Luke Gostelow

Luke Gostelow


At the end of my bachelor's degree, I began to consider the possibility of research and undertook a research project in multi-dimensional Lotka-Volterra systems. I completed my master’s the following year, in 2020, attaining the HL Price Prize for applied mathematics as well as a first-class degree, and submitted a dissertation titled “Surface and Internal Gravity Waves”. Since then I have been working on a PhD project with David Hughes and Stephen Griffiths on “Shear Flow Instabilities in Quasigeostrophic Shallow-Water MHD”.

Research interests

The equations of (rotating) shallow-water magnetohydrodynamics ((r)SWMHD) were derived in Gilman’s seminal work of 2000 with obvious application to stars, and the Solar tachocline in particular. Within these equations a vast array of dynamics is possible and we have set our sights on an investigation of shear instabilities and the class of nonlinear dynamics that can follow them, particularly in the “rapidly rotating” (QG) limit, thought to be broadly applicable to the tachocline. Our work so far has included the linear stability analysis of general shear flows as well as a closer look at some analytic flow profiles. We have then gone on to develop a numerical code for simulating these flows past the regime of linear instability into the nonlinear where it is well-known that Kelvin-Helmholtz vortices develop (in kinematic systems). Less well-known is that these vortices can exhibit secondary instabilities, and a significant focus of our recent work has been such instabilities in weak-field MHD, how they develop, and how this affects the long-term evolution of QGMHD systems, such as the Solar tachocline.


  • Mathematics MMath, University of Leeds (2017-2020)