GK BATCHELOR LABORATORY
Potential PhD Projects 2015

 

Geophysical Fluid Dynamics

Environmental Fluid Dynamics

Fundamental Processes

Other

Publications

 

This page outlines some (but not all) of the potential PhD projects on offer (starting 2015) from the following

Colm Caulfield (H.0.10): webpage at BPI and webpage at DAMTP,

Stuart Dalziel (H.0.11): webpage at DAMTP,

Paul Linden (H.1.18): webpage at DAMTP,

Nathalie Vriend (H.0.12): webpage at DAMTP,

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. Dynamics of downdrafts and their role in monsoon rainfall patterns

Colliding gravity currents producing updrafts to
initiate convection.

Under the impacts of climate change, variations in rainfall intensities and patterns associated with monsoons can cause huge human, agricultural, ecological and economic costs. The West African Monsoon in 2012 caused the third largest food crisis to hit the region of Niger, Chad, Senegal, and Nigeria in the last seven years, while in 2013, there was severe flooding.

 

Rainfall in these systems is associated with strong convective storms that create descending columns of cold air and rain. These downdrafts interact with the ground and then spread out horizontally as pools of cold air, often colliding with neighbouring pools to produce strong vertical motions on impact. These motions, in turn, can trigger further convective activity and rainfall. This cycle of events thus determines the spatio-temporal distribution of the rainfall patterns, as well as creating severe winds and storms at low levels.

 

The dynamics include the role of nonlinear waves such as bores or solitons resulting from collisions, radiation of energy to internal waves, leading to the development of a statistical description of rainfall patterns and the relation to large-scale atmospheric conditions. The student will carry out laboratory experiments on the various components of the flow to determine the main physical processes that control the generation of secondary convection and rainfall patterns and intensities. These experiments will be interpreted in terms of mathematical models of simplified representations of the physics and then extrapolated to the meteorological context.

Tomographic reconstruction of density fields from a
laboratory experiment where a sphere is oscillated off-axis
in a paraboloidal container. (a) Ray tracing showing
expected location of wave energy after first few reflections.
(b) The expected location after many reflections.

 

This is a NERC Earth System Science DTP project, more information about deadlines can be found on the webpage.

 

For further information, contact Paul Linden.

 

 

2. Focusing internal and inertial waves

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 degrees 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.

 

For further information, contact Stuart Dalziel.

 

 

Environmental Fluid Dynamics

1. The dynamics of layered stratified shear flows

Density (left) and perturbation vorticity (right)
in a layered plane Couette flow subject to the so-called
`Taylor instability' of layered stratified shear flows.

 

Statically stable stratification is ubiquitous in the environment. There is also commonly vertical shear in the prevalent velocity distribution, and so there has been a large amount of research investigation into the dynamics of stratified shear flows.

 

Recently however, there has been an accumulation of evidence pointing to the conclusion that such flows generically develop into `layers', i.e. relatively deep regions of weak density gradient separated by relatively thin `interfaces' of strong density gradient. Surprisingly, although such layered flows were the first stability problem considered by G. I. Taylor, their nonlinear dynamics and mixing properties are very poorly understood, and new numerical tools are finally making it possible to investigate the dynamics of layered stratified shear flows in environmentally relevant parameter ranges.

 

For further information, contact Colm Caulfield.

 

 

2. Advanced low-energy buildings

 

The New York Times building in Manhattan
designed by Renzo Piano and opened in 2008
uses underfloor air conditioning.

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.

 

We use laboratory experiments coupled with simplified models to provide predictions of the ventilation flows and the internal temperatures. These models have proved to be very successful in suggesting new designs and optimal operations of existing buildings.

 

Recently, as part of a Leverhulme Programme Grant on `Natural Material Innovation for Sustainable Living', we are investigating the potential of natural materials for building construction and performance. This interdisciplinary project involves the departments of Architecture, Chemistry, Biochemistry, and Plant Sciences and the performance of natural materials relevant to ventilation will be an active area of research. More information about the project can be found on the project webpage.

 

Note that this project is sponsored by our industrial partner ARUP with an available studentship EPSRC iCASE on `Airflow modelling for atria and other tall spaces'.

 

For further information, contact Paul Linden.

 

 

3. Focus on the particle: segregation in monolayer avalanches

Avalanche debris from Val Prada
demonstrating the formation of lateral levees.

 

Granular segregation is the separation of grains with different size or density due to a variety of physical processes. In the natural environment, segregation results in enhanced avalanche mobility and needs to be considered in assessing risks to communities and infrastructure. In these natural avalanches, larger particles rise to the surface, and consequently move to the front and the side of the flow, while smaller particles sink to the bottom.

 

This project aims to obtain a thorough understanding of the essence of granular segregation in avalanches employing optical techniques and photoelasticity. Recent experiments cannot measure the internal structure of a flow; channel side-walls influence the flow dynamics and the complicated 3D structure in free-flowing avalanches is not captured by imaging the top surface only. The physics influencing individual grains during segregation is difficult to probe and instead average properties are measured. This project investigates the grain-grain interaction directly using a segregating bimodal layer of cylinders in a narrow avalanching channel.

