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Postgraduate Projects in Geophysical and Astrophysical Fluid Dynamics
Some possible PhD research projects are listed below. Thise that are funded are marked with **, but those without funding are also marked for potential students who have their own funding or who want to contact a potential to see if possible funding sources are available. Please contact the supervisors for more information.
Fluid Dynamics of Weather and Climate
 Datadriven stochastic subgrid parametrization in weather and climate modelling
 Predicting critical transitions in dynamical systems from time series
 Boundary layer dynamics in cyclone systems
 Physicsdynamics coupling in weather and climate models
 Highresolution numerical weather prediction
 Improving turbulence representation in highresolution numerical weather prediction
 Validating weather and climate models using asymptotic limits
 Understanding scale interactions in weather and climate models
 Highperformance computing for geo and astrophysics
 NEMO towards Exascale Computing
 Understanding and Improving the Path of the Gulf Stream extension in moderate resolution climate models
 Exploring the dynamics and thermodynamics of the Arctic Ocean
 Modelling of Planetary Atmospheres
 Circulation and Climate Change
 **The General Circulation of Planetary Atmospheres
Theoretical Fluid Dynamics
 Variations on slow manifolds: theory and parallelintime numerical methods
 Mixing in coherent vortices
 Dynamics and motion of microswimmers
Astrophysical Fluid Dynamics
 Linkage, knottedness and topology of magnetic fields
 Magnetic field generation, the solar tachocline and experimental dynamos
 Magnetohydrodynamic Turbulence & Dynamos
 Modelling the partially ionised solar chromosphere
 Flux expulsion in shallow water MHD
SolarTerrestrial Plasmas and Space Weather
 Magnetic Helicity Flow in the Sun and Heliosphere
 Multispacecraft investigations of solar and heliospheric plasmas
Datadriven stochastic subgrid parametrization in weather and climate modelling
Supervisor: Dr Frank Kwasniok
The dynamics of weather and climate encompass a wide range of spatial and temporal scales. Due to the nonlinear nature of the governing equations, which are the laws of fluid dynamics, thermodynamics, radiative energy transfer and chemistry, the different scales are dynamically coupled with each other. Finite computational resources limit the spatial resolution of weather and climate prediction models; smallscale processes such as convection, clouds or ocean eddies are not properly represented. The necessity arises to account for unresolved scales and processes through some form of subgrid modelling. This is usually referred to as a closure in fluid dynamics and theoretical physics, and as a parametrization in meteorology and climate science.
The project will develop and explore novel approaches to databased stochastic subgrid parametrization in atmospheric and ocean models. The performance of these schemes in prediction and longterm simulation will first be assessed in idealised settings before transferring them to more realistic atmospheric and ocean models.
Predicting critical transitions in dynamical systems from time series
Supervisor: Dr Frank Kwasniok
Complex dynamical systems subject to slowly varying external conditions may exhibit critical transitions or tipping points, that is, a qualitative change in the observed macroscopic behaviour. An attractor or dynamical regime of the system becomes unstable and an alternative one emerges. Realworld examples of possibly huge socioeconomic importance are the climate system, ecological systems or financial markets. Critical transitions in stochastic dynamical systems may be classified as bifurcationinduced, noiseinduced or rateinduced.
In recent years, there has been much research activity on identifying earlywarning signals of critical transitions in time series in order to detect, anticipate or predict impending tipping points. However, the robustness and sensitivity versus specificity of such earlywarning indicators is still under debate.
The present studentship project will discuss new modelbased approaches to prediction of critical transitions from data. It will draw on concepts and methods from dynamical systems theory and statistics.
Boundary layer dynamics in cyclone systems
Supervisor: Dr Bob Beare
Midlatitude and tropical cyclones contribute some of the most high impact weather including high winds and extreme precipitation. The atmospheric boundary layer (approximately the lowest 1 km of the atmosphere) plays a key role in the dynamics of these systems, providing significant forcing to both the momentum and thermodynamic budgets. In this project, the student will investigate a novel theory for the coupling of the boundary layer to cyclone systems. They will use the theory to diagnose the circulations associated with the boundary layer in cyclone and hurricane systems. The theory, developed by Beare and Cullen, is a comprehensive way of combining momentum balances and thermodynamic forcings in the boundary layer. The project will provide the student with a thorough training in numerical methods and fluid dynamics of the atmosphere. There will also be opportunities for collaboration with scientists at the Met Office, Exeter.
