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# PhD Students

## Huda Ramli

I am looking at the synchronisation of grid-based Eulerian and particle tracking Lagrangian methods in solving advection-diffusion model problems that are potentially relevant in the large-scale atmospheric transport, such as chaotic advection regimes and boundary layer processes. The model examined in the picture here is a simple two dimensional, non-autonomous flow in a chaotic advection flow. This problem is selected so that the Eulerian spectral method is very accurate to be compared to the Lagrangian stochastic method. The aim of my research is to develop strategies for an accurate global estimation of the field concentration at all points x in the domain at a fixed time t, i.e. C(x,t) from the Lagrangian solution.

## Pietro Servini

Placing small dynamic roughnesses - bumps and dips that oscillate up and down - on a surface was first looked at by Huebsch (2006) in the context of laminar flow control.  He showed that this had the potential to alter the flow in a laminar boundary layer in such a way that it suppresses stall and reduces drag: goals of vital importance to the aeroplane industry as they seek to improve safety and cut down on fuel costs.  Further work since then has done nothing to diminish this potential and my PhD sees me delve deeper into this novel technique.

Aircraft wings account for around 25% of the total drag experienced by an aeroplane cruising at subsonic speeds.  Investigating techniques to reduce drag here or delay stall could save the airline industry considerable amounts of money and improve aeroplane safety

## Olly Southwick

Eddies ranging from tens to hundreds of kilometres in diameter are known as mesoscale eddies. These can persist for months or even years and play an important role in the ocean circulation as they can transfer significant amounts of heat, salt and momentum. Understanding the ocean circulation is of importance for many reasons, one of the most important is to better understand changing climate. The oceans are responsible for the majority of the recent increase in energy in the climate system. Indeed, the heat capacity of the top 2.5m of the ocean is equivalent to that of the entire depth of the atmosphere.

I work on a very simple model for ocean eddies in which they are represented as a point vortex. My model aims to better understand how one mechanism for the generation of eddies may operate in the oceans.

Theoretically a fluid flowing around a sharp corner would have infinite velocity as it turned around the tip of the corner. In reality viscosity stops this happening and the fluid instead 'separates' at the tip. This means that instead of turning the corner the fluid continues straight on. This leaves a line separating the flow above and below the corner. Across this line the fluid velocity is not continuous ie the line is a line of infinite vorticity. This vortex line rolls up into a concentrated spiral - the shed eddy.

My research area is complex fluids: fluids that don't behave in the way that we would expect more standard Newtonian fluids (like water, air and honey) to. So this might include mayonnaise, blood or chocolate. Indeed, my master's project was looking at the fluid dynamics of chocolate fountains-a particularly interesting/tasty study into the behaviour of such non-Newtonian fluids.

In my PhD research, I am currently modelling flows of viscoelastic suspensions. Many industries use non-Newtonian liquids with particles in them (think paint, adhesives and even blood), and I'm looking at how these particles move, whether we can model certain non-Newtonian fluids using these suspensions, and whether I can explain some odd phenomena observed when dropping things through these suspensions. I do this all using Python code based on a procedure called Stokesian Dynamics.

## Ashley Whitfield

I am interested in applying numerical techniques such as accurate spectral integrations to geophysical nonlinear wave problems, with a particular interest in internal solitary wave propagation and its consequences in the ocean.

## Chunxin Yuan

My main interests are on oceanic waves, especially internal waves, from the view point of theories and numerical simulations.

I have successfully used the variable coefficient Korteweg-de Vries equation (well-known as the KdV equation) to simulate internal solitary waves in the real ocean. Based on this equation, we can comprehensively consider the effect of topography, stratification and background current (usually tides or barotropic flows in the ocean) on the propagation and dissipation of internal solitary waves. Currently, I'm working on the variable coefficient Kadomtsev-Petviashvili equation, which is a three-dimensional problem and is intuitively better at describing the real ocean, though more complicated and much harder to develop.

Except the theory, I'm also running a numerical model, the MIT General Circulation Model (MITgcm), to simulate internal waves in the South China Sea, and hope to give a cradle-to-grave picture of internal waves on a basin scale. This model is driven by real tides, using real topography, temperature and salinity.