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 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.
Project title : 'Wetropolis: Natural Flood Management demonstrator'

I am now in the middle of my PhD project looking at mathematical and numerical modelling of hydrodynamic convection in a rotating spherical shell.
Project title: 'Force balances and dynamical scaling of rotating convection'.

Research interests

Convection within the Earth’s fluid core generates the planetary magnetic field. The underlying fluid mechanics responsible for maintaining the magnetic field are still not completely understood. Core convection is vastly complicated with many ingredients such as rotation, the spherical geometry and how the mantle extracts heat from the top of the core all having important effects. My work uses the Leeds Spherical Dynamo code to investigate the fluid dynamic mechanisms of hydrodynamic (thermal) rotating convection.

Scaling behaviour of rotating convection

Rotating convection in a plane layer is known to exist in different dynamical regimes depending on the values of the control parameters. We wanted to know if we can find similar regimes in spherical shell rotating convection. To answer this 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 Earth's core.

Boundary layers in rotating convection

Thermal and viscous boundary layers in convection systems are responsible for controlling the global 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 (e.g. at the core-mantle boundary). 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