Physicsdynamics coupling in weather and climate models
Supervisor: Dr Bob Beare
In weather and climate models, spatial scales that are resolved by the grid scale can typically be represented by its advective dynamics. In addition there is a large range of important processes with scales smaller than the grid scale such as moist convection and boundarylayer turbulence. These processes are represented by subgrid parametrizations. A challenge for weather and climate modelers is understanding the coupling between the subgrid parametrizations and the resolved dynamics. It is arguable that such coupling has received much less research effort relative to the separate development of the dynamical core and parametrizations. More research on the physicsdynamics coupling might therefore lead to significant improvements in future model performance.
The aim of this project is to develop the theory of coupling the boundary layer and convection to the largescale dynamics. The theory will exploit concepts of balance. This will lead to the design of a new suite of idealised test cases for use in weather and climate models.
Highresolution numerical weather prediction
Supervisors: Dr Bob Beare and John Thuburn
The atmospheric boundary layer is the region adjacent to the surface in which there are significant turbulent fluxes of heat, moisture and momentum. The boundary layer diurnal cycle thus plays a key role in many highimpact aspects of weather such as: surface temperature, the dispersion of pollutants and chemical species, low level cloud and fog, and the onset of thunderstorms. Nevertheless, there are important limitations in our understanding and ability to forecast the diurnal cycle of the boundary layer at high resolution. During the diurnal cycle, the typical length scale of the boundary layer eddies varies between of order 1 km by day to much smaller values at night. Until recently, numerical weather prediction (NWP) models used a horizontal grid length much larger than the size of the boundarylayer eddies. The scale separation meant that columnbased parametrizations were formally justified. However, with current supercomputer power, and in order to provide more skilful regional forecasts, operational weather centres now run limited area models at horizontal grid lengths as small as a few kilometres. The ratio of the horizontal grid length to the boundary layer eddy size is now of order one; such a regime is called the grey zone. The grey zone is now a pressing practical issue for NWP of the atmospheric boundary layer. Whilst many weather centres run models at these resolutions, there is currently little theoretical and numerical modeling basis for how to represent the boundary layer.
Improving turbulence representation in highresolution numerical weather prediction
Supervisors: Dr Bob Beare (UoE), Dr Adrian Lock (Met Office) and Prof. John Thuburn (UoE)
Highresolution numerical weather prediction (HRNWP) provides forecasts for lifethreatening events such as: thunderstorms, frosts, fog and severe wind storms. The atmospheric boundary layer is the region adjacent to the surface in which there are significant turbulent fluxes of heat, moisture and momentum. These fluxes connect with the evolution of cumulus and other cloud types. The boundary layer thus plays a key role in the HRNWP system.
Until recently, HRNWP models used a horizontal grid length much larger than the size of the boundarylayer eddies. The scale separation meant that columnbased subgrid models (models that represent the fluxes at scales below the grid scale) were justified. However, operational weather centres now run limited area models at horizontal grid lengths as small as a few kilometres, and sometimes even smaller. The ratio of the horizontal grid length to the boundarylayer eddy size is now of order one; such a regime is called the grey zone (see attached figure illustrating the grey zone). The boundarylayer grey zone is now a pressing practical issue for HRNWP (Beare 2014).
The student will implement and compare novel subgrid models in the grey zone. The Met Office Largeeddy model will be used as the initial testbed, followed by implementation in the Met Office Unified Model (MetUM). A key aim is to improve the Smagorinsky model currently implemented in the MetUM. A focus will be the transition from the early morning boundary layer to the subsequent triggering of cumulus clouds. They will also build on the work of the NERC GREYBLS project ("modelling GREY zone Boundary LayerS", PIs Bob Beare and Bob Plant) at the Universities of Exeter and Reading. It is an exciting opportunity for the student to make an impact on stateofthe art weather prediction. It will also provide an excellent environment for training the student in current HRNWP techniques.
