Robert G. Cooper

After lots of hard work we finally managed to publish our recent results on knotting in superfluid turbulence. This was based on the work I did during my MMATH where I wrote a code which computed the Alexander polynomial of various knots.

Cooper, R.G., Mezgarnezhad, M., Baggaley, A.W. and Barenghi, C.F. (2019), Knot spectrum of turbulence, Scientific Reports, 9, 10545

https://www.nature.com/articles/s41598-019-47103-w

Streamlines, vortex lines and magnetic flux tubes in turbulent fluids and plasmas display a great amount of coiling, twisting and linking, raising the question as to whether their topological complexity (continually created and destroyed by reconnections) can be quantified. In superfluid helium, the discrete (quantized) nature of vorticity can be exploited to associate to each vortex loop a knot invariant called the Alexander polynomial whose degree characterizes the topology of that vortex loop. By numerically simulating the dynamics of a tangle of quantum vortex lines, we find that this quantum turbulence always contains vortex knots of very large degree which keep forming, vanishing and reforming, creating a distribution of topologies which we quantify in terms of a knot spectrum and its scaling law. We also find results analogous to those in the wider literature, demonstrating that the knotting probability of the vortex tangle grows with the vortex length, as for macromolecules, and saturates above a characteristic length, as found for tumbled strings.

I really enjoyed helping out yesterday at Newcastle University’s STEM Family Fun Day. I was teaching families about the expansion and possible fates of the universe using balloons and (apparently permanent) marker. I have a whole universe still on my hands!

So on Monday I gave an external talk at the MHD/GdRI conference hosted by HZDR in Dresden, Germany. I presented my recent PhD research with Celine Guervilly and Paul Bushby studying subcritical Cartesian convection-driven dynamo action. Please find my talk below:

MHD-Days-GdRI-2018

I enjoyed the tour of the HZDR experimental facilities, their new precession dynamo experiment, which is under construction, should be interesting in the future. Dresden was also very cold but I still managed to visit the Christmas market!

Dresden Christmas Market – it was huge.

Astro-Lunch-2018

Please find my talk below to be given at University of Southampton for the STFC Advanced Summer School:

stfc-southampton-2018

My talk will be on my recent work aiming to reproduce and extend the results of Stellmach & Hansen (2004) where they numerically simulate Cartesian convection-driven dynamos at low Ekman numbers and produce a subcritical dynamo. That is, dynamo action below the convective onset. I have recently managed to reproduce this subcritical dynamo and now aim to extend the study to lower Ekman numbers and further into the subcritical regime.

So yesterday we had the annual PG Applied Conference here at Newcastle University. It was great to get the chance to see what everybody else is researching and present my own work.

I gave a talk on Localized States in Rotating Convecti0n at Low Prandtl Number which can be found below.

PG-Applied-Conference-2018

Basically, we numerically simulate 2D rotating convection in a Boussinesq fluid looking at how rotation affects the presence of spatially localized convective states at low Prandtl numbers relevant to planetary cores. Such localized states may explain why some planets such as Mercury have weak magnetic fields. We find both steady (time-independent) and oscillatory (time-dependent) localized states where convection is suppressed in regions of cyclonic vorticity and have an effective Taylor number which is below the onset at which convection occurs. Where convection does occur we see that the vorticity is anticyclonic and this region is effectively non-rotational. Like in magnetoconvection where magnetic fields inhibit convection, we see here that rotation is able to inhibit convection. We also find localized convective states that extend into the subcritical regime (convection at values where it should be suppressed) and hence rotation is able to aid convective motions in the subcritical regime. This may be relevant to the Martian dynamo since subcritical dynamo action is a possible explanation for its termination.

Localization in the temperature in 2D rotating convection at low Prandtl number.

Piazza Liberta in Udine, Italy

Last week I had a great time at CISM in Udine, Italy attending a course on the Fluid Mechanics of Planets and Stars.

We had lovely weather, with the sun always shining. The CISM palazzo-style building was fascinating and I particularly enjoyed the views from the castle and the many evenings sat with a glass of wine in Piazza Matteotti Giacomo with the other participants and speakers.

Course-wise, I wouldn’t say too much was immediately relevant to my PhD project, however there were a lot of things I had read mentioned in papers which I did not fully understand but after this course now do. The speakers were all excellent so thank you to Michael Le Bars, Daniel Lecoanet, Benjamin Favier, Bruce Sutherland, Gordon Ogilvie and Renaud Deguen for organising and giving such great talks.

So this week we hosted a conference at Newcastle University in honour of Prof. Carlo Barenghi’s 65th birthday. There were some fascinating talks and it was great to see so many people travel to Newcastle from all over the world in celebration of my Masters supervisor and colleague.

I’ll take this as an opportunity to say a few words about Carlo myself. I have only been working with Carlo for around 2 years now, but in that time I can honestly say he has had such a large impact on my academic career already. During my Masters project he really pushed me to be better and taught me how to be a better researcher. He always gave me great advice regarding a career in academia and it was because of him that I wanted to do a PhD and stay in research. I would be more than happy to achieve half of what he has in my career and to hear somebody talk about their work with such passion is a real inspiration to me. Even now, whilst my PhD is in another area of mathematics we continue to work together and he still takes such an interest in my work and how I am doing.

So thank you Carlo for all that you have done for me and I look forward to continuing our work together.

Had a great couple of days in St Andrews for UK MHD.

Here is the poster I took with me based on my PhD work so far on localized states in rotating convection with Dr. Celine Guervilly & Dr. Paul Bushby. Prof. Carlo Barenghi also gave a talk on some of my work with him on the topology of superfluid turbulence.

There were so many interesting talks and it was good to meet plenty of new faces and catch up with a few PhD students I saw at previous meetings. Hopefully next year I will give a talk.

It was sad to wake up to the news of the passing of Stephen Hawking this morning. As a mathematician and physicist, he was an inspiration to all of us in the scientific community. His achievements and work have been remarkable and he is certainly someone the world will never forget. I could only hope to achieve a small percentage of what he has achieved in his lifetime. Rest in peace.

“Remember to look up at the stars and not down at your feet. Try to make sense of what you see and wonder about what makes the universe exist. Be curious. And however difficult life may seem, there is always something you can do and succeed at. It matters that you don’t just give up.” – Stephen Hawking, 1942-2018