 

The student will design a monolayer experiment where a thin layer of bimodal disks avalanche down a narrow channel of one particle thickness. As the wall effects cancel out, a uniform flow in 2D exists which allows imaging through the side walls. With advanced experimentation, including particle tracking for position, rotation and velocity and photoelasticity for resultant forces, the precise grain-grain interaction during segregation will be investigated in great detail. Consecutively, the student will model the interactions of this system in a discrete element code using the particle interaction forces measured in the experiment.

 

This is a NERC Earth System Science DTP project, more information about deadlines can be found on the webpage.

 

For further information, contact Nathalie Vriend.

 

 

4. Plumes from complex sources

Buoyant plume in which
the buoyancy flux has
been decreased impulsively.

 

While much is now known about the behaviour of buoyant plumes, the vast majority of studies have been from relatively simple point, line or area sources, often steady but occasionally multi-phase. This project will look at a hierarchy of problems where the source conditions are more complex, reflecting aspects occurring in plumes in both environmental and man-made contexts. For example, if the source continually switches between plumes and fountains, respectively), then what is the character of the resulting flow? Other potential problems include exploring ideas on how to contain a plume to limit the entrainment, and the interaction of a plume with either other flows or structures. The project will tackle a range of such problems using a combination of analytical theory, numerical simulation and laboratory experiments.

 

For further information, contact Stuart Dalziel.

 

 

5. Stratified Taylor-Couette Flow

Spatio-temporal shadowgraph showing
quasi-periodic mixing structures in
turbulent stratified Taylor-Couette flow.

 

As part of an EPSRC Programme grant on the 'Mathematical Underpinnings of Stratified Turbulence (MUST) in collaboration with the School of Mathematics at Bristol University we are studying the fundamental dynamics of turbulent mixing in fluids with statically stable density distributions. A particularly convenient flow for studying such mixing is the flow of a stratified fluid in the annular gap between two vertical cylinders rotating at different rotation rates, i.e (stratified) Taylor-Couette flow. The presence of a vertical stratification modifies in complex, and still incompletely understood ways the classical unstratified Taylor-Couette problem, which itself has a rich history dating back to the pioneering work of G. I. Taylor and Maurice Couette. Recently, we have demonstrated that such flows spontaneously form layers, with the dominant mixing across the dividing interfaces being driven by a quasi-periodic, though still imperfectly characterized mixing mechanism.

 

The proposed project will aim to explore the properties of this mixing mechanism in detail, and specifically to understand its onset and subsequent nonlinear dynamics. This largely experimental project will have access to state-of-the-art 3D particle image velocimetry, planar laser induced florescence for concentration measurements and other forms of image processing.

 

The experiments are fully integrated into a broader computational and theoretical activity and offer the student an opportunity to work within a large team involved in the MUST project. More information can be found at the MUST webpage.

 

For further information, contact Colm Caulfield.

 

 

The formation of granular fingering on a
rough base.

Fundamental Processes

1. Instabilities in granular flows

 

Geophysical mass flows are large movements of snow, mud or rocks down steep mountains. Varying topography and the 3D structure of the flow create a complicated interplay between internal friction and segregation, resulting in a mobile and volatile mass flow obtaining much higher velocities and impact pressures than otherwise expected. The effect of basal friction on flow instabilities, e.g. granular fingering and roll waves, is poorly understood.

 

This project aims to obtain a thorough understanding of the influence of the basal surface on the onset and development of instabilities such as a fingering and roll waves in granular flows. Careful initial experimentation on the release of a mass of particles down an incline show a variety of outcomes mimicking processes observed in nature. The fundamental understanding of the instabilities mechanisms in a moving mass and the influence of the composition of particles and the basal surface on a released volume will be the focus of this project.

 

The student will conduct granular experiments on an incline under specific, fine-tuned conditions. A release of a volume of particles can initiate the fingering instability for certain basal and mixture conditions. A continuous release of particles can reveal the roll wave instability and create surges in the flow. A central but unquantified parameter is the influence of the base. The project aims to measure wavelengths, wavenumbers and amplitudes and to advance a mathematical model to explain the onset and development of these granular instabilities.

 

This is a NERC Earth System Science DTP project, more information about deadlines can be found on the webpage.

 

For further information, contact Nathalie Vriend.

 

 

Optimal initial vorticity distributions (top) and final
concentration distributions (bottom) which maximize mixing
in a plane channel flow.

2. Variational approaches to generalised stability theory

 

A central problem in fluid dynamics is the consideration of whether a particular flow is `stable', or whether perturbations to this base flow can grow strongly, making it highly unlikely that the base flow will be observed in practice. A relatively new method, called the `Direct-Adjoint-Looping' (DAL) method is revolutionizing this field of stability theory, as it allows the consideration of fully nonlinear problems, where the growing perturbation feeds back and modifies the underlying base flow. The DAL method, which is still being developed, and for which there are several important outstanding mathematical issues which need to be resolved, has opened a range of new and exciting research avenues.

