GK BATCHELOR LABORATORY
Potential PhD Projects 2012
This page outlines some (but not all) of the potential PhD projects on offer (starting 2012) from the following
Colm Caulfield (H.0.10)
Stuart Dalziel (H.0.11)
Paul Linden (H.1.18)
Nathalie Vriend (H.0.14)
Please feel to contact any of us to discuss these (or other) possibilities further.
Click here for other PhD studentship opportunities within DAMTP.
Geophysical Fluid Dynamics
1. Discharge of rivers into the North Sea
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The number of days the North Sea is |
The North Sea, which is typically of shallow continental shelves, stratifies in the summer due to solar heating. In the shallower regions where tidal flows are strong the heat input by the sun is mixed throughout the water column but in deeper parts with weaker tides there is insufficient energy to mix this heat and it accumulates in the upper part of the water column leading to stratification. The transitions between these regions are marked by sharp fronts that act as barriers to transport of heat and also biological matter and pollutants. This process is well understood since the solar radiation is essentially uniform in space.
Rivers such as the Rhine and Elbe also input buoyancy in the form of fresh water and in this case the inputs are very localized in space, leading to large horizontal inhomogeneities. The subsequent dispersion and mixing of this fresh water and the pollutants (particularly nitrogen) are poorly understood, but vital to the water quality of much of the North Sea. What is known is that buoyancy-driven flow, mixing and advection by the tides and the influence of the rotation of the Earth all play important roles in the ultimate destination and properties of this water.
This project would involve laboratory experiments on a high-precision rotating turntable and study both the qualitative and quantitative features of the spread of buoyant water through a turbulent environment. This project will offer the opportunity to collaborate with oceanographers who observe and model these flows numerically.
For further information, contact Paul Linden.
2. Internal gravity waves in time-varying flows
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Phase of internal waves reflected from smooth |
Much of the atmosphere and oceans are stably stratified in density. Cold, dense water formed in polar regions spreads over the ocean floor beneath warmer, less-dense water near the surface. When a parcel of fluid is perturbed vertically away from its equilibrium position in this stable density stratification it experiences a restoring force that attempts to bring the parcel back into equilibrium. This restoring force combines with inertia to create internal gravity waves. Unlike surface waves, with which we are all familiar, these waves propagate at an angle relative to the vertical, with the wave crests moving at 90° relative to the direction in which energy is propagating. Understanding the dynamics of these internal gravity waves is critical for weather forecasting and climate models. In the atmosphere, the 'wave drag' of air moving across hills and mountains provides a significant momentum transfer. In the ocean, the breaking of internal waves provides an important contribution to the mixing within the ocean that ultimately provides a strong feedback on our climate.
While much is known about internal gravity waves, our knowledge is far from complete. Issues such as wave breaking, how the waves interact with complex topography and the influence of time-varying mean flows are vital but poorly understood. A PhD in this area would utilise a combination of analytical theory, numerical modelling and laboratory experiments to advance our knowledge and help us discover some of the missing ingredients responsible for mixing in the ocean.
Internal wave reflection of lee waves from positive shear in a stratified flow.
For further information, contact Stuart Dalziel.
3. Marine snow
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A typical biological structure |
The goal of this study is to predict the terminal velocity of small biological particles as they fall through the ocean - so called 'marine snow'. The ocean is stratified and as these particles fall they drag buoyant fluid down with them in their wake thereby reducing their terminal velocity. These particles are small enough that they move at low Reynolds number and are porous so that fluid can flow through them as well as around them.
The study will begin with the simpler problem of a solid sphere falling through a stably stratified fluid. There is a problem of fundamental fluid dynamics interest here. In the frame of reference moving with the sphere, surfaces of constant density approach and must pass around the sphere. At the stagnation point at the bottom of the sphere these density surfaces accumulate and diffusion must play a key role in avoiding a singularity in density. The first part of the project will be to study the diffusion boundary layer near the front of the sphere and its influence, if any, on the wake structure behind the sphere. In the second phase of the work, the descent of a porous sphere will be examined, first by having discrete holes in the solid sphere and then a more general porous body.
Laboratory experiments will be conducted to measure the flow around the sphere and the distortion of the density field including any internal waves that are generated. A theoretical model based on Stokes flow round a sphere will be developed in the limit of small diffusivity (large Schmidt number) where the diffusion boundary layer is thin compared to the radius of the sphere.
For further information, contact Paul Linden.
