Dr Stephen Griffiths

Dr Stephen Griffiths

Research interests

My research lies within the mathematical geosciences, and is mainly oriented towards the fluid dynamics of the Earth's atmosphere and ocean. My aims are to understand observed dynamical phenomena, either by numerical simulations or through mathematical analysis of simplified theoretical models. Particular interests are:

  • Instability theory: analytical and numerical modelling of linear and nonlinear instabilities in rotating, stratified shear flows; inertial instability; symmetric instability. 
  • Nonlinear waves: analytical and numerical modelling of coupled nonlinear wave equations.
  • Waves in the atmosphere and ocean: analytical and numerical modelling; internal waves; equatorial waves; convectively-coupled waves. 
  • Ocean tides: global numerical modelling; regional numerical modelling of internal tides; paleotides and climate; ice-tide interactions; self-gravitation and Earth loading.
  • Magnetohydrodynamics: instabilities, and shallow-water magnetohydrodynamics.
  • Martian dynamics: numerical modelling of subsurface temperature and ice.
  • Numerical methods: finite-difference schemes and boundary schemes for irregular domains.

I currently supervise several PhD students working in these areas:  

  • Alexander Kimbley: Axisymmetric instabilities in stellar and planetary magnetohydrodynamics (co-supervised with David Hughes). 
  • Jacob Perez: Regime behaviour of the eddy-driven jet (co-supervised with Amanda Maycock and Steven Hardiman). 
  • Luke Gostelow: Stability of zonal flows in quasi-geostrophic plasmas (co-supervised with David Hughes).  
  • Nouf Altalhi: Inverse modelling of corrosion (co-supervised with Daniel Lesnic).
  • Matt Vine: Stability of internal gravity waves in stellar radiative zones (co-supervised with Adrian Barker). 
  • William Luty: Impact of oceanic mesoscale eddies on the productivity of the western Bay of Bengal (co-supervised with Fatma Jebri & Meric Srokosz (NOC), Andrew Ross).

Former PhD students are

  • Sam Myers:  Magnetohydrodynamic instabilities in thin shells (co-supervised with Steve Tobias) 
  • Joseph Elmes: Internal tide generation (co-supervised with Onno Bokhove). 
  • Sam Williams: Theoretical and numerical simulation of atmospheric downbursts (co-supervised with Alan Blyth and John Marsham). 
  • John Ashcroft: Understanding and predicting high impact tropical cyclones (co-supervised with Juliane Schwendike and Andrew Ross). 
  • Lucy Recchia: Dynamics of the Indian Monsoon (co-supervised with Doug Parker). 
  • Megan Bickle: Interactions of environmental wind-shear and deep moist convection in the tropics (co-supervised with John Marsham and Andrew Ross). 
  • Dan Rumgay: Instabilities in shallow-water magnetohydrodynamics (co-supervised with David Hughes). 
  • Najib Zakaria: Wave propagation in staggered-grid finite-difference models with boundaries.
  • Thomas Goodfellow: Layer formation in double-diffusive convection (co-supervised with David Hughes and Peter Jimack).
  • Oliver Halliday: Atmospheric convection and gravity waves (co-supervised with Doug Parker). 
  • Sarah O’Mahony: Inertial instability in two-layer flows (co-supervised with Steve Tobias). 
  • Sam Hunter: Waves in shallow-water magnetohydrodynamics (co-supervised with David Hughes). 
  • Vijay Teeluck: Surface and internal tides over sea-floor topography (co-supervised with Chris Jones). 
  • Julian Mak: Shear instabilities in shallow-water magnetohydrodynamics (co-supervised with David Hughes). 
<h4>Research projects</h4> <p>Any research projects I'm currently working on will be listed below. Our list of all <a href="https://eps.leeds.ac.uk/dir/research-projects">research projects</a> allows you to view and search the full list of projects in the faculty.</p>


  • PhD (Cantab)
  • Certificate of Advanced Study in Mathematics (Part III Maths)
  • MA (Cantab)

Student education

I teach modules in applied mathematics, and supervise projects at level 2, level 3 and level 5 in computational mathematics, geophysical fluid dynamics, and data science.  

Research groups and institutes

  • Applied Mathematics
  • Astrophysical and Geophysical Fluid 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="https://phd.leeds.ac.uk">research opportunities</a> allow you to search for projects and scholarships.</p>