8 September 2016: A topological study of gravity free-surface waves generated by bluff bodies using the method of steepest descents
This paper, now published in the Proceedings of the Royal Society A (PRSA) has a few interesting distinctions. It's the first paper I've published in PRSA—but hopefully not the last as it's certainly a strong journal with an illustrious history. It's the first solo paper I've published. And it has the longest title of any other paper I've worked on.
In any case, it's a paper where I explore exponential asymptotic techniques for free-surface flows (now well known) from a slightly different viewpoint. It turns out that the situation of gravity waves permits the governing equations to be re-formulated in a particularly simple way: that of a first-order nonlinear differential equation. In this paper, I show how the differential equation is studied using steepest descents. What results is a visual and beautiful way of understanding wave-structure interactions through a correspondence with the topology of certain Riemann surfaces (seen above).
You can download a copy of the paper here. This paper technically forms Part 2 of a two-part series of which the first is still in review.