Evolution of Semiconvective Staircases in Rotating Flows: Consequences for Fuzzy Cores in Giant Planets

J. R. Fuentes, Bradley W. Hindman, Adrian E. Fraser and Evan H. Anders
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Abstract

Recent observational constraints on the internal structure of Jupiter and Saturn suggest that these planets have “fuzzy” cores, i.e., gradients of the concentration of heavy elements that might span a large fraction of the planet’s radius. These cores could be composed of a semiconvective staircase, i.e., multiple convective layers separated by diffusive interfaces arising from double-diffusive instabilities. However, to date, no study has demonstrated how such staircases can avoid layer mergers and persist over evolutionary timescales. In fact, previous work has found that these mergers occur rapidly, leading to only a single convective layer. Using 3D simulations, we demonstrate that rotation prolongs the lifetime of a convective staircase by increasing the timescale for both layer merger and erosion of the interface between the final two layers. We present an analytic model for the erosion phase, predicting that rotation increases the erosion time by a factor of approximately Ro−1/2, where Ro is the Rossby number of the convective flows (the ratio of the rotation period to the convective turnover time). For Jovian conditions at early times after formation (when convection is vigorous enough to mix a large fraction of the planet), we find the erosion time to be roughly 109 yr in the nonrotating case and 1011 yr in the rotating case. If these timescales are confirmed with a larger suite of numerical simulations, the existence of convective staircases within the deep interiors of giant planets is a strong possibility, and rotation could be an important factor in the preservation of their fuzzy cores.
旋转流中半流动阶梯的演变:巨行星模糊内核的后果
最近对木星和土星内部结构的观测制约表明,这些行星有 "模糊 "的内核,即可能跨越行星半径很大一部分的重元素浓度梯度。这些内核可能由半对流阶梯组成,即多个对流层被双扩散不稳定性产生的扩散界面隔开。然而,迄今为止,还没有研究证明这种阶梯如何避免层合并并在进化时间尺度上持续存在。事实上,之前的研究发现,这些合并发生得很快,只会导致一个对流层。通过三维模拟,我们证明了旋转可以延长对流阶梯的寿命,因为它同时增加了层合并和最后两层之间界面侵蚀的时间尺度。我们提出了侵蚀阶段的解析模型,预测旋转会使侵蚀时间增加约 Ro-1/2 倍,其中 Ro 是对流的罗斯比数(旋转周期与对流周转时间之比)。对于形成后早期的约维亚条件(此时对流足够旺盛,可以混合大部分行星),我们发现非旋转情况下的侵蚀时间大约为 109 年,旋转情况下为 1011 年。如果这些时间尺度在更大规模的数值模拟中得到证实,那么巨行星内部深处存在对流阶梯的可能性就非常大了,而自转可能是保留其模糊内核的一个重要因素。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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