P025-0003
Application of the mixed length theory to assess the generation of melt in planetary bodies
Application of the mixed length theory to assess the generation of melt in planetary bodies
Wednesday, 9 December 2020
Poster
Abstract:
Generation of melt is crucial for the evolution of a planetary body, because: (i) melting is a very efficient way of transporting heat, so that that it may alter importantly the thermal state of the body; (ii) in terrestrial planets, melting of rocks and its associated volcanism induce chemical differentiation producing rocks with a large range of chemical compositions. However, melt generation is extremely simplified in analytical models and 3D numerical simulations. For instance, in 3D numerical simulations, the chemical composition of the produced rocks are set independently of the pressure-temperature of melting. This simplification induces large uncertainties on the chemical evolution calculated
Alternatively, we propose a new analytical framework allowing to estimate precisely the amount and depths of melting in a 1D evolution model. To do so, we develop an approach, partly based on an extended version of the mixed length theory, able to estimate the distribution of the hottest temperatures in natural systems. Due to the novelty of the approach, we apply our framework to a simplified convective system consisting of a purely internally heated fluid in a Cartesian geometry. The approach involves several free parameters that are calibrated by fitting 3D numerical simulations. We then successfully compare the amount of melting estimated from our 1D analytical approach to results of 3D numerical simulations. Building on this success, we develop an algorithm able to calculate the 1D thermal evolution of our simplified convective system including the effects of melting, secular cooling and radioactive heating. We then apply our algorithm to the long-term evolution of a generic planetary mantle and compare successfully to the evolution calculated with 3D numerical simulations. Future work will be dedicated to apply our analytical approach to the icy shell of icy satellites and the silicate mantle of terrestrial planets.
Alternatively, we propose a new analytical framework allowing to estimate precisely the amount and depths of melting in a 1D evolution model. To do so, we develop an approach, partly based on an extended version of the mixed length theory, able to estimate the distribution of the hottest temperatures in natural systems. Due to the novelty of the approach, we apply our framework to a simplified convective system consisting of a purely internally heated fluid in a Cartesian geometry. The approach involves several free parameters that are calibrated by fitting 3D numerical simulations. We then successfully compare the amount of melting estimated from our 1D analytical approach to results of 3D numerical simulations. Building on this success, we develop an algorithm able to calculate the 1D thermal evolution of our simplified convective system including the effects of melting, secular cooling and radioactive heating. We then apply our algorithm to the long-term evolution of a generic planetary mantle and compare successfully to the evolution calculated with 3D numerical simulations. Future work will be dedicated to apply our analytical approach to the icy shell of icy satellites and the silicate mantle of terrestrial planets.