Joseph Elmes

Joseph Elmes


Originally from Northampton, I started my undergraduate studies in French and Mathematics BSc at the University of Leeds in 2014. As part of my studies, I went on a mandatory year abroad to Université de Charles de Gaulle, Lille III, where I studied Mathématiques Appliquées aux Sciences Humaines et Sociales; in short, a lot of Statistics, Game Theory and Machine Learning. With regards to my degree at Leeds, I took all core modules of French language, leaving two-thirds of my degree dedicated to Mathematics. This was made up of not just core aspects of Statistics and Pure, but for the large-part of my degree, there was a heavy focus on Fluid Dynamics.

After my year abroad, I was successfully granted a research scholarship from the London Mathematical Society, working alongside my current supervisor, Dr Stephen Griffiths, on Self-Gravitating Water Waves on Rotating Elastic Spheres. The research was later presented in November 2017 to the Astrophysical and Geophysical Fluid Dynamics research group. A year later, between having graduated and starting my PhD, I volunteered with Dr Cédric Beaume on the Instability of Diluted States in the Gray--Scott Model, which is due to be presented on the 22/01/19 at Leeds' Applied Non-Linear Dynamics research group.

Alongside my PhD, I am currently a volunteer for the UK Mathematics' Trust where I mentor individuals in Secondary school across the country. I am also Postgraduate representative for Applied Mathematics at the UniversityIn my free-time, I work on the original project associated with Dr Beaume. The hope is to eventually have this work published. It is my aspiration also to carry out a research placement at a French academic institution in either the second or third year of my PhD studies.


  • Pathways for Potential
  • Kenneth Horne Foundation Bursary
  • 3x Dean's Excellence Scholarship in Mathematics
  • London Mathematical Society Summer Research Bursary 2017
  • The School of Languages, Cultures and Societies Prize 2018
  • NERC Sphere's DTP

Research interests

PhD: Generation of Internal Waves by Ocean Tides

This PhD project will look at developing simple mathematical models of internal tide generation and propagation in idealised three-dimensional geometries, building on previous two-dimensional cases. This will involve the combination of simplifying assumptions around the fluid motion, density stratification and sea-floor topography so that the governing system of non-linear partial differential equations may be reduced to a more tractable system. Consequently, both analytical and numerical solution shall be sought, allowing a wide range of parameter space to be investigated. This will in turn give a better understanding of the energy transfer from surface tides to internal tides in varying forcing scenarios, which is known to have a non-trivial dependence upon topographic width and height.

A particular focus would be on extending the solutions and methods of (Griffiths & Grimshaw, 2007), which accounted for arbitrarily large topographic variations but only in two-dimensions, to three-dimensional settings. The main goals are to

  • Understand internal tides generated by a three-dimensional surface tide (in particular, the Kelvin wave) about a two-dimensional topography (representing a continental slope). The Kelvin wave is the dominant form of the surface tide in many coastal zones, and the implied energy transfers are significant on a global scale.
  • Understand the role of topographic undulations in the along-shore direction, i.e., for a three-dimensional tide above a fully three-dimensional topography. It is known from observations that canyons for example, lead to enhanced internal tide generation (and dissipation)

Potential for High Impact Outcomes:

Internal tide generation at continental slopes (by Kelvin waves and other such tidal modes) is thought to be a major source of tidal dissipation, and thus of energy for vertical mixing and drag on the surface tide. However, observational estimates of the global energy transfer at continental slopes are imprecise, so additional models (or constraints) are of significant interest.

Other Mathematical Interests include:

  • Effects of retarding forces upon tidal waves
  • Numerical Methods
  • Non-Linear Dynamical Systems
  • Transition into Chaos
  • Machine Learning


  • French and Mathematics BSc Hons, University of Leeds (2014--2018)

Research groups and institutes

  • Applied Mathematics
  • Astrophysical and Geophysical Fluid Dynamics
  • Fluids and MHD
  • Leeds Applied Nonlinear Dynamics