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 intend to 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. Our unifying philosophy is to investigate and explain the underlying fundamental physical interactions in these astrophysical fluids whilst also providing a theoretical underpinning to the latest high-resolution observations. We propose to investigate the following specific problems:(1) The most exciting recent observational discovery in solar physics is the identification of the "solar tachocline", a thin region of strong velocity shear, deep in the Sun, sandwiched between the convective and radiative zones. This was entirely unexpected theoretically. We shall investigate the nature of the shear-dominated turbulent flow in the tachocline to investigate how quantities such as temperature, magnetic field and angular momentum are transported, and hence to understand why the tachocline does indeed exist.(2) 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). We shall study the interaction between the convection and the magnetic fields to explain these observed ranges in scale.(3) The large-scale magnetic field erupts through the solar surface to cause sunspots in the photosphere and to trigger sometimes violent magnetic activity in the solar atmosphere. The velocity shear in the tachocline winds up the weak poloidal magnetic field into a strong toroidal field, which then escapes, to rise and eventually to appear at the surface. We have developed a new set of equations designed specifically to describe the magnetic field in the tachocline. We shall use these to explain the scale and morphology of the escaping magnetic field, and will then relate our findings to observations of emerging solar magnetic fields.(4) Most planets have magnetic fields, which vary widely in their strength and spatial form. By considering planet-specific computational models,we shall investigate the nature of the dynamo mechanism responsible for generating magnetic field in the gas giants, Jupiter and Saturn, and in the ice giants, Uranus and Neptune. Our results will be related to those of the JUNO mission to Jupiter.