**Daniel Goodair **

#### Project Title:

Stochastic Partial Differential Equations with Applications in Ocean and Atmosphere

#### Project Details:

I am a Research Postgraduate in the Pure Mathematics Section, working under the supervision of Professor Dan Crisan. I am interested in the theory of Stochastic Partial Differential Equations, and in particular the well-posedness of a new class of stochastic fluid dynamics models on a bounded domain. These models add uncertainty in the transport of fluid parcels to reflect the unresolved scales, whilst affording proper energy circulation and preserving fundamental properties of their deterministic counterparts. The analysis of these equations has just begun: although some well-posedness results have been achieved on the torus, the influence of a boundary is not yet known. We hope to prove such results in analogy with those achieved in the deterministic setting, and perhaps even explore the regularising affect adding stochasticity could have

#### Supervisor:

Prof Dan Crisan** **

**Melanie
Kobras**

#### Project Title:

Low order models of storm track variability

#### Project Details:

The storm tracks in the Earth’s atmosphere are the main locus of midlatitude weather systems and they show variability on a broad range of timescales. Where baroclinic instability works on relatively fast timescales, it is the non-linear properties of the storm tracks that produce the slow timescales of 10 days or more, up to climate time scales. The aim of my PhD project is to better understand the underlying non-linear dynamics leading to slow variability and how these dynamics would react to changing external forcing.

#### Supervisor:

Prof Maarten Ambaum and Prof Valerio Lucarini (Mathematics)

**Connor
Ward**

#### Project Title:

Low Latency Code Generation for Extreme-Scale Continuum Mechanics

#### Project Details:

In high performance computing, the strong-scaling performance of an application describes how efficiently a problem can be divided among increasing numbers of processors. With exascale machines just around the corner, this has become an increasingly important metric for modern simulation codes.

In my research project I will be investigating, and hopefully improving, the strong-scaling behaviour of Firedrake, a code-generation framework for solving PDEs with the finite element method.

#### Supervisor:

Dr David Ham

**Theo
Diamantakis**

#### Project Title:

Dynamics on Rough Paths

#### Project Details:

The field of our research is in the intersection of geometric mechanics and stochastic analysis applied to oceanography. It has been recently shown that the equations of SALT (Stochastic Advection by Lie Transport, a reformulation of fluid dynamics as a stochastic variational principle on an infinite dimensional Lie group) can be understood as a rough partial differential equation. Our current project is understanding the effects of coloured noise for SDE, and the appearance of noise induced drift terms, a surprising phenomenon where using other models of randomness than the more idealised mathematical white noise leads to approximating solutions for an equation with an altered drift term. We aim to apply this theory to SALT, and to learn what sort of noise induced drift arises in these equations and whether this can create some unstable behaviour with physically relevant consequences. Understanding of what noise induced drift appears in SALT, if any, will allow us to decide the most natural choices of modelling when it comes to climate and weather simulations, similar to the often encountered choice between Ito and Stratonovich interpretations, which mathematical convenience sometimes comes at the cost of introducing “ficticious forces”. It is our aim that this research will lead to a more accurate understanding of small-scale effects in fluid dynamics, such Langmuir circulations and wave-current interaction, as well as link with some interesting theoretical aspects from statistical mechanics.

#### Supervisor:

Prof Darryl Holm and Prof Greg Pavliotis

**Jamie Meacham **

#### Project Title:

Transport and Clusterisation of Floating Particles in the Ocean

#### Project Details:

My project is based around developing an understanding of the dynamics of buoyant tracers in the upper ocean e.g. plastic, oil spills or biological life such as plankton. In particular, the interest is in how these form dense clusters in the ocean currents, due to effects like surface divergence of the flow or inertial effects due to the mass of the floating particles.

#### Supervisor:

Dr Pavel Berloff

**Jasmine
George **

#### Project Title:

Towards a theory for the surface layer of the ocean

#### Project Details:

The ocean plays an essential role in climate change as the air-sea interface allows the transfer of turbulent fluxes of momentum, heat and gases and other processes between the atmosphere and ocean. Turbulent mixing can be numerically modelled using turbulence closure techniques; which can be modified to take into account the effect of surface waves within the ocean surface boundary layer, namely the Stokes drift and Langmuir circulations.

With this research, I aim develop the knowledge that will allow modifying an existing turbulence closure model, KPP (K-Profile Parameterisation), to investigate the vertical mixing in the ocean boundary surface layer by comparing the results to real datasets, BODC OSMOSIS and ECMWF ERA-reanalysis data. Hence, I ultimately aim to develop an improved parameterisation of the impact of non-breaking surface waves for the upper ocean.

#### Supervisor:

Dr. Miguel Teixeira,

Mr. Alan Grant

Prof. Valerio Lucarini (Mathematics)

Dr. Jean Bidlot (ECMWF)