4. Cloud physics
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The Asian 'brown cloud'. |
Atmospheric dust particles are vital for cloud formation and precipitation. Historically, the particles were all of a natural origin, although in recent years particles have been introduced intentionally to 'seed' clouds and artificially trigger rain fall. The biggest change, however, has come about because of pollution. Indeed, it is feared that the 'brown cloud' of pollution that has formed in the rapidly developing Asian region is fundamentally changing the patterns of rainfall, not only in Asia, but globally.
This project concerns the transport of particles, from both natural and artificial sources, and how they can penetrate through the density stratification within the atmosphere to promote the droplet formation. Fundamentally, this is a problem of Lagrangian transport of particles by inhomogeneous turbulence in a density stratification, and how this couples with chemical kinetics and droplet formation. The project would involve laboratory experiments of a simplified situation along with novel numerical treatments to couple statistics of the turbulence with the related transport of particles and subsequent interactions that lead to droplet formation.
For further information, contact Stuart Dalziel.
Environmental Fluid Dynamics
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The New York Times building in Manhattan |
1. Advanced low-energy buildings
Buildings are responsible for about 40% of electricity use in Europe and contribute to approximately 30% of greenhouse gas emissions. Research over the past 20 years has led the design and construction of advanced low-energy buildings, which use novel ventilation technologies and which interact with the external environment to maintain comfortable internal conditions. This raises many fluid dynamical challenges to provide a comfortable internal environment in the face of fluctuating external conditions.
Laboratory experiments coupled with simplified models that provide predictions of the ventilation flows and the internal temperatures have proved to be very successful in suggesting new designs and optimal operations of existing buildings. However, many issues remain and possible projects include
the design and operation of
'mixed-mode' buildings with a component of mechanical ventilation
the interaction of internal
components such as chilled ceilings with the ventilation flow
time-dependent behaviour
associated with changing internal demands
the transport of pollutants
through complex building geometries
the properties of very tall
buildings.
For further information, contact Paul Linden or Colm Caulfield.
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Avalanche debris from Val Prada |
2. Snow Avalanches
Snow avalanches are geophysical flows that pose a significant threat to life in alpine areas – around 150 people are killed in the Alps every winter. To assess the risk of avalanches models are necessary that can accurately predict shallow granular flows in complicated topography that includes obstacles. Field data is very sparse, unrepeatable and hard to obtain so laboratory experiments are necessary to develop and validate models. One particular effect that is poorly understood is channelling. If an avalanche is laterally confined is may dramatically increase the runout distance causing more damage to buildings. The goal of this project is to quantify the effects of channelling of a granular flow on its velocity and power. The project will combine laboratory experiments on channelled granular with the development of models and comparison with field data from natural avalanches.
For further information contact Nathalie Vriend or Stuart Dalziel.
3. Resuspension
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Resuspension by a vortex ring colliding with a bed of particles. |
Many natural and industrial flows carry particles in suspension, altering the bulk density and momentum transfer in sometimes counter-intuitive ways. If the particles are denser than the fluid then there is the possibility that they will settle onto a boundary, but the flow may also be able to raise them from the boundary into suspension. Indeed, this 'resuspension' process is the main source of suspended particles in most natural flows. Despite the importance of resuspension, we know relatively little about the interaction of even simple flows with the porous, mobile boundary a layer of particles represents. How important is the flow within the boundary? What role is played by distinct topographic and surface features? These are amongst the simpler issues that would be addressed in a project on this subject.
For further information, contact Stuart Dalziel.
4. Melting snow
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Layers of dust deposited in |
The Himalayas have been referred to as the 'Third Pole' and the glaciers on the Tibetan plateau provide water to over 1 billion people. These glaciers, along with others in the Alps, the Andes and Antarctica are retreating at an alarming rate. In other areas of the world, e.g. the Sierra Nevadas in California, the snow pack is diminishing steadily with large impacts on agriculture and water supplies.
There are two main contributors to this process - rising temperatures associated with climate change and changing albedo resulting from black carbon from air pollution depositing on the snow allowing for more solar radiation to be absorbed. The relative importance of these two effects is unknown -- or even if they are additive or the combination leads to nonlinear effects. In order to predict the behaviour of the snowpacks in these critical regions it is necessary to understand how the melting is influenced by temperature and albedo.
Experiments will be carried out in the 'cold room' in the laboratory and will investigate the melting process in detail in particularly the interactions between pollutant deposition, the crystal structure and temperature.
For further information, contact Paul Linden.
Fundamental Processes
Publications
Colm Caulfield (Google Scholar or here)
Stuart Dalziel (Google Scholar or here)
Paul Linden (Google Scholar)
Nathalie Vriend (Google Scholar or here)