Abstract The presence of 40Ar in Titan's atmosphere and the replenishment of methane argue for the exchange between the interior and the atmosphere. These observations triggered the present study that aims to determine the conditions under which the high-pressure (HP) ice layer, likely present between the deep ocean and the silicate core, poses a barrier for the exchange of volatiles. We model heat and water transport through this convecting HP ice layer using a two-phase numerical model of solid ice-liquid water mixture. We observe that for a large range of heat fluxes from the silicate core and HP ice layer thicknesses, a few percent of liquid water forms at the interface with the silicates. Liquid water being less dense than the HP ice, it creates additional buoyancy, thus facilitating the transport of volatiles towards the ocean. Our results also show that convection is characterized by the presence of hot and the absence of cold plumes. We derive a scaling law that describes the dependence of a critical heat flux for the onset of melting at the silicates interface on the thickness of the HP ice layer and the ice viscosity. We also study the processes at the interface with the base of the ocean where a few tens of kilometers thick layer of temperate (partially molten) ice is present. We find a scaling law for its thickness that depends mainly on the ice viscosity and the density difference between the ice and water. Water from this partially molten, temperate layer flows into the ocean thus completing the connection with the silicate core. The water flux depends primarily on the amount of heat supplied from the silicates. Future evolution models that will use the scaling laws derived in this study will place bounds on the timing of these exchange processes. Using Cassini data and reasonable values of HP ice viscosity and silicate heat flux, we predict melting at the silicates/HP ice interface at present time.

中文翻译：

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泰坦高压冰层动力学

摘要 泰坦大气中40Ar的存在和甲烷的补充为内部与大气之间的交换提供了依据。这些观察触发了本研究，旨在确定可能存在于深海和硅酸盐核心之间的高压 (HP) 冰层对挥发物交换构成障碍的条件。我们使用固体冰-液水混合物的两相数值模型模拟通过这个对流 HP 冰层的热量和水传输。我们观察到，对于来自硅酸盐核心和 HP 冰层厚度的大范围热通量，在与硅酸盐的界面处形成了百分之几的液态水。液态水的密度低于高压冰，它会产生额外的浮力，从而促进挥发物向海洋的输送。我们的结果还表明，对流的特点是有热羽流和没有冷羽流。我们推导出一个标度定律，该定律描述了硅酸盐界面开始融化的临界热通量对 HP 冰层厚度和冰粘度的依赖性。我们还研究了海洋底部界面的过程，那里有几十公里厚的温带（部分熔融）冰层存在。我们发现其厚度的标度定律主要取决于冰的粘度和冰与水之间的密度差异。来自这个部分熔融的温带层的水流入海洋，从而完成了与硅酸盐核心的连接。水通量主要取决于硅酸盐提供的热量。将使用本研究中得出的标度定律的未来进化模型将对这些交换过程的时间设置界限。使用 Cassini 数据和 HP 冰粘度和硅酸盐热通量的合理值，我们预测目前硅酸盐/HP 冰界面的融化。