PhD Studentship: Three-dimensional Water-waves

Over 50 years ago at Caltech, Richard Feynman stated that ``Waves easily seen by everyone and which are usually used as an example of waves in elementary courses are water waves. [...] They are the worst possible example because they are in no respects like sound and light; they have all the complications that waves can have.''

In the present day, the mathematical and computational study of water waves still remains a challenging and important research topic, with applications ranging from modelling tsunamis, rogue waves, and ice floes to informing ship design and coastal management. The accurate computation and characterisation of water waves is therefore of paramount scientific importance.

Classically, water waves are assumed to be two-dimensional (one horizontal direction), steady (do not change in time) and irrotational (no `twisting' motion). Yet recently there has been a fresh focus on characterising water-waves that are i) three-dimensional, ii) time-dependent and iii) rotational. This new impetus has revealed several open problems and challenges. This PhD project will strive to resolve some of these problems/challenges by utilising a mixture of tools from applied mathematics and computational techniques.

In particular, we are looking for curious, enthusiastic and hard-working candidates with the following expertise:

-- strong understanding of concepts in nonlinear waves and fluid dynamics using analytical and numerical methods to solve partial differential equations,

-- excellent oral and written communication skills.

Prior experience in nonlinear waves, fluid dynamics and numerical modelling will be a big advantage, but we seek, above all, a willingness to engage rigorously with challenging concepts.

The selected candidate will work closely with the supervisor through informal lectures on advanced topics, regular research discussions, and problem-solving sessions. There will be opportunities to broaden scientific knowledge and gain further insight by disseminating research at conferences. Throughout the PhD, the candidate’s career aspirations will be well-supported.

Candidates are encouraged to make an informal inquiry with Dr Jack Keeler (j.s.keeler@bham.ac.uk).

For application details, see Dr Keeler's personal page https://www.birmingham.ac.uk/staff/profiles/maths/keeler-jack

Funding notes:

This project is directly funded, through the School of Mathematics for a suitably strong candidate. The scholarship will cover tuition fees, training support, and a stipend at standard rates for 3-3.5 years.

References:

1) Keeler, J. S. et al. ``Towards eliminating the nonlinear Kelvin wake'', J. Fluid Mech. 1013, A10, 2025. (3D Waves)
2) Keeler, J. S. et al. ``On the stability of fully nonlinear hydraulic-fall solutions to the forced water wave problem'', J. Fluid Mech. 1013, A9, 2024. (Time-dependent Waves)
3) Keeler, J. S. et al. ``Exact solutions for submerged von Kármán point vortex streets co travelling with a wave on a linear shear current'', J. Fluid Mech. 969, A5, 2023. (Waves with vorticity)
4) Keeler, J. S. et al ``Parameter-free higher-order Schrödinger systems with weak dissipation and forcing''. Proc. Roy. Soc. A, 481, 2025. (Asymptotic methods on waves)

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