Small‐scale convection in the D″ layer

Abstract

[1] Small-scale convection has been suggested as a possible explanation for seismic heterogeneities in the D 00 layer of the Earth's mantle. Recently developed scaling laws for convection with realistic viscosities allow quantitative assessment of this hypothesis. Large temperature and viscosity contrasts across the thermal boundary layer at the core-mantle boundary suggest that small-scale convection starts at the bottom of the thermal boundary layer and propagates upward before the thermal boundary layer as a whole becomes unstable. The convection boundary is likely to become a chemical boundary as a result of mixing within the convective layer. This implies that the D 00 discontinuity can represent both convective and chemical boundary and that the presence or absence of small-scale convection can be responsible for the observed intermittent nature of the D 00 discontinuity. Most lateral heterogeneities in the D 00 layer are concentrated near the convection boundary, consistent with seismic data. The length scale of lateral temperature variations, the topography of the core-mantle boundary, and the viscosity of the D 00 layer are in agreement with observational constraints. The thickness of the secondary thermal boundary layer formed at the bottom of the convective layer is similar to the thickness of the ultralow-velocity zone. The magnitude of lateral variations in temperature can only marginally be responsible for lateral variations in seismic velocities. Variations in the topography of the convection boundary and chemical heterogeneities are likely to be more important factors. A large seismic velocity drop in the ultralow-velocity zone cannot be explained by thermal effects alone and must be caused by other factors such as partial melting.

Plume formation in strongly temperature-dependent viscosity fluids over a very hot surface

“…In this regime, plumes form after an extended period of small-scale convection in the thermal boundary layer. A simple analysis based on the stagnant lid convection theory 19 and the RayleighTaylor instability theory 21 suggests that plume formation can approximately be described as a Rayleigh-Taylor instability of the two-layer system consisting of the vigorously convecting thermal boundary layer and a nearly isothermal layer above it. Plumes form when the growth rate of the largescale instability of this two-layer system exceeds the growth rate of the convective thermal boundary layer.…”

“…This interface is defined by an isotherm TϭT L . The value of T L can be chosen as the isotherm T L ϭ1Ϫ3.7 Ϫ1 Ϸ0.73 defining the boundary of the actively convecting region ( Ϫ1 is the scale for the typical temperature variations in the convective region and the coefficient 3.7 is estimated numerically and experimentally in previous studies 19 ͒. However, the fluctuations in the position of this isotherm are substantial because of the time-dependent character of small-scale convection.…”

“…3. The temperature profile is characterized by two nearly isothermal regions separated by a sharp interface ͑this structure was described in detail by Solomatov and Moresi 19 ͒. The viscosity of the lower layer can be considered approximately constant because the convective mixing in this region maintains a nearly uniform temperature such that 1ϪT 1 ϳ Ϫ1 ͑Ref.…”

“…Smallscale convection is not sensitive to the exact perturbation function because the cell size is self-regulated and increases during the growth of the convective boundary layer. 19 Once developed, small-scale convection generates perturbations which, theoretically, can cause large-scale instability and produce a plume. However, at the Rayleigh numbers that we can reach the growth rate of these, very short wavelength perturbations is so small that the convective boundary layer propagates through the entire layer without producing plumes.…”

Survival of Archean cratonal lithosphere

“…This amount is not in gross error. Solomatov and Moresi [2002] give a preferred range of 1.1-1.3T h for the related case of secondary convection within D 00 . The temperature contrast ÁT 3 and the ratio q/q S decrease with the viscosity ratio h C /h 0 ( Figure E2).…”