地球发电机模拟中力平衡和流动长度尺度的关系
Relating force balances and flow length scales in geodynamo simulations
摘要：
在流体动力学中，流动长度尺度的标度行为通常用于推断系统的支配力平衡。成功方法的关键是测量代表溶液中所含能量（能量相关）和指示所建立的力平衡（动态相关）的长度尺度。在旋转对流和磁流体动力发电机在球壳的数值模拟中，它仍然很难测量的长度尺度，都是积极的和动态相关的，这导致了相互矛盾的解释的基本力平衡。通过分析一组广泛的磁性和非磁性模型，我们专注于两个长度尺度，实现能量和动力学的相关性。第一个是极向动能谱的峰值，我们成功地将其与力平衡谱表示上的交叉点进行了比较。在大多数发电机模型中，这一结果证实了系统的主导长度尺度是由准地转（QG-）MAC（Magneto-Archimedean-Coriolis）平衡控制的。在非磁对流模型中，分析倾向于QG-CIA（科里奥利-惯性-阿基米德）平衡。在发电机模型中，我们引入了第二个与流中轴向不变性损失相关的能量相关长度尺度。我们再次将这个长度尺度与尺度相关的力平衡图中的交叉点联系起来，该交叉点标志着大尺度地转（科里奥利力和压力的平衡）和小尺度磁旋之间的过渡，其中洛伦兹力超过科里奥利力。这两个积极的和动态相关的长度尺度的尺度分析表明，地球的发电机是由QG-MAC平衡控制在一个占主导地位的规模约为200公里，而磁旋效应被推迟到小于50公里的规模。
英文摘要：
In fluid dynamics, the scaling behaviour of flow length scales is commonly used to infer the governing force balance of a system. The key to a successful approach is to measure length scales that are representative of the energy contained in the solution (energetically relevant) and indicative of the established force balance (dynamically relevant). In numerical simulations of rotating convection and magneto-hydrodynamic dynamos in spherical shells, it has remained difficult to measure length scales that are both energetically and dynamically relevant, which has led to conflicting interpretations of the underlying force balance. By analysing an extensive set of magnetic and non-magnetic models, we focus on two length scales that achieve both energetic and dynamical relevance. The first one is the peak of the poloidal kinetic energy spectrum, which we successfully compare to crossover points on spectral representations of the force balance. In most dynamo models, this result confirms that the dominant length scale of the system is controlled by a quasi-geostrophic (QG-) MAC (Magneto-Archimedean-Coriolis) balance. In non-magnetic convection models, the analysis favours a QG-CIA (Coriolis-Inertia-Archimedean) balance. In dynamo models, we introduce a second energetically relevant length scale associated with the loss of axial invariance in the flow. We again relate this length scale to a crossover point in scale-dependent force balance diagrams, which marks the transition between large-scale geostrophy (the equilibrium of Coriolis and pressure forces) and small-scale magnetostrophy, where the Lorentz force overtakes the Coriolis force. Scaling analysis of these two energetically and dynamically relevant length scales suggests that the Earth's dynamo is controlled by a QG-MAC balance at a dominant scale of about 200 km, while magnetostrophic effects are deferred to scales smaller than 50 km.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
