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

Lead Research Organisation: University of Leeds
Department Name: Applied Mathematics


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.

Planned Impact

NASA's mandate is to build, fly and operate spacecraft in the hostile environment of space. In order to carry this out successfully, it is necessary for NASA to anticipate the orbital decay of spacecraft (including Hubble), which arises from orbital drag, leading to the need for reboosting. Moreover it must assess radiation hazards in order to design orbits. Both orbital drag and radiation depend on the level of solar activity and so an accurate long-term forecast of solar activity is vital. To this end, NASA has constituted a solar cycle prediction panel in order to predict the level and date of the next solar maximum. The results of this prediction are utilised by a number of end-users including satellite builders and operators and policy-makers.

There is particular impact of the research into the origins and consequences of solar magnetic activity, conducted at Leeds, that is valuable to NASA in formulating its predictions of future solar magnetic activity via its solar prediction panel. In recognition of this, SMT was invited to act as a consultant for the NASA prediction panel for cycle 24. The research described in the solar projects will continue to inform NASA as the cycle progresses, and will feed into future predictions of magnetic activity. In advising the panel, SMT has utilised the research conducted at the University of Leeds to detail the lack of predictability of the dynamo models that predicted a high level of activity. The research had shown that the inherently nonlinear nature of the dynamo equations, together with uncertainties over the size and even sign of the transport coefficients in the models, make prediction impossible. In the light of these results, the panel split its initial forecast with half forecasting a high cycle and half a low cycle (based on timeseries predictions). As the solar cycle progressed, the panel met several times and gradually revised its forecast downwards. The maximum of solar magnetic activity for the cycle now seems to have passed, and was indeed exceptionally low, thus corroborating the Leeds group's research, which cast doubt on dynamo predictors. As a result of the research, focus has now turned to data assimilation methods for prediction. NASA make their predictions publicly available through the site:

We shall exploit the results of the solar physics research in the proposal (projects 1, 2 and 3) in our continued consultations with members of the NASA prediction panel. In particular, the research into the dynamics of the tachocline and into the formation of active regions will have implications for future predictions of magnetic activity; we shall continue to advise the NASA prediction panel of the consequences of these implications. Moreover, the UK has a vibrant satellite sector and this is evidenced by the Technology Strategy Board's recent decision to invest millions in a centre to support the UK satellite industry. The Astrophysical Fluid Dynamics and MHD group is aware of the TSB's recent announcement that it will support a Catapult centre for the UK satellite industry and proposes to engage with the centre to make its advice more readily available to the industry.

More generally, the research performed by members of the group also has significant impact via our outreach. Members of the group often give talks in schools, to students between the ages of 11 and 18, and always incorporate some of their research interests into the talks. This is a very important means of inspiring the next generation of scientists.


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Description Cambridge 
Organisation University of Cambridge
Department Department of Applied Mathematics and Theoretical Physics (DAMTP)
Country United Kingdom 
Sector Academic/University 
PI Contribution Collaborative research projects.
Collaborator Contribution Collaborative research projects.
Impact Several joint papers.
Description Chicago 
Organisation University of Chicago
Department Department of Astronomy and Astrophysics
Country United States 
Sector Academic/University 
PI Contribution Collaborative research project. Shared computer resources.
Collaborator Contribution As above.
Impact Several journal papers.
Description Courant Institute, NYU 
Organisation New York University
Country United States 
Sector Academic/University 
PI Contribution Collaborative research project between David Hughes (Leeds) and Profs Steve Childress and Antoine Cerfon (NYU). Research visit of Hughes funded by the Royal Society, Oct-Nov 2016.
Collaborator Contribution Fully collaborative research, tackling problems in dynamo theory and in plasma theory.
Impact None as yet, very new collaboration.
Start Year 2016
Description Newcastle University 
Organisation Newcastle University
Country United Kingdom 
Sector Academic/University 
PI Contribution Collaborative research on problems in convection.
Collaborator Contribution Joint research collaboration.
Impact So far, one paper in Physics Rev Fluids. More joint papers in preparation.
Start Year 2017