skip to content

Cambridge NERC Doctoral Training Partnerships

Graduate Research Opportunities

Supervisor: Peter Haynes (DAMTP)  

Importance of the area of research:

Transport  and mixing by fluid motion is an important aspect of both atmosphere and ocean. The term ‘tracer' is often used to denote a quantity that is transported with the fluid. The distribution of chemical and biological tracers is of great practical interest and also scientific interest, since observations of such tracers provide important constraints on aspects of the circulation that are almost impossible to observe directly. State-of-the-art atmospheric and oceanic models give a