 

For example, we have been able to identify the initial perturbation that can optimally mix a passive scalar, and to identify control strategies that can guarantee the prevention of the onset of turbulence. There is a wide range of opportunities for students who are interested in using numerical simulation and optimization tools to solve problems of fundamental, environmental and industrial significance to make substantial contributions.

 

For further information, contact Colm Caulfield.

 

 

3. Effect of Surface Roughness and Hydraulic Jumps in Fast Granular Flows

Froude number regimes and hydraulic jump on the
recirculating granular chute with varying roughness.

 

The recirculating granular chute is an unique piece of machinery that moves large quantities (Q = 20 kg/s) of granular material down an 2.5 m incline at high speeds (V = 6 m/s). In preliminary experiments (Holyoake & McElwaine 2012) the surface of the chute consisted of either a smooth acrylic base or a rough, homogeneous base plate made from coarse-grained sandpaper. Further work (Caplan, Dalziel and Vriend) investigated the behavior of a fast flow on a rough base around an obstacle, creating shock waves and expansion fans. Little work exists in literature, however, to study the effect of surface roughness, or changes therein. Surfaces with constant roughness are the exception rather than the rule, whether considering granular flows in natural or industrial contexts. Indeed, changes in roughness may often occur over small length scales and so it is important to understand the response of the flow to both abrupt and gradual changes.

 

Experiments are proposed where the roughness of the base in the chute changes either abruptly or continuously along the length. The significant change in roughness has the possibility of inducing the granular equivalent of a hydraulic jump where the flow changes from supercritical to subcritical. A well-known analogy between hydraulics and gas-dynamics exists and a limited amount of work has been conducted to look at hydraulic jumps in granular flows. The structure of the hydraulic jump in granular flows, however, reveals that properties of the underlying dynamics vary significantly from shocks in gas flows, and these differences provide a new opportunity explore the effective rheology of granular materials and the complex dynamics of how they behave.

 

The project will involve both mathematical modeling and laboratory experiments, with scope for supporting numerical simulations of these granular flows. The experiments will include granular flows across a variety of bases with varying roughness, initially on a chute with low flow rates, but progressing to the recirculating chute. By triggering hydraulic jumps at different speeds, relationships between the depth profile of the jump, roughness changes and velocity will be investigated. By reversing the base from rough to smooth, the distance over which steady-state is reached reveals important rheological information.

 

For further information, contact Nathalie Vriend or Stuart Dalziel.

 

 

Other

1. Extracting mathematical structure using data assimilation of laboratory experiments

Simultaneous measurement of 3D velocity
(vectors in-plane, colour out-of-plane) and
density (contours) in Rayleigh-Taylor instability.

 

The term `data assimilation' describes a range of techniques where scattered observations are `assimilated' into numerical models to match the conditions within the simulations to the observations. This technique is widely used in weather forecasting where it is important that the observations and the predictions generated by the forecast models bear at least some relationship with each other. However, it is a technique that also has a role to play in scientific research. In particular, the interplay between laboratory experiments and numerical simulations has the potential to be enhanced greatly with the development of suitable data assimilation tools.

 

At a superficial level, data assimilation could be viewed as simply providing a more effective method of interpolating experimental data, but the real power in coupling the experiments with the numerics come from our ability to use the numerics to probe the sensitivity of the solutions, to project the solution to other points in the parameter regime, and to explore the mathematical structure of experimentally realized flows in a manner that is hitherto impossible. Indeed, the idea of data assimilation itself can be extended to incorporate information spanning control parameters as well as space and time.

 

This combined experimental and numerical project will begin by adapting existing data assimilation strategies to utilise experimental data in corresponding direct numerical simulations (DNS), and then extend this approach to build a more complete picture of the mathematical structure underlying the flows.

 

For further information, contact Stuart Dalziel or John Taylor.

 

 

2. How to fly a canoe: unsteady hydrodynamics near a free surface

 

A canoe paddle must provide stability as well as motive power.

Unsteady aerodynamics and hydrodynamics is of considerable interest to understand the locomotion of flying and swimming animals. Increasingly, it is also of interest in the pursuit of building flying and swimming `robots' for a variety of uses. Most of the existing research, however, has focused on the mechanisms at play within a homogeneous fluid. There are contexts, however, where the surface providing the lift and/or drag used for propulsion crosses between the air and the water.

 

Rowing and kayaking are good examples of craft propelled in this way. In both cases it is predominantly the drag force on the blade as it is pulled through the water that drives the craft forwards, and the blade then `disappears' through the free surface before reappearing to take another stroke. With a canoe propelled by a single blade (or for more advanced kayak paddle strokes), the picture is more complex as lift as well as drag forces on the blade are utilised to keep the craft moving in the required direction. The dynamics of paddling are affected not only by what the blade is doing now, but also by the history of the motion of the blade and the disturbances it has made in the water. This project would explore the unsteady hydrodynamics using a variety of experimental, theoretical and possibly numerical tools.

 

For further information, contact Stuart Dalziel.

 

 

Publications

Colm Caulfield (Google Scholar or here)

Stuart Dalziel (Google Scholar or here)

Paul Linden (here)

Nathalie Vriend (Google Scholar or here)