Thermal and hydrodynamic relationships between the melt in the thermochemical plume conduit and the horizontal mantle flow

Abstract

When modeling the formation and dynamics of thermochemical plumes, geologists and geophysicists of the world use equations of free convection in the Boussinesq approximation with addition of the mass transfer equation [1]. It is assumed that the base of the mantle corresponds to a dense chemical layer that was formed owing primarily to accretion of the oceanic crust in the lower mantle. The plume is forming in the thermal boundary zone in the presence of this dense chemical layer at the base of the mantle. The ascending migration of the plume under thermal and concentration gravitational convection is stimulated by the high temperature gradient between the core‐mantle interface and the surrounding mantle (750 K). The ascending movement of the plume is accompanied by the capture of material from the dense chemical layer. Our model of the thermochemical plume [2] differs from that accepted in [1]. Its difference from the latter is discussed in detail elsewhere [3]. According to our model, thermochemical plumes form at the core‐mantle interface under the influence of the heat flow from the outer core and local influx of a chemical dope that reduces the melting point of the lower mantle substance, which results in mantle substrate melting and upward plume migration [2, 3]. The heat and mass transfer due to interaction between horizontal free convection mantle flows and the conduit of the thermochemical plume located under the oceanic plate away from the mid-oceanic ridge (MAR) is considered in [4] with presentation of the main equations for calculating the heat and mass transfer by the thermochemical plume interacting with the horizontal convective mantle flow and quantitative correlation between the dope concentration at the plume base and the Lewis number. The purpose of this study is calculation of the heat exchange between the conduit of the thermochemical plume ascending from the core‐mantle interface and the horizontal mantle flow. We present the model of the plume conduit interacting with horizontal free convection flows in the upper and lower mantle and determine local coefficients of the heat transfer at the interface between the melt and the surrounding mantle (plume conduit boundary), as well as the diameter of the Hawaiian plume interacting with horizontal mantle flows. Based on the calculated heat exchange between the plume and the horizontal lower mantle flow, we also estimate the main parameters of the lower mantle. Let us consider the possible structure of the conduit and head part of the Hawaiian plume based on experimental modeling and seismic studies of the upper mantle beneath the Island of Hawaii. The thermal power of the Hawaiian plume is estimated to be 3 · 10 11 W, and the Raleigh number (Ra) for the free convection flow in the conduit of the Hawaiian plume is