Beare R J (2014) A Length Scale Defining PartiallyResolved BoundaryLayer Turbulence Simulations, BoundaryLayer Meteorology, volume 151, p. 3955.
Validating weather and climate models using asymptotic limits
Supervisors: Dr Bob Beare and Prof. John Thuburn (UoE), and Prof Mike Cullen (Met Office)
Society benefits greatly from the weather and climate forecasts provided by the Met Office and other organisations. Validation of weather and climate models is thus a vital process. Although the governing equations are known, their exact solutions are not computable. However, many important asymptotic limits are computable, and these can be used to validate models in cases of the most physical interest. The main aim of this project is to design idealised tests that employ these limits.
In weather and climate models, spatial scales that are resolved by the gridscale are represented by its advective dynamics. In addition there is a large range of important processes smaller than the gridscale such as moist convection and boundarylayer turbulence. These processes are represented by subgrid parametrizations. A challenge for weather and climate modelers is understanding the coupling between the subgrid parametrizations and the resolved dynamics. Such coupling has received much less research effort relative to the separate development of the dynamics and parametrizations. Moreover, the coupling of tropical convection and boundary layer to the dynamics is currently a hot topic in weather and climate model development (Holloway et al. 2014). More research on the physicsdynamics coupling might therefore lead to significant improvements in future model performance.
In this project, we will develop new tests of the coupled system that use asymptotic limits. Beare and Cullen (2013) developed the theory for the limit involving the dynamics and boundary layer. In this project, the student will extend the theory to the coupling of the boundary layer and convection in tropical circulations. This will lead to the design of a new suite of idealised test cases for use in the Met Office Unified model. The project will provide the student with a thorough training in numerical methods and fluid dynamics of the atmosphere. The cosupervision by Prof Cullen will also provide opportunities for collaboration at the Met Office.
Beare RJ, Cullen MJP. (2013) Diagnosis of boundarylayer circulations, Philosophical Transactions A, Royal Society, volume 371, article no. 20110474
Holloway CE, Petch JC, Beare RJ, Bechtold P, Craig GC, Derbyshire SH, Donner LJ, Field PR, Gray SL, Marsham JH. (2014) Understanding and representing atmospheric convection across scales: Recommendations from the meeting held at Dartington Hall, Devon, UK, 2830 January 2013, Atmospheric Science Letters, volume 15, no. 4, pages 348353
Understanding scale interactions in weather and climate models
Supervisors: Dr Bob Beare and Prof. John Thuburn (UoE), and Dr Ben Shipway (Met Office)
Society benefits greatly from the forecasts produced using weather and climate models at the Met Office and other organisations. This PhD project has potential for producing a stepchange in developing these models. Weather and climate models involve a chain of interlinked components spanning a large range of temporal and spatial scales. Hence the performance of these models is often limited by the “weakest link” in the chain. The resolved scales are handled by the “dynamics” and those smaller than the gridscale by the “physics”. At weather services, significant effort is applied to improving the dynamics and physics components individually. However much less research has been done on understanding how they couple. A common problem in the development of a new version of a weather and climate model is that the dynamics and physics are coupled at a late stage in the development cycle. Consequently, unforeseen interactions between the components can result, affecting the model performance.
The aim of this PhD project is to improve our understanding of physicsdynamics coupling. Such work also involves valuable training in both largescale dynamics and subgrid scale parametrizations. The student will pursue the problem using the following approaches:
 Idealised models and theory.
 Novel numerical methods.
 Clarifying cause and effect in the coupling of physics and dynamics.
 Testing the ability of models to maintain fundamental physical constraints such as balance and conservation.
The student will be cosupervised by the Ben Shipway at the Met Office and will thus work at the interface of operational modelling and theory. The project also involves collaboration with scientists on the NERC Understanding and Representing Atmospheric Convection across Scales programme, where physicsdynamics coupling is being researched for the moist convection problem.
