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

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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.