论文标题
混合长度理论的应用来评估内部加热系统中熔体的产生
Application of the mixing length theory to assess the generation of melt in internally heated systems
论文作者
论文摘要
行星地幔中熔化的影响在其热化学演化中起关键作用。由于熔化的横向异质性质，因此3D数值模拟原则上是必要的，禁止我们探索宽阔的条件范围。为了克服这个问题，我们提出了一个新的分析框架，允许在1D分析模型中估算简化对流系统中熔化的数量和深度。为此，我们开发了一种方法，部分基于混合长度理论的扩展版本，能够估算自然系统中最热温度的分布。该方法涉及通过拟合3D数值模拟校准的几个自由参数。我们证明，我们的算法在稳态上提供了熔融曲线，以及与3D数值模拟中获得的算法相当良好的一致性。然后，我们将框架应用于各种行星尺寸和加热速率。我们发现，行星大小的增加会增加小行星的熔化深度，但大行星减少。趋势的这种变化是由固相的压力依赖性引起的。
The effect of melting in planetary mantles plays a key role in their thermo-chemical evolution. Because of the laterally heterogeneous nature of melting, 3D numerical simulations are in principle necessary prohibiting us from exploring wide ranges of conditions. To overcome this issue, we propose a new analytical framework allowing to estimate the amount and depths of melting in a 1D analytical model 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 3D numerical simulations. We demonstrate that our algorithm provides the melting profile at steady-state as well as the long-term evolution in fairly good agreement with the ones obtained in 3D numerical simulations. We then apply our framework for a wide variety of planetary sizes and heating rates. We find that an increase in planetary size increases the depth of melting for small planets but decreases for large planets. This change in the trend is caused by the pressure dependence of the solidus.