Highperformance computing for geo and astrophysics
Supervisor: Dr. Martin Schreiber
The simulations of realistic geo and astrophysical processes have a strong demand on computational requirements. Highperformance computers (HPC) are therefore mandatory to run such simulations within a reasonable time. Additionally, efficient implementations on HPC architectures are currently faced with a significant change in the computing architectures towards massive parallelism. This forces redesigning the algorithms to assure that they are able to run efficiently on millions of computing cores which is a nontrivial task. Therefore, a codesign involving knowledge on mathematics as well as future HPC architectures is required, hence located in an interdisciplinary field.
Various topics for an HPCfocussed PhD project (in mathematics and computer science) are available: e.g. HPC optimizations of weather and oceanic simulations, parallelizationintime with focus on weather and climate simulations, solar tomography, etc.
The PhD candidate should have strong knowledge and understanding of parallel programming models (MPI/OpenMP), HPC computing architectures (CPU/GPU/XeonPhi) as well as strong knowledge on scientific computing (Linear algebra, timedepending PDE solvers, etc.).
NEMO towards Exascale Computing
Supervisors: Dr. Martin Schreiber (UoE), Dr. Tim Graham (Met Office), Dr. Mike Bell (Met Office), Dr. Simon McIntoshSmith (University of Bristol), Dr. Paul Selwood (Met Office) and Dr. Christopher Maynard (Met Office)
Ocean simulations play an important role in understanding and predicting climate changes. The Nucleus for European Modelling of the Ocean (NEMO) model is one of the leading ocean simulation frameworks and its development was started decades ago. However, certain changes in hardware architectures currently lead to limitations in its performance and scalability. With the ongoing trend towards massive parallelism in highperformance computing (HPC), unlocking the potential high performance is becoming even more challenging. This interdisciplinary PhD project bridges the areas of oceanic modelling and HPC. On the one hand, this project involves understanding the numerical methods used in the NEMO model and how these are implemented. On the other hand, the current implementation of this mathematical formulation has to be optimized for stateoftheart HPC architectures.
The main goal of this project is a significant and sustainable performance boost of the NEMO model for use in earth system model applications, hence including also coupling issues with 3rd party software which are known to be highly challenging in HPC. As part of this project, the performance of the NEMO model will be investigated to understand the performance issues on both serial and parallel parts. This requires understanding of the underlying mathematical model, as well as cutting edge HPC hardware. Possible solutions and new optimization strategies have to be identified to apply such optimizations to an existing code infrastructure. In particular, a strategy will be devised that will achieve excellent performance on the HPCs that will be used over the next 510 years and have minimal impact on the scientific development of the code. To assure a longterm impact of this project, these optimizations will be made in close cooperation with the NEMO consortium.
This project will directly contribute to the NEMO project, which has a wellestablished development consortium consisting of the MetOffice, NOC, CMCC, CNRS, INGV and Mercator Ocean as well as several other users including ECMWF and the ECEarth earth system model. Hence, this PhD project would lead to significant improvements for these user groups by reducing the computation time on current architectures and assuring performance and scalability compatibility also for the future architectures. With the expectation of a significant reduction in computation time, this results in benefits for the entire community of NEMO project: Faster decision making, running highresolution simulations within a reasonable time scale, reduction of computation time and therefore lower costs for executing each simulation on HPC clusters, improvements of reliability of simulations by allowing the execution of more ensemble runs and allow better exploitation of the available computing resource such as the new MetOffice supercomputer.
Understanding and Improving the Path of the Gulf Stream extension in moderate resolution climate models
Supervisors: Prof. Beth Wingate and Dr. Mike Bell
Industrial CASE joint UoE Met Office Phd studentship: The Gulf Stream plays an important role in the prediction of weather and climate throughout northern Europe. This project aims to improve the predicted dynamics of the Gulf Stream in coarse resolution ocean models by understanding gained through 1) analysis of high resolution ocean model dynamics and 2) the development of new mathematical and numerical methods.
The Gulf Stream plays an important role in the prediction of weather and climate throughout northern Europe. Coarse resolution ocean models misrepresent the path of the Gulf Stream which leads to poor predictions for northern Europe. This project aims to improve the understanding of the dynamics of the Gulf Stream. This understanding will then be applied to develop new mathematical and numerical methods with the goal of improving the representation of the Gulf Stream in Nemo.
