open access

https://hdl.handle.net/2115/85087

Application of the mixing length theory to assess the generation of melt in internally heated systems

英語

Planetary volcanism

2022-04

Oxford University Press

Geophysical journal international

229(1)

328-344

Melting in planetary mantles plays a key role in their thermochemical evolution. Assessing the amount and location of melting generally requires the 3-D temperature fields of the system, such that 3-D numerical simulations are in principle necessary prohibiting us from exploring wide ranges of conditions. To overcome this issue, we propose a new 1-D analytical framework estimating at first order the amount and depths of melting for a simplified convective system. To do so, we develop an approach, partly based on an extended version of the mixing length theory, able to estimate the distribution of the hottest temperatures in natural systems. The approach involves several free parameters that are calibrated by fitting 3-D numerical simulations. We demonstrate that our algorithm produces melting profiles at steady-state and long-term evolutions in fairly good agreement with 3-D numerical simulations. We then apply our framework to a wide variety of planetary sizes and heating rates. We find that an increase in planetary radius R increases the depth of melting for small planets (R < 800 km) but decreases it for larger planets. This is caused by the pressure dependence of the solidus.

学術雑誌論文

Version of Record

This article has been accepted for publication in Geophysical Journal International ©: 2021 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society. All rights reserved.

0956-540X

1365-246X