Robert G. Cooper
email: r.cooper4@newcastle.ac.uk
Office 4.06, Herschel Building, School of Mathematics, Statistics and Physics, Newcastle University, Newcastle-upon-Tyne, NE1 7RU
My name is Robert and I am in my second year of a PhD at Newcastle University. I am an applied mathematician primarily interested in fluid dynamics and magnetohydrodynamics.
My PhD involves studying convection-driven dynamos, particularly in the subcritical range (below the critical Rayleigh number for the onset of convection). Subcritical dynamo action is a possible explanation for the cessation of the Martian dynamo and so we hope to better understand the key properties of a dynamo in this regime. This work is supervised by Dr Celine Guervilly and Dr Paul Bushby.
Prior to my PhD, I finished my 4th year MMath research project in 2017 entitled Topology of Superfluid Turbulence: Computing the Alexander Polynomial supervised by Prof. Carlo Barenghi and in October 2016 I co-authored my first paper with M. Mezgarnezhad, A.W. Baggaley and C.F. Barenghi.
All opinions expressed on this blog are my own and are not on behalf of Newcastle University.
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Convection and Dynamos in Planetary Interiors
In the first year of my PhD we investigated the simplest case of rotating convection; in a uniformly heated, rotating box. I wrote a pseudo-spectral code which solves the two-dimensional Boussinesq equations using a minimal number of Fourier modes in the vertical direction whilst maintaining nonlinearity. I explored the parameter space with particular interest in subcritical and localised convective states and was able to maintain both steady and oscillatory localised states which extended into the subcritical regime. In these localised states, convection was allowed to occur in areas of anticyclonic vorticity with convection completely suppressed in regions of cyclonic vorticity.
More recently I have been using the local, Cartesian geometry code from Cattaneo, Emonet & Weiss (2013) to explore convection-driven dynamos. First I reproduced the work of Stellmach & Hansen (2004) before expanding the parameter space and further studying subcritical dynamo action. In our simulations we are able to maintain dynamo action well below the critical Rayleigh number for the onset of convection and it appears as though we can move further into the subcritical regime at more rapid rotation.
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Topology of Superfluid Turbulence
Prior to my PhD my research had mostly been focussed on quantifying the topological complexity of superfluid turbulence and relating the complexity to the geometry and dynamics of the system. Modelling superfluid vortices as filamentary structures we witnessed the formation of dense tangles whereby the topology continuously changes as vortices reconnect. To quantify topological complexity I wrote, developed and tested a code from scratch which computes a knot invariant known as the Alexander polynomial. To see what we discovered please refer to my MMath dissertation entitled Topology of Superfluid Turbulence: Computing the Alexander Polynomial or our paper Helicity and Topology of a Small Region of Quantum Vorticity.
We are continuing to explore other superfluid flows and systems in a similar manner.
My code computing the Alexander polynomial is freely available upon request by email to r.cooper4@newcastle.ac.uk