The first step in the PhD project will be to calculate dynamical diagnostics of the Gulf Stream path using models of in 1°, 1/4°, and 1/12° resolution. Depending on the results and the interests of the student, the PhD could develop in the following directions: indepth investigation and interpretation of aspects of the vorticity dynamics, the theory and dynamics of western boundary currents in the presence of sloping bathymetry, assessment of the impact of alternative representations of momentum advection or physical parameterisations of eddy fluxes on the Gulf Stream path. The student will be encouraged to formulate and experiment with novel ideas in numerics, diagnostics, and theory for ocean physics and dynamics. Research questions to be addressed include: 1) What processes control the dynamics in the Gulf Stream extension? 2) What are the roles of mesoscale fluctuations in western boundary currents? 3) How do mesoscale fluctuations strengthen the interactions with bathymetry?
Exploring the dynamics and thermodynamics of the Arctic Ocean
Supervisor: Prof. Beth Wingate
The earth’s high latitudes are undergoing rapid changes due to climate warming. For example, in September 2007, 2.5 million km2 of seawater was exposed for the first time in many years. Because of the changing nature of the Arctic Ocean, understanding its unique dynamics and thermodynamics is important for understanding impacts of changing sea ice cover on the circulation. First, the Arctic Ocean may be one of the most dynamically active in the world. Measurements of the surface dynamics have revealed high eddy densities, and even more surprising, deep eddies have been discovered that span the weakly stratified deep layer. These eddies can travel at speeds of order 25 cm/s and are as much as 2000 m deep. Second, there is enough heat in the Atlantic layer to melt the surface ice many times over. Why doesn’t it melt? A cold surface layer resides above a warm Atlantic layer and creating some of the longest doublediffusion layers in the world, layers that are 1 meter in depth each spanning a thousand kilometers. These layers maintain their properties in the face of strong perturbations such as eddy events.
The aim of this project is to understand the energetics and thermodynamics of key processes in the Arctic Ocean and focus on questions such as: Which types of energy transformations dominate the Arctic Ocean? Are they dominated by baroclinic instability? Are there other important energy transformations such as symmetric instability? Do these change with changing ice cover? How do these energy exchanges help drive the largescale circulation? What sets the layer thicknesses of the 1000kmlong doublediffusive layers? What makes the Arctic Ocean’s doublediffusive layers so robust to perturbations? Does this stability change with different surface forcing? This project will explore different aspects of these questions through theory and idealized numerical simulations.
Modelling of Planetary Atmospheres
Supervisor: Professor Geoffrey Vallis
We invite applications for a Ph.D. studentship in the area of modelling and theory of the general circulation of the atmosphere of planetary atmospheres. The aim of the research will be to understand the possible ranges of such atmospheres and their relation to that of Earth. The work may involve theory and modelling the atmospheres of other solar system planets, such as Venus or Jupiter, and/or planets outside the solar system. The research will investigate how the circulation might depend on such parameters as atmospheric composition, size and rotation rate of the planet and the composition of the atmosphere. You will join a vibrant group of scientists in the Mathematics and Physics department at Exeter engaged in similar geophysical and astrophysical problems.
Circulation and Climate Change
Supervisor: Professor Geoffrey Vallis
We invite applications for a Ph.D. studentship in the area of modelling and theory of the response of the circulation of the atmosphere or ocean to climate change, such has occurred in the past (ice ages, hothouse climates) and will occur in the future (global warming). Changes in circulation are poorly understood because they involve feedbacks between different components of the climate system. Thus, they are a considerable scientific challenges as well as being of great societal importance. The research will investigate how such largescale features, such as the position of the jet stream or the winddriven circulation of the ocean will change as the planet warms. You will join a vibrant group of scientists in the Mathematics and Physics department at Exeter engaged in similar problems in climate and geophysical fluid dynamics.
**The General Circulation of Planetary Atmospheres
Supervisor: Professor Geoffrey Vallis
Earth is but one planet. There are at least seven others in the solar system, and millions, perhaps billions, beyond. This project will explore some of the general principles governing the circulation of planetary atmospheres, including the Earth, and will seek to determine the relationship of Earth's circulation to that of other planets. The project will focus on terrestrial planets, which are planets like Earth that have a welldefined atmosphere with a definite lower boundary.
