标题： 浅壳模型对冰质卫星地形松弛的影响 显示英文标题

标题： Implications of shallow-shell models for topographic relaxation on icy satellites

摘要： 冰质卫星在许多长度尺度上都存在地形，从小型的裂谷和古老地盾到赤道-极地区域壳层厚度差异，这些差异与这些天体的周长相当。 地形演化的速率取决于冰壳的流变学性质、壳层与潜在全球地下海洋之间的密度差异、冰壳厚度分布以及壳层中潮汐热耗散的速率。 在这里，我们从粘性流体流动的斯托克斯方程出发分析地形的松弛。 我们列出了浅壳模型（包括有刚性地壳和没有刚性地壳的情况），并将得到的时间尺度与之前的工作进行比较。 使用三维线性化流动来处理小振幅地形扰动，我们从浅壳模型以及非浅壳中恢复了松弛的时间尺度。 对于粘度恒定的壳层，我们发现当波长大于冰层厚度时，地形松弛时间尺度是恒定的，这一观点与现有的范式相矛盾。 对于粘度随深度呈指数下降的壳层，我们通过数值模拟表明存在一个区域，在该区域中较大的粘度外层地壳充当几乎刚性边界。 在这种情况下，松弛时间尺度依赖于波长。 对于最大的空间尺度，时间尺度再次与波长无关，其值由平均壳层粘度决定。 然而，这种转变发生的空间尺度随着粘度对比度的增加而增大，限制了无尺度松弛率的适用性。 这些关于地形松弛的结果对解释松弛的陨石坑剖面、从地形推断冰壳厚度以及对外太阳系任务的未来观测具有重要意义。 显示英文摘要

摘要： Icy satellites host topography at many length scales, from rifts and craters on the small end to equatorial-pole shell thickness differences that are comparable to these bodies' circumference. The rate of topographic evolution depends on the rheology of the ice shell, the difference in density between the shell and potential global subsurface oceans, the ice shell thickness distribution, as well as the rate of tidal heat dissipation in the shell. Here we analyze relaxation of topography starting from the Stokes equations for viscous fluid flow. We write out the shallow-shell models (with and without a rigid crust) and compare the resulting time scales to previous work. Using three-dimensional linearized flow for small-amplitude topographic perturbations, we recover the time scales of relaxation from the shallow models as well as shells that are not shallow. For a shell of constant viscosity, we find that the topographic relaxation time scale is constant for wavelengths larger than the ice thickness, an idea that runs contrary to the existing paradigm. For a shell with a viscosity that decreases exponentially with depth, we show numerically that there is a regime where the larger viscosity outer crust acts as a nearly rigid boundary. In this case, the relaxation time scale depends on the wavelength. For the largest spatial scales, the time scale becomes independent of wavelength again and the value is set by the average shell viscosity. However, the spatial scale that this transition occurs at becomes larger as the viscosity contrast increases, limiting the applicability of the scale-independent relaxation rate. These results for the relaxation of topography have implications for interpreting relaxed crater profiles, inferences of ice shell thickness from topography, and upcoming observations from missions to the outer solar system.