Professor Colm-cille Caulfield, Editor -in-Chief of Journal of Fluid Mechanics (JFM) discusses his career. Colm-cille discusses common themes in his research, Mathematical and computational tools for research and teaching. As well as his favourite fluid type. 

Colm-cille also provides insight into his favourite JFM paper, advice for students and prospective JFM authors.

Transcript follows below…

Filmed and Produced by Tom Crawford an Early-Career Teaching and Outreach Fellow in Mathematics at St Edmund Hall and Social Media Editor for JFM.

“Be curious, Be resilient, Be kind… I think those three aspects are really central to the way I have enjoyed my research career..”

Transcript:

My Research

My research has common themes, I think that I can always see my research interests. I’ve been very interested, since my PhD, in how flows become unstable. And my PhD work was on stratified shear flow instability. So, I was very interested in the dynamical significance of density variations interacting with shear. That has naturally led to being interested in processes by which mixing occurs. You start off with the variation in density, there will be the example and then the instability will tend to stir things up. And so, how does that stir lead to mixing? Irreversible mixing inevitably brought me to be interested in various aspects of turbulence because that’s a very efficient way of mixing and it also has clear importance in various applications.

The applications also attracted me. Understanding oceanographic flows, talking to oceanographers, also understanding various industrial flows, where you can have density differences, but there’s still mixing, turbulence, the transition is an important phenomenon. A connected strand is the mathematical and computational tools that you use to understand such phenomena. How flows become unstable, how they become turbulent, how they cease being turbulent, and how mixing occurs. So, I’ve also been interested in using different mathematical tools, computational tools, to understand and quantify those various processes. You’re often interested in in some idea of how likely an event is. An optimal perturbation for example, to trigger a flow. And so, I’ve also been interested in in constructing mathematical and computational tools to consider broader generalized stability problems. How does the flow at relatively high Reynolds number become unstable and become turbulent and or remain turbulent, and how that interacts with mixing.

The reason I like fluid mechanics. I think about this when I talk to people about becoming my PhD students, is that it is beautiful. You can see so many of the phenomena in everyday life and we are continually interacting with fluids, fluids are really important on such enormous range of scales with different dynamics. When I discuss the different dynamics: that then is the other side of the coin for somebody from a scientific or mathematical or engineering bent. There are beautiful problems in it. The aesthetic of the problems, the different understanding f the physics, the different significance of boundary conditions, the inherent nonlinearity. So often these are interesting puzzles to solve, that are pretty mathematics or physical modelling or numerical codes as well.

The problems are all around and you can always see fluids.

The underlying mathematical physics is just so elegant when you do work it out. It’s just a beautiful intersection of them.

My Favourite Paper

For me, my favourite JFM paper was undoubted. There is a number one. it’s a paper by Louis N. Howard the ‘Note on a paper of John W. Miles’*  where he very elegantly produces short general proof of the Miles-Howard theorem. The sufficient condition for the flow to be stable to linear perturbations is for the Richardson number to be greater than a quarter everywhere and so, I suppose, a necessary condition for an instability is that somewhere within the flow the Richardson number drops below a quarter. Richardson number of course being the ratio of the buoyancy frequency squared to the shear squared it’s the gradient Richardson number that matters. It is just such a masterpiece of explanation mathematics that really is significant and is important. I remember during my thesis, reading that paper, and just thinking: ‘wow, this is incredible’ because also the original papers, on which it is a note, by John Miles were also incredible papers to actually arrive at establishing this result. But ‘there was more than one way to skin a cat’, right and there were. Lou Howard’s result just amazes me, how insightful the matter is. And that’s the thing. It showed you how the mathematics could tell you something deep about the fluid mechanics having a physical significance.

And I just thought it was so elegant. So that is undoubtedly my favourite JFM paper.

My Advice

I think the advice I’d have for the students starting out on the journey would be: ‘be curious’.

I found it so valuable and enriching to read journal papers, not necessarily narrowly, in particularly what I thought I wanted to do, but contiguous areas, because then you can have new ideas, which come from those contiguous areas. Particularly in my first JFM paper, I applied some ideas from plasma physics, that hadn’t been so well connected with the classical fluids community. And so that was an experience for me, which was good. So, I’d say ‘Be curious, be resilient’. The vast majority of the time, things don’t work out. You know, codes have bugs, experiments malfunction, solutions cannot be found of the analytic pen and paper exercises. But no day doing research is wasted, because you’re always learning, always thinking of different things, and it is through those thinking of different things and trying different approaches you will get somewhere. And so ‘be curious, be resilient. And also, it sounds trite but, be kind’. I think it is broadly defined as: always be open to working with other people. This is a collaboration, not a competition. To understand that doing research is about finding answers and humanity is pushing back the boundaries of knowledge.

I have found it incredibly useful in my career, to be open to talking to other people sharing ideas with other people trying to learn off of other people. And, and also, in some sense trying to help other people, you know,  because the number of times, I have been astounded by what one of my students has said or the insight they have given is just really enriching to me.

More broadly to the whole situation. If you want to do research, I think the fact of wanting to find answers to problems is reflected by the curiosity, the resilience is reflected by interesting problems to solve. These are typically not immediately easy to do, and so you do need to keep on going and keep on going. But I really do think it’s important to be open to working with other people and open to sharing your ideas, and to treating other people with respect. And that’s what I mean by ‘be kind’. Because I joke about this with people. When you are a reviewer, you are the most reasonable person in the world, and you’re trying to give constructive comments to the author. And when you’re an author and you have some response that says anything other than ‘this paper is the best paper I’ve ever seen’, you inevitably, I do, inevitably get defensive but you have to think of the other person on the other side. So as a reviewer be constructive, even if you think you’ve found a fundamental flaw and as an author appreciate that this other person has read your paper carefully and is trying to make it better, is trying to make your work better. And so, I think those three aspects are really central to the way I have enjoyed my research career. And I really think that they are the best way for people starting out to feel fulfilled through their research career.

My Favourite Fluid

I have favourite fluid, its sea water. Yes definitely, sea water.

So why do I love sea water?

Well, I like going I love looking at the sea it’s amazing how restful I find looking at the sea, you know, because you see the different sea states and you can understand the surface wave properties and then you see the critically important mass transfer of the white horses of the gas water transfer and then you but then you know inside it is stratified and it has all these fascinating different dynamics, perhaps the most.

The first time I ever heard of double diffusion, it was just astounded me, because the salts diffuse is much slower than the heat. So, you have these incredible convective motions going on inside. And also because it’s stratified, it has internal waves bouncing around, and then there is this argument you can have about the Garrett-Munk particular spectrum of the waves that are there, there’s a particular empirical law that seems to be quite well described, but then those internal waves interact with velocity share that can lead to these different instabilities and these different mixing processes.

And I just find that it’s amazing and it’s 70% of the surface area of the planet. It’s it literally is all around us. I know you need air to breathe, and you need liquids to drink. But the seawater is if I’m allowed to be that specific about a particular fluid because it has the stratifying agents in it. There’s variation in temperature and the variation in salinity.

I just find that that’s amazing. I think that’s the thing.

Read Colm-cille’s favourite JFM article:

‘Note on a paper of John W. Miles‘ by Louis N. Howard, Journal of Fluid Mechanics