Robert Long

Robert Long


I graduated from Coventry University with a BSc in Applied Mathematics and Theoretical Physics. My final year project involved developing a generalised shallow water model for rotating flows with a turbulent Ekman layer which was then implemented numerically using a finite difference scheme.
Project title : 'A two-dimensional model for Oceanic and Atmospheric flows with a turbulent Ekman layer'

I am now a member of the EPSRC Centre for Doctoral Training (CDT) in Fluid Dynamics here at Leeds. During the MSc component of the course I participated in a group project which involved numerical modelling of a flood demonstration model - 'Wetropolis'. The numerical findings ultimately led to a redesign and a new physical model to be used for outreach activities.

I am now in the middle of my PhD project looking at mathematical and numerical modelling of hydrodynamic rotating convection in a spherical shell. 

Research interests

Convection within the Earth’s fluid core generates the planetary magnetic field. Seismic, geomagnetic, and geodynamic observations indicate that lateral variations in heat flow are present at the core-mantle boundary, these heterogeneous boundary conditions at the top of the core can significantly reorganise the pattern of convection. My work uses the Leeds Spherical Dynamo code to investigate the fundamental fluid dynamic mechanisms of hydrodynamic rotating convection. We have performed a systematic parameter study varying the control parameters representing the strength of rotation (Ekman number) and buoyancy (Rayleigh number) allowing us to developing scaling laws describing the flow properties and heat transfer. By correlating the observed changes in scaling behaviour we have constructed a regime diagram which allows us to specifically choose parameter values for future runs to investigate the dynamics most relevant to Earths core.

Thermal and viscous boundary layers in convection systems are responsible for controlling the heat transfer and flow dynamics. Most studies have prescribed a fixed-temperature on the boundaries however for many astro- and geophysical applications fixed-flux thermal boundary conditions are appropriate. Recently I have been evaluating different methods for defining the thermal layer thickness to find a robust definition allowing direct comparison between the different models used to study rotating convection.


  • MSc Fluid Dynamics, University of Leeds
  • BSc Hons Applied Mathematics and Theoretical Physics, Coventry University

Research groups and institutes

  • Deep Earth
  • Institute of Geophysics and Tectonics
  • Planetary Exploration