Dampening effect of global flows on Rayleigh–Taylor instabilities: implications for deep-mantle plumes vis-à-vis hotspot distributions

Abstract

SUMMARY It is a well-accepted hypothesis that deep-mantle primary plumes originate from a buoyant source layer at the core–mantle boundary (CMB), where Rayleigh–Taylor instabilities (RTIs) play a key role in the plume initiation process. Previous studies have characterized their growth rates mainly in terms of the density, viscosity and layer-thickness ratios between the denser overburden and the source layer. The RTIs, however, develop in the presence of global flows in the overlying mantle, which can act as an additional factor in the plume mechanics. Combining 2-D computational fluid dynamic (CFD) model simulations and a linear stability analysis, this paper explores the influence of a horizontal global mantle flow in the instability dynamics. Both the CFD simulation results and analytical solutions reveal that the global flow is a dampening factor in reducing the instability growth rate. At a threshold value of the normalized global flow velocity, short- as well as long-wavelength instabilities are completely suppressed, allowing the entire system to advect in the horizontal direction. Using a series of real-scale numerical simulations, this paper also investigates the growth rate as a function of the density contrast, expressed in Atwood number ${A}_T = ({{{\rho }_1 - {\rho }_2}})/({{{\rho }_1 + {\rho }_2}})$, and the viscosity ratio $\ {\mu }^* = \ {\mu }_1/{\mu }_2$, where ${\rho }_1,\ {\mu }_{1\ }$ and ${\rho }_{2,}\ {\mu }_{2\ }$are densities and viscosities of the overburden mantle and source layer, respectively. It is found that increase in either ${A}_T$ or ${\mu }^*$ promotes the growth rate of a plume. In addition, the stability analysis predicts a nonlinearly increasing RTI wavelength with increasing global flow velocity, implying that the resulting plumes widen their spacing preferentially in the flow direction of kinematically active mantle regions. The theory accounts for additional physical parameters: source-layer viscosity and thickness in the analysis of the dominant wavelengths and their corresponding growth rates. The paper finally discusses the problem of unusually large inter-hotspot spacing, providing a new conceptual framework for the origin of sporadically distributed hotspots of deep-mantle sources.