## Geophysical & Astrophysical Fluid Dynamics (G&A Fluids)

Welcome to the homepage of the G&A Fluids Group. We are a team of researchers interested in exploring the fascinating fluid dynamics of stars and planets. In particular, our interest lies in the interaction of magnetic fields with electrically conducting fluids - a subject called magnetohydrodynamics. Our research involves a mixture of fundamental theory, mathematical modelling and high performance computing, and further details are found in the links to our publications below.

We invite you to browse the staff pages for more insight into our specific research interests. For potential PhD students, please take a look at the possible projects on offer or contact a particular member of staff directly. To find out more about applying to the School officially, please see Postgraduate research opportunities.

## Group Members

**Staff:**

#### Professor Radostin Simitev

**Research interests: **Self-consistent** **dynamo simulations, convection in rotating systems, applications to solar, stellar and geomagnetism

**Email: **radostin.simitev@glasgow.ac.uk

**Publications: **Link to University Repository

**Personal website: **https://www.maths.gla.ac.uk/~rs

#### Dr David MacTaggart

**Research interests: **Magnetic topology, magnetic helicity, solar flux emergence, magnetic instabilities

**Email: **david.mactaggart@glasgow.ac.uk

**Publications: **Link to University Repository

**Personal website: **http://www.maths.gla.ac.uk/~dmactaggart/

#### Dr Robert Teed

**Research interests: **Magnetohydrodynamics, dynamo theory, convection in astrophysical and geophysical bodies, the geodynamo and other planetary dynamos, the solar dynamo and solar cycle** **

**Email: **robert.teed@glasgow.ac.uk

**Publications:** Link to University Repository

**Personal website: **http://www.maths.gla.ac.uk/~rteed/

**PhD students:**

**Email: **p.gupta.1@research.gla.ac.uk

**Email: **2245872h@student.gla.ac.uk

**Sage Stanish**

**Email:** 2789167s@student.gla.ac.uk

**Former staff members:**

**Professor David Fearn (retired)**

**Dr Luis Silva (industry)**

**Dr James F Mather (industry)**

**Dr Tom Elsden (lecturer, St Andrews)**

**Dr Simon Candelaresi (researcher, Stuttgart)**

## Geophysical & Astrophysical Fluid Dynamics - Example Research Projects

#### Numerical simulations of planetary and stellar dynamos (PhD)

**Supervisors:** Radostin Simitev, Robert Teed**Relevant research groups:** Geophysical & Astrophysical Fluid Dynamics, Continuum Mechanics

Using fluid dynamics and magnetohydrodynamics to model the magnetic fields of Earth, planets, the Sun and stars. Involves high-performance computing.

#### Observationally-constrained 3D convective spherical models of the solar dynamo (Solar MHD) (PhD)

**Supervisors:** Radostin Simitev, David MacTaggart, Robert Teed**Relevant research groups:** Geophysical & Astrophysical Fluid Dynamics, Continuum Mechanics

Solar magnetic fields are produced by a dynamo process in the Solar convection zone by turbulent motions acting against Ohmic dissipation. Solar magnetic activity affects nearEarth space environment and can harm modern technology and endanger human health. Further, Solar magnetism poses fundamental physical and mathematical problems, e.g. about the nature of plasma turbulence and the topology of magnetic field generation. Current models of the global Solar dynamo fall in two classes (a) mean-field dynamos (b) convection-driven dynamos. The mean-field models are only phenomenological as they replace turbulent interactions by ad-hoc source and quenching terms. On the other hand, spherical convection-driven dynamo models are derived from basic principles with minimal assumptions and potentially offer true predictive power; these can also be extended to other stars and giant planets. However, at present, convection driven dynamo models operate in a wrong dynamical regime and have limited success in reproducing a number of important 1 observations including (a) the sunspot cycle period, polarity reversals and the sunspot butterfly diagram, (b) the poleward migration of diffuse surface magnetic fields, (c) the polar field strength and phase relationships between poloidal/toroidal components. The aims of this project are to (a) develop a three-dimensional convection-driven Solar dynamo model constrained by assimilation of helioseismic data, and (b) start to use the model to estimate turbulent properties that determine the internal dynamics and activity cycles of the Sun.

