Consolidated Grant in Solar and Planetary Studies: Department of Applied Mathematics, University of Leeds

许多天体物理现象涉及磁场、旋转和湍流之间复杂的相互作用。我们将进行系统和综合的研究方案，在太阳系和行星科学的各种情况下调查这种相互作用。我们将利用分析和数值技术的结合（包括应用为大规模并行机器优化的尖端数值算法）来理解这些现象。我们建议研究以下具体问题：(1)在太阳上，观测到的磁场存在于从大的、长寿命的到小的、短寿命的一系列时空尺度上。此外，太阳表面的对流也有一系列尺度，从超颗粒（直径约20,000公里）到颗粒（直径约1,000公里）。利兹开发了一种新的非弹性代码，我们将用它来探索对流和磁场之间的相互作用，以解释这些尺度上观察到的范围。我们将讨论观测到的小尺度磁场是被击穿的大尺度磁场，还是由小尺度发电机重新产生的重要问题。我们还将探讨近地表剪切层的作用，看看它是如何影响光球层下面的太阳磁场的。(2)太阳物理学的一个重要观测发现是“太阳速斜”的发现，这是太阳深处一个夹在对流带和辐射带之间的高速切变薄区。最近对太阳的卫星观测显示，除了11年的活动周期外，太阳还出现了新的短周期活动周期。对日冕中亮点的长期观测揭示了慢波。这些波和活动周期很可能产生于速斜。我们将探讨速斜可以支持哪些类型的波，以及它们如何在非线性状态下发展。这将使我们能够发现这些新的观测结果是否可以从速斜动力学的角度来理解，以及这些内部深处的信号是如何传输到太阳表面的。(3)速斜下方辐射内部磁场的性质和强度是太阳研究的一大未知问题。我们将探索一种被称为磁浮力的机制，通过这种机制，磁场向上上升。众所周知，这在接近太阳表面的地方很重要，但它也可能在太阳最深处发挥作用。磁浮力和双扩散对流之间有相似之处，这发生在我们的海洋中。最近发现，通过形成密度层，海洋中的热量和盐的传输可以大大加强。通过研究三维非线性模型来研究磁环境下的这种分层过程，我们将探索这种分层是否会发生在太阳内部深处。这将对太阳辐射区磁场提供重要的新约束。朱诺号太空任务传回了木星表面令人惊叹的照片，我们现在也有了关于木星磁场和重力场的更精确的数据。重力场数据表明，在木星表面看到的强风深入到行星内部。我们也从卡西尼号大结局中获得了类似的土星数据，当时卡西尼号探测器潜入土星，记录了土星被吞没之前的近距离数据。我们现在计划将这些精确的数据吸收到我们的巨行星发电机模型中，从而以一种迄今为止不可能的方式约束内部模型。我们的目标是发现木星是否有一个致密、紧凑的核心，还是像最近提出的那样有一个大而稀的核心。我们还将探讨我们的发电机模型预测的深风是否与观测到的风一致。

Many astrophysical phenomena involve the complex interaction between magnetic fields, rotation and turbulent fluid flows. We will undertake a systematic and integrated programme of research to investigate this interaction in a variety of contexts in solar system and planetary sciences. We shall utilise a combination of analytical and numerical techniques (including the application of cutting edge numerical algorithms optimised for use on massively parallel machines) to gain an understanding of such phenomena. We propose to investigate the following specific problems:(1) On the Sun, magnetic field is observed to exist over a range of spatial and temporal scales, from the large and long-lived to the small and short-lived. Furthermore, the convection at the solar surface also has a range of scales, from supergranules (which are about 20,000 km across) down to granules (about 1000 km). A new anelastic code has been developed in Leeds, and we will use this to explore the interaction between the convection and the magnetic fields to explain these observed ranges in scale. We will address the important issue of whether the observed small-scale magnetic field is broken-down large-scale field, or whether it is generated afresh by a small-scale dynamo. We shall also explore the role of the near-surface shear layer to see how it affects the solar magnetic field just below the photosphere. (2) A key observational discovery in solar physics was the identification of the "solar tachocline", a thin region of strong velocity shear, deep in the Sun, sandwiched between the convective and radiative zones. Recent satellite observations of the Sun have revealed new short period activity cycles in addition to the 11 year activity cycle. Long term observations of bright points in the corona have revealed slow waves. These waves and activity cycles most likely arise in the tachocline. We will explore what types of waves the tachocline can support, and how they develop in the nonlinear regime. This will enable us to discover if these new observations can be understood in terms of tachocline dynamics, and how these signals in the deep interior are transmitted to the solar surface.(3) The nature and strength of the magnetic field in the radiative interior below the tachocline is a major unknown of solar research. We will explore a mechanism known as magnetic buoyancy, by which magnetic fields rise upwards. This is known to be important nearer the surface, but it might also play a role in the deepest regions of the Sun. There is an analogy between magnetic buoyancy and double diffusive convection, which occurs in our oceans. It has recently been discovered that by forming density layers, the transport of heat and salt in the ocean can be much enhanced. By studying three-dimensional, nonlinear models to investigate this layering process in the magnetic context, we will explore whether such layering can occur in the deep solar interior. This will provide important new constraints on the magnetic field in the solar radiative zone. (4) The Juno space mission has sent back stunning pictures of Jupiter's surface, and we now also have much more accurate data about Jupiter's magnetic field and its gravity field. The gravity field data has shown that the strong winds seen at the surface of Jupiter penetrate deep into the interior of the planet. We also have similar data for Saturn from the Cassini Grand Finale, when the Cassini probe dived into Saturn, recording close up data just before it was swallowed up. We now plan to assimilate this accurate data into our dynamo models for giant planets, and hence constrain interior models in a way that has hitherto not been possible. We aim to discover if Jupiter has a dense, compact core or a large, dilute core as recently suggested. We will also explore whether the deep winds predicted by our dynamo models are consistent with the observed winds.