The student will explore how the circulation depends on the fundamental parameters of the planet, such as the planetary rotation rate, the atmospheric mass and composition, the distance from its host star. In particular we will seek to understand if and how Earth's atmosphere is connected to other planetary atmospheres, and so put it in a more general context. Is the Earth's atmosphere a very special case, or is it really rather ordinary, or generic? The project will involve a combination of numerical modelling and theory, using a flexible, idealized numeric model of planetary atmospheres that can be configured to almost any planet in conjunction with basic geophysical fluid dynamics theory. The student will his or herself choose the precise direction of the project, in consultation with the supervisor.
The successful candidate will have a strong undergraduate background in physics, applied mathematics or similar and ideally some experience in computational methods and computer programming. The candidate will have an opportunity to be a part of a dynamic team looking at the atmospheres of both Earth and other planets, and will develop both theoretical and numerical skills of wide applicability beyond this particular project. This is a fully funded PhD studentship for 3.5 years.
Variations on slow manifolds: theory and parallelintime numerical methods
Supervisor: Prof. Beth Wingate
For many years the geophysical fluid dynamics community has been studying the 'slow manifold', which was motivated by understanding the large scale circulation of the atmosphere and has intimate connections to numerical modeling of the weather and climate. The key idea behind a slow manifold is that, for large scales, only the slow dynamics matters and that fast dynamics has only a small impact on the evolution of the dynamics. These ideas have been discussed in key papers with titles like "On the existence of a slow manifold." "On the nonexistence of a slow manifold," and "The slow manifold  what is it?" More recent work shows that the wave part of the dynamics puts energy on and takes energy off of the slow manifold itself, modifying its evolution.
The aim of this project is not to delve into the slow manifold's mathematical existence but instead to ask questions such as: "What is the role of the fast, fast/slow and slow dynamics on the total energy and potential enstrophy? In some systems of equations there is more than one slow manifold. Are these related to one another? Can the energy be shifted from one manifold to another? If so, how?". Then other questions can be asked such as, "How can we use what we know about physics to improve numerical methods such as parallelintime methods?" This project can be primarily numerics or physics, or a mixture.
Mixing in coherent vortices
Supervisors: Professor Andrew Gilbert and Professor John Thuburn
Many fluid flows are dominated by coherent vortices: regions of spinning fluid. Examples include ocean eddies, hurricanes and tornadoes, vortices that spread from the tips of aircraft wings, and the finescale vortices that make up the 'sinews' of turbulent flow. Many flows can be thought of purely in terms of interacting vorticity and dominated by the dynamics of vortices, both their internal structure and the way different vortical structures interact.
The aim of this project is to understand mixing processes in coherent vortices in two dimensions. Recent papers indicate that a vortex subjected to an external random forcing will develop vorticity 'steps': the diffusion of vorticity is large in the flat regions, and highly suppressed in between. This was established in a theoretical model with a variety of simplifying assumptions in the way nonlinearity was treated, and in the types of external forcing employed. The aim of this project would be to study the development of such stepped distributions in more realistic situations and would involve the writing and running of codes to follow vorticity in twodimensional flows. There are also a number of interesting extensions and possible research directions including placing the problem in a spherical geometry and relating it to the presence of banded structure on giant planets.
Dynamics and motion of microswimmers
Supervisors: Professor Andrew Gilbert and Dr Feodor Ogrin (Physics)
The aim of the project is the mathematical modelling of tiny magnetic swimming devices (on scales of 10100 micrometers), which have biomedical applications in terms of drug delivery and labonachip devices. On these scales fluid flows are in a regime where inertia is negligible and viscosity dominates: one has to imagine swimming through treacle. Theory developed for understanding the motions of living organisms in this regime can be applied to manmade swimming devices, in which tiny metal balls are controlled by external magnetic fields. For example it is important that any motion is not timereversible, otherwise there can be no persistent swimming (the socalled Scallop Theorem). The aim of the project is to extend the mathematical modelling of these swimming devices, which has commenced in a collaboration between the Applied Mathematics and Biophysics groups, using a combination of numerical solution of ODEs and PDEs, and asymptotic approximations.
