## Research Overview

I am particularly interested in the following three research areas: the dynamical systems interpretation of fluid flow, the categorisation of geophysical mixing events, and the modelling of compressible porous media. I also have interests in the effects of stochastic perturbations on bifurcations of dynamical systems, and the migration of salt through sea ice and overlying snow.

##### Dynamical Systems Interpretation of Fluid Flow – Boundary Layer Drag Reduction

It is becoming increasingly evident that turbulent fluid flows can be described as a trajectory in state space that sequentially visit nonlinear invariant solutions to the Navier–Stokes equations such as equilibria and periodic orbits. My research interest in this area concerns the recent observation that substantial reductions in turbulent fluid drag can be made in turbulent boundary layers by introducing spanwise oscillation at the fluid boundary. From a dynamical systems viewpoint, it appears that the boundary oscillation excites certain invariant solutions which exert less drag on the boundary; the chaotic trajectory then visits these invariant solutions more frequently than it would otherwise, thus reducing the long-term turbulent drag. I aim to understand the effect of periodic forcing on the periodic orbits that form the skeleton of chaotic dynamics, and have been conducting preliminary investigations with my late collaborator Prof. Bruno Eckhardt.

##### Geophysical Mixing Events – Linear and Nonlinear Categorisation of Stratified Shear Flows

An understanding of the processes by which fluids of different densities are mixed in the ocean is crucial in order to properly constrain global climate circulation models. Local, rapid mixing processes are controlled by shear and density stratification, and such processes lie below the grid-scale resolution in climate models so that realistic parameterisation of this mixing is required. For such flows, there are three instabilities which can lead to mixing: the Kelvin–Helmholtz, Holmboe, and Taylor–Caulfield instabilities. The nonlinear evolution of each instability has distinct mixing characteristics, but it is not clear in what proportion each of these three mixing events occurs in the ocean. I have recently published an algorithmic methodology for classifying these flows at a linear and nonlinear level, based upon conserved quantities of the equations of motion which capture their large-scale features. This classification works well for identifying the dynamics for relatively quiescent flows, and so I am now investigating to what extent the methodology adequately coarse-grains realistic flow data to provide robust categorisation of oceanographic mixing events.

##### Compressible Porous Media – Informing the Design of Industrial Paper-making Presses

During my postdoctoral research at the University of British Columbia, I was sponsored by Valmet Ltd, who build industrial machines for the paper-making industry. Our research is aimed towards optimising the design of roll- and screw-presses. We developed a compressible elasto-visco-plastic rheology describing the behaviour of wood-fibre pulp suspensions, a suite of laboratory-scale experiments to benchmark this rheology, and simplified models which apply this rheology to the complex geometries associated with the industrial machines. The equations used to model such suspensions are related to those in soil mechanics, models of biological tissue, and other plastically deformable porous media, and my most recent investigations help develop a clearer picture of how the microscale properties of these porous media manifest in their macroscopic behaviour.

I am also collaborating with the VTT Technical Research Centre of Finland, to provide a predictive tool to inform the design and operating principles for prototype paper presses.