by considering the boundary layer flow emanating from a point source of heat in an axisymmetric geometry. This model includes the effects of temperature and shear stress on viscosity and incorporate depth-dependent viscosity and thermal expansivity. Plumes with variable viscosity have upward velocities of 0.30--100 m/yr and radii of 30--250 km, depending on temperature, rheology, and buoyancy flux. These results demonstrate the small lateral scale of plume features relative to the resoluton of most large-scale convection models and seismological studies. All of the plumes studied showed significant entrainment of ambient mantle surrounding the plume conduit, driven by the radial conduction of heat from the plume. This heat raises the buoyancy and lower the viscosity of the ambient mantle, thereby entraining it into the conduit flow. For buoyancy fluxes of 0.1--10 Mg/s, similar to the range estimated for plumes in the Earth's mantle, we calculate a range of entrainment of >90% to <5% ambient mantle, correlating negatively with buoyancy flux. Examination of the streamlines of mantle material which is entrained into into thermal plumes indicates that most of the entrained fraction originates from approximately the lower half of the layer traversed by the plume, and shows minor entrainment of upper level material.

This is especially true for non-Newtonian and depth dependent rheologies, and for depth-dependent thermal expansivity. Upwelling of depleted upper mantle, viscously coupled to the plume flow, is proposed as a mechanism for generating post-shield stage alkalic basalts erupted on oceanic island chains and their associated flexural arches. The existing Sr-Nd-Pb isotope data for for oceanic basalts indicate the presence of a component which is common to hotspot basalts worldwide, and which is distinct from the upper mantle source of mid-ocean ridge basalts. This component et al. (1992)> has moderately depleted Sr and Nd signatures, radiogenic Pb isotopes, and elevated 3He/4He ratios. The high He isotope ratios of FOZO suggest an origin for this component in the lower mantle, and would appear to provide independent evidence to support the fluid dynamic observations for significant entrainment of lower mantle in plumes and exclusion of upper mantle. If the composition of FOZO is representative of the isotopic composition of the lower mantle, then it would appear that this reservoir has been differentiated relative to estimates for the bulk silicate earth (BSE). This may be due either to melting and differentiation at higher levels in the mantle, or to fractionation of high pressure phases from a terrestrial magma ocean. ¿American Geophysical Union 1994