Linkage, knottedness and topology of magnetic fields
Supervisors: Professor Mitchell Berger and Professor Andrew Gilbert
Magnetic fields play an important role in astrophysics and geophysics. In the Sun the field undergoes an 11year solar cycle of activity, seen from the presence of sunspots, flux tubes of field poking through the solar surface. These tubes of field come and go, on a time scale of weeks and months, and can undergo violent rearrangements releasing large amounts of energy in the form of solar flares. Here the magnetic field lines may be thought of as elastic, and the fields that protrude through the surface (the photosphere) have a twisted and tangled nature, as seen in satellite observations. Solar flares can arise when the field lines reconnect, allowing very rapid untwisting and untangling, releasing vast amounts of energy and literally catapulting material into the solar wind. Seen from the Earth, such increases in solar activity can disrupt communications systems, particularly when satellite based.
The aim of this project is to characterise the complex topological and geometrical properties of magnetic fields such as those generated in the Sun: here tubes of field poke through the surface of the Sun, and have a complex twisted and knotted structure. Such topological structure can be measured in several different ways. Coherent measures include linking numbers and helicity integrals. These measures require a lack of reflexional symmetry. Other numbers measure topological complexity. Knots, for example, are commonly classified according to the minimum number of crossings as seen in projection. The project involves the application of modern ideas of topology and knot theory to applications in astrophysical magnetic fields. Previous knowledge of magnetohydrodynamics or topology would not be required, but interest in and some experience of applied mathematics (for example fluid mechanics or electromagnetism) would be valuable.
Magnetic field generation, the solar tachocline and experimental dynamos
Supervisors: Professor Andrew Gilbert and Professor Mitchell Berger
Magnetic fields play an important role in astrophysics and geophysics. In an ordinary dynamo, the motion of electrical conductors, coils of wire, leads to the amplification of magnetic fields and generation of electrical currents, thus converting mechanical energy into useful electrical power. In the Sun the same process occurs through the motion of electrically conducting plasma. The resulting fields give sunspots and solar flares.
In the Sun, a thin layer of shear called the 'tachocline' is believed to play an important role in the generation of coherent magnetic fields. In particular, while the appearance of sunspots and similar magnetic structures on the surface of the Sun is fairly random, there is an underlying 22year cycle of solar activity. This project involves modelling magnetic field generation in idealised fluid flows with shear, the aim being to understand how this mixture of order and complexity can emerge in simple models.
An alternative area of study is to understand how magnetic fields may be generated in idealised laboratory dynamos: in a number of laboratories (France, Germany, Latvia, USA) swirling flows of liquid sodium are being used to generate magnetic fields and so model those in astrophysical objects and in the Earth. Again there is interest in developing simplified models of these in order to understand fundamental mechanisms of generation and feedback, and so to feed into the design and interpretation of experiments.
Previous knowledge of magnetohydrodynamics would not be required, but interest in and some experience of applied mathematics (for example fluid mechanics or electromagnetism) would be valuable.
Magnetohydrodynamic Turbulence & Dynamos
Supervisor: Dr Joanne Mason
Throughout the universe electrically conducting fluids interact with magnetic fields. The resulting state, known as magnetohydrodynamic (MHD) turbulence, is believed to be responsible for a great variety of astrophysical behaviour. Probably the most well known example is the 22 year sunspot cycle.
Recent highresolution numerical simulations of MHD turbulence have revealed that beneath the apparent disorder resides a fascinating aligned structure of the velocity and magnetic field vectors. The reason for the existence of dynamic alignment and its likely implications on the evolution of astrophysical magnetic fields are topics of great interest.
Working within the Centre for Geophysical and Astrophysical Fluid Dynamics at Exeter, the student will investigate the interaction between electrically conducting fluid flows and magnetic fields by building simplified mathematical models and conducting and analysing numerical simulations. An interest in fluid dynamics is required, but no prior experience of astrophysics or computational MHD is expected.
