Professor Steven Tobias

Professor Steven Tobias


I am Professor of Applied Mathematics at the University of Leeds.

Previous to coming to Leeds I was a Research Fellow in Mathematics at Trinity College Cambridge (1995-2000) and a Research Associate at JILA, University of Colorado (1996-1998).

My PhD (1995) was on "Solar and Stellar Dynamos" at DAMTP, University of Cambridge under the supervision of Professor Nigel Weiss (FRS)

I am currently Director of The Leeds Institute of Fluid Dynamics


  • DIrector of Leeds Institute for Fluid Dynamics

Research interests

My research covers fluid dynamics with particular emphasis on Geophysical and Astrophysical Fluid Dynamics...from turbulence in the Earth's oceans and atmosphere to the interaction of magnetic fields and plasmas in tokamaks, experiments, planets, stars and accretion disks.

For a more detailed description please see my Personal Homepage.

I am primarily interested in the dynamics of astrophysical and geophysical fluids and the generation and behaviour of magnetic fields.

My research includes investigations into the following topics:

Solar Dynamo Theory:

The magnetic field of the sun is believed to be generated by a hydromagnetic dynamo operating at the base of the solar convection zone in a thin region of shear called the tachocline. This magnetic field leads to the formation of the well-known 11-year solar activity cycle. The strong magnetic field has profound terrestrial implications, leading as it does to solar flares, coronal mass ejections and changes in the total solar irradiance. I conduct research into how this systematic magnetic field is generated deep within the sun and its dynamics in reaching the solar surface.

Dynamics of the Solar Tachocline:

As noted above, the solar tachocline is a region of strong shear at the base of the solar convection zone. The fundamental question concerning the tachocline is 'Why is it still there?'. The answer to this problem lies in an understanding of stably stratified magnetohydrodynamic (MHD) turbulence. Current research includes quantifying the role of magnetic field in modifying transport in the tachocline and analysing the consequences for angular momentum transport in the Sun.

Statistical Approaches to Fluid Mechanics and MHD:

An exciting new approach to fluid mechanics comes from solving equations for the statistics of the fluid rather than the fluid equations themselves. This approach seems to work well when strong shear flows or large-scale magnetic fields are present. I am currently interested in researching how these methods perform in problems such as
(i) The generation of astrophysical and geophysical jets, such as the jet-stream or the jets found on Jupiter and Saturn.
(ii) The interaction of turbulence with magnetic fields in stably stratified layers.
(iii) The instability of magnetic fields in the tachocline, accretion discs, extra-solar planets and experiments
(iv) The driving of mean flows in Tokamaks.

Stably Stratified Turbulence

I am currently researching the dynamics of stably stratified turbulence, to examine whether 'layering' ever occurs in a realistic setting. This turbulence is important for transport in the oceans and atmosphere and also in many situations of astrophysical interest.

<h4>Research projects</h4> <p>Any research projects I'm currently working on will be listed below. Our list of all <a href="">research projects</a> allows you to view and search the full list of projects in the faculty.</p>


  • PhD (Cantab) 1995

Professional memberships

  • London Mathematical Society
  • Royal Astronomical Society
  • Editorial Board Proceeding of the Royal Society A
  • Editor Journal of Plasma Physics

Research groups and institutes

  • Applied Mathematics
  • Astrophysical and Geophysical Fluid Dynamics
  • Applied Nonlinear Dynamics

Current postgraduate researchers

<h4>Postgraduate research opportunities</h4> <p>We welcome enquiries from motivated and qualified applicants from all around the world who are interested in PhD study. Our <a href="">research opportunities</a> allow you to search for projects and scholarships.</p>
    <li><a href="//">Direct Statistical Simulation of Multiscale Fluids</a></li>