## Research

My main research interest is in Computational Fluid Dynamics (CFD) . I am involved with projects studying the fluid mechanics of classical and MHD Taylor–Couette flow, as well as the quantum fluid mechanics of Bose–Einstein condensation. I have developed two parallel numerical codes, one of which I used in my PhD research, and one which solves the Gross–Pitaevskii equation (GPE) in 3D using MPI.

Both are freely available under the Apache 2.0 licence, and can be obtained from my GitHub repository.

## Bose–Einstein condensation and superfluidity

Below are animations of the results of some runs of the GPE code. I also maintain a manual for the GPE code. If you are interested in using the code, or would like to help develop it further, please get in touch. Also see the GitHub repository.

## PhD

I completed my PhD in Applied Mathematics at Newcastle University under the supervision of Professor Carlo Barenghi. My thesis is entitled Bifurcations in forced Taylor–Couette flow .

In my PhD research I studied the fluid flow between co-axial, concentric, rotating cylinders (Taylor–Couette flow). See below for a brief description.

I developed a Fortran 90 numerical code to solve the Navier–Stokes equations for the above problem. See the GitHub repository for the code if you are interested.

## Taylor–Couette flow

The classical Taylor–Couette problem is the flow of an incompressible, viscous fluid contained in the gap between two concentric, rotating cylinders. The Couette apparatus was developed by Maurice Couette in 1890 as a means for measuring the viscosity of a fluid at small imposed angular velocities of the cylinders.

Schematic of the Couette apparatus.

The simplest case is that when the outer cylinder is at rest. At small angular velocities of the inner cylinder the flow driven around it is purely azimuthal (circular Couette flow, or CCF). In 1923 Sir Geoffrey Ingram Taylor found that when the angular velocity of the inner cylinder exceeds some critical value, then the circular Couette flow becomes unstable to axisymmetric perturbations. The radial and axial velocity components grow exponentially in time and then saturate nonlinearly to a flow pattern which consists of axisymmetric vortices stacked on top of one another in the axial direction, with radial inflows and outflows (see the figure below). This pattern is known as Taylor vortex flow (TVF).

Schematic of Taylor vortex flow. Shown is a pair of Taylor vortices over one axial wavelength.

If the rotation rate of the inner cylinder is further increased TVF becomes unstable to non-axisymmetric perturbations, and azimuthal waves are formed which rotate around the inner cylinder at some wavespeed. A further increase in the rotation rate of the inner cylinder leads to an even wider variety of flows, each with clearly defined stability boundaries; due to the exact way in which more and more spatial and temporal symmetries are broken, Taylor–Couette flow is an ideal setting in which to study instabilities and nonlinear behaviour in a fluid system. See the photographs below for an example of the wide variety of flows that can be observed.

Photographs of various flows using Kalliroscope flakes (reflective flakes which align themselves with the flow). Light and dark areas define the vortices. From left to right: Taylor vortex flow, wavy vortex flow, spiral vortex flow, twisting vortex flow, turbulent vortex flow.