**Flux expulsion in shallow water MHD
Supervisors: Prof. Andrew Gilbert and Dr. Joanne Mason
Magnetic fluids of the Earth, Sun, stars and galaxies are generated by the motion of electrically conducting fluid, for example hydrogen plasma in the case of the Sun, liquid metal for the Earth. The project concerns a fundamental process in the interaction of magnetic field and fluid called flux expulsion, where field is expelled from regions of closed streamlines, for example a fluid vortex. This process was first identified by Nigel Weiss in the 1960s, but it was only recently that studies included the magnetic field feedback on the flow through the Lorentz force, e.g. Gilbert, Mason and Tobias (2016). The goal of the project is to study flux expulsion in a thin layer using the equations of shallow water magnetohydrodynamics (MHD) where the fluid motion is coupled to gravity waves. Such models are relevant to the solar tachocline and other systems where the fluid is stratified. The study would initially use numerical simulations in periodic geometry, but the goal would be also to develop scaling laws and analytical models.
A.D. Gilbert, J. Mason & S.M. Tobias 2016 Flux expulsion with dynamics, J. Fluid Mech. 791, 568588
Modelling the partially ionised solar chromosphere
Supervisors: Dr Andrew Hillier
The solar chromosphere is a highly dynamic layer of the solar atmosphere and is of great importance for understanding the energy flow and dissipation mechanisms in the atmosphere. We understand that magnetic forces are crucial in this layer, but the plasma is only partially ionised making the couple between the plasma and the magnetic field imperfect. In this project the student will explore and develop models of the coupling between the magnetic field and the fluid of the chromosphere to understand how observed dynamic phenomena are created and how the friction between charged species moving with the magnetic field plays a role in the heating of the chromosphere. The project will involve combining numerical modelling, theory, and observations to understand how fundamental magnetohydrodynamic (MHD) phenomena develop in a partially ionised system including regimes (e.g. MHD shocks) beyond those where a single fluid approximation holds. The student will choose the precise direction of the project, in consultation with the supervisor.
The successful candidate will have a strong undergraduate background in physics, applied mathematics or similar and ideally some experience in computational methods and computer programming. The candidate will have an opportunity to be a part of a dynamic team studying the solar atmosphere, and will develop both theoretical and numerical skills of wide applicability beyond this particular project. This is a fully funded PhD studentship for 3.5 years.
Magnetic Helicity Flow in the Sun and Heliosphere
Supervisors: Professor Mitchell Berger and Dr Claire Foullon
This project will investigate the mathematics and physics of magnetic helicity transport. Applications will include plasma physics (helicity transport and decay in laboratory devices), space physics (the atmosphere of the sun and the heliosphere), and elasticity theory (twisting and buckling of elastic rods and molecules).
Helicity integrals measure geometric and topological properties of a magnetic field such as twisting, writhing, and linking of field lines. While they are readily calculated in volumes with planar or spherical boundaries, other volumes of interest (e.g. cubes, tori, hemispheres) present interesting complications. Using tools from differential geometry such as the Gauss Bonnet theorem, we will develop computer codes for calculating helicity in these volumes. One applications lies in finding the net helicity flow into each hemisphere of the sun and heliosphere, taking advantage of recent and upcoming observations (e.g. SoHO, SDO, STEREO and Cluster). Another application involves providing tools for analysing numerical experiments in MHD theory which employ rectangular volumes. The expressions for helicity flow through boundaries can be employed in analysing vortex motion on surfaces. The twist and writhe of polymer molecules with ends pinned on a surface can also be studied using the techniques we will develop.
**Multispacecraft investigations of solar and heliospheric plasmas
Supervisor: Dr Claire Foullon
Heliophysics is in its golden age, with an unprecedented number of satellites providing observations of unparalleled quality, either (remotely) of the Sun or (insitu) of the solar wind. The project will be to investigate plasma and dynamical properties using the complementarities of multispacecraft observations. The objective is to reveal phenomena and unravel the physics governing key regions of our SunEarth system in the chain of space weather events that can affect our radiation environment, our communication systems and our climate. As well as joining the Centre for Geophysical and Astrophysical Fluid Dynamics, the PhD student will directly benefit from links with the Astrophysics cluster and the nearby Met Office space weather activities. This brand new PhD project will equip the student with skills suited to address future science with Solar Orbiter, the ESA mission to be launched in 2020.