#### Modelling the force balance in planetary dynamos (PhD)

**Supervisors:** Robert Teed, Radostin Simitev**Relevant research groups:** Geophysical & Astrophysical Fluid Dynamics, Continuum Mechanics

Current simulations of magnetic field (the 'dynamo process') generation in planets are run, not under the conditions of planetary cores and atmospheres, but in a regime idealised for computations. To forecast changes in planetary magnetic fields such as reversals and dynamo collapse, it is vital to understand the actual fluid dynamics of these regions. The aim of this project is to produce simulations of planetary cores and atmospheres with realistic force balances and, in doing so, understand how such force balances arise and affect the dynamics of the flow. The importance of different forces (e.g. Coriolis, Lorentz, viscous forces) determine the dynamics, the dynamo regime, and hence the morphology and strength of the magnetic field that is produced. This project would involve working with existing numerical code to perform the simulations and developing new techniques to determine the heirarchy of forces at play.

#### Identifying waves in dynamo models (PhD)

**Supervisors:** Robert Teed**Relevant research groups:** Geophysical & Astrophysical Fluid Dynamics, Continuum Mechanics

This project would involve using existing (and developing new) techniques to isolate and study magnetohydrodynamic (MHD) waves in numerical calculations. Various classes of waves exist and may play a role in the dynamo process (which generates planetary magnetic fields) and/or help us better understand changes in the magnetic field.

#### Magnetic helicity as the key to dynamo bistability (PhD)

**Supervisors:** David MacTaggart, Radostin Simitev**Relevant research groups:** Geophysical & Astrophysical Fluid Dynamics, Continuum Mechanics

The planets in the solar system exhibit very different types of large-scale magnetic field.The Earth has a strongly dipolar field, whereas the fields of other solar system planets, such as Uranus and Neptune, are far more irregular. Although the different physical compositions of the planets of the solar system will influence the behaviour of the large-scale magnetic fields that they generate, the morphology of planetary magnetic fields can depend on properties of dynamos common to all planets. Here, we refer to an important and recent discovery from dynamo simulations. Remarkably, two very different types of chaotic dipolar dynamo solutions have been found to exist over identical values of the basic parameters of a generic model of convection-driven dynamos in rotating spherical shells. The two solutions mentioned above can be characterised as ‘mean dynamos’, MD, where a strong poloidal field dominates and ‘fluctuating dynamos’, FD, where the poloidal component is weaker and the large-scale field can be described as multipolar. Although these two states have been shown to be bistable (co-exist) for a wide range of identical parameters, it is not clear how a particular state, MD or FD, is chosen and how/when one state can change to the other. Some of the bifurcations of such states has been investigated, but a deep understanding of the dynamics that cause the bifurcations remains to be developed. Since the magnetic topology of MD and FD states are fundamentally different, an important part of this project will be to probe the nature of MD and FD states by studying magnetic helicity, a magnetohydrodynamic invariant that combines information on the topology of the magnetic field with the magnetic flux. The role of magnetic helicity and other helicities (e.g. cross helicity) is currently not well understood in relation to MD and FD states, but these quantities are conjectured to be very important in the development of MD and FD states.

Bistability is also related to a very important phenomenon in dynamos - global field reversal. A strongly dipolar (MD) field can change to a transitional multipolar (FD) state before a reversal and then settle into another dipolar equilibrium (of opposite polarity) again after the reversal.This project aims to develop a coherent picture of how bistability operates in spherical dynamos. Since bistability is a fundamental property of dynamos, a characterisation of how bistable solutions form and develop is key for any deep understanding of planetary dynamos and, in particular, could be crucial for understanding magnetic field reversals.

#### Stellar atmospheres and their magnetic helicity fluxes (PhD)

**Supervisors:** Radostin Simitev, David MacTaggart, Robert Teed**Relevant research groups:** Geophysical & Astrophysical Fluid Dynamics, Continuum Mechanics

Our Sun and many other stars have a strong large-scale magnetic field with a characteristic time variation. We know that this field is being generated via a dynamo mechanism driven by the turbulent convective motions inside the stars. The magnetic helicity, a quantifier of the field’s topology, is and essential ingredient in this process. In turbulent environments it is responsible for the inverse cascade that leads to the large-scale field, while the build up of its small-scale component can quench the dynamo.

In this project, the student will study the effects of magnetic helicity fluxes that happen below the stellar surface (photosphere), within the stellar atmosphere (chromosphere and corona) and between these two layers. This will be done using two-dimensional mean field simulations that allow parameter studies for different physical parameters. A fully three-dimensional model of a convective stellar wedge will then be used to provide a more detailed picture of the helicity fluxes and their effect on the dynamo. Using recent advancements that allow us to extract surface helicity fluxes from solar observations, the student will make use of observations to verify the simulation results. Other recent observational results on the stellar magnetic helicity will be used to benchmark the findings.