From September 2016 I have been working as a Postdoctoral Research Fellow in the Mathematics Department at the University of British Columbia, working with Prof. Neil Balmforth and Prof. Mark Martinez. I am primarily looking at the mathematical fluid dynamics behind the paper making process, but am also persuing a number of directions in my research interests listed below.

I completed my PhD research in June 2016 as a SIMS Scholar at St John's College, University of Cambridge, working with Prof. Colm Caulfield in the Department of Applied Mathematics and Theoretical Physics. My PhD research focussed on the dynamics of stratified shear flow instabilities and minimal seeds for turbulence in stratified plane Couette flow. I investigated transition to turbulence in stratified shear flows from a dynamical systems viewpoint, and how the coherent structures in such flows change with the strength of stratification. My thesis is entitled "Generalised nonlinear stability analysis of stratified shear flows: adjoint-based optimisation, Koopman modes, and reduced models".

My CV can be found here.

In Session 2 of the Winter Term at UBC I am teaching MATH 256 (Section 202). The course website can be found here.

In Cambridge I supervised undergraduate students in the following courses:

- IB Methods
- II Dynamical Systems
- II Asymptotic Methods
- II Mathematical Biology

In addition to supervising undergraduate students in the above courses, I also gave examples classes for IB Methods as a college teaching assistant at St John's College, University of Cambridge.

My research to date has focussed on the dynamical systems viewpoint of fluid flows. In particular, my current interests include:

- Nonlinear optimisation problems in fluid dynamics: minimal seeds for turbulence (the smallest amplitude perturbations to a base flow that eventually transition to turbulence), energy stability, optimal mixing in stratified shear flows.
- New methods for the identification of unstable periodic orbits embedded in chaotic attractors.
- The Koopman operator and its application to transient trajectories.
- The stratified extension of the "self-sustaining process" (SSP) or "vortex-wave interaction" (VWI) edge states.
- Stratified shear flow instabilities, in particular the Taylor‒Caulfield instability, and their subsequent nonlinear evolution.
- Dymamics of rotating stratified shear flows in the presence of baroclinic critical layers.
- Stochastic dynamics of near-homoclinic or near-heteroclinic systems.

Eaves, T. S. and Balmforth, N. J.,

**Instability of sheared density interfaces**,*under review, J. Fluid Mech.*(2018).Ponetti, G., Balmforth, N. J. and Eaves, T. S.,

**Instabilities in a staircase stratified shear flow**,*Geophys. Astrophys. Fluid Dyn.***112,**1-19 (2018).Eaves, T. S. and Caulfield, C. P.,

**Multiple instability of layered stratified plane Couette flow**,*J. Fluid Mech.***813,**250-278 (2017).Eaves, T. S. and Balmforth, N. J.,

**Noisy homoclinic pulse dynamics**,*Chaos***26,**043104 (2016).Eaves, T. S. and Caulfield, C. P.,

**Disruption of SSP/VWI states by a stable stratification**,*J. Fluid Mech.***784,**548-564 (2015).Brun, P.-T., Audoly, B., Ribe, N. M., Eaves, T. S. and Lister, J. R.,

**Liquid ropes: A geometrical model for thin viscous jet instabilities**,*Phys. Rev. Lett.***114,**174501 (2015).

**Office:** LSK 203C

**Address:**
Department of Mathematics, University of British Columbia,

1984 Mathematics Road, Vancouver, BC, V6T 1Z2

**Telephone:** +1-(604)-827-3299

**Email:** tse23@math.ubc.ca