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 final year 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 Earth’s fluid core generates the planetary scale magnetic field. The underlying fluid mechanics responsible for maintaining the magnetic field are still not completely understood. Core convection occurs on a vast range of spatio-temporal scales and is 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 numerical simulations to investigate the fluid dynamical 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 in which different regimes are identified, each being governed by their own flow physics. The regime diargam is a useful tool allowing us to specifically choose parameter values for future dynamo runs to investigate the dynamics most relevant to Earth's core. 
This work has been published in the Journal of Fluid Mechanics.

Boundary layers in rotating convection

The dynamics and interplay of the thermal and viscous boundary layers in convecting systems are responsible for controlling the global heat transfer and flow properties. 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). I have been evaluating different methods for defining the thermal boundary layer thickness to find a robust definition allowing direct comparison between the different model configurations which are often used to study rotating convection.

High latitude convection in Earth’s core

The natural geometry when considering convection in Earth’s core is a rotating spherical shell. Practical considerations have led to many numerical and laboratory investigations using plane layer and cylindrical domains with the (constant value) gravity vector antiparallel to the rotation axis. This configuration is thought to be representative of convection at high latitudes. The behaviour of the heat transport (Nusselt number) and flow speeds (Reynolds number) behaves differently for spherical shell cases than the equivalent plane layer or cylindrical case. I visited Prof. Jon Aurnou at Spinlab,  UCLA and we performed a series of rotating convection experiments in a cylindrical tank using water. In these experiments we measured the heat transfer and flow speeds simultaneously. We are quantitatively comparing the results of the laboratory experiments against harvested cylindrical regions of the spherical shell models at high latitude to explicitely test if these simplified analogues are representative of the global system.



  • 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