[SIT25-01] Application of the mixed length theory to assess the generation of melt in internally heated systems
Keywords:Internal heating, Convection, Melting, Parameterized convection, Mixed Length Theory, Mantle dynamic
Alternatively, we propose a new analytical framework allowing to estimate the amount and depths of melting in 1D parameterized convection. 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 compared 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 convective system including the effect of melting on the heat budget. We then apply our algorithm to the long-term evolution of a generic planetary mantle and compare to the evolution calculated with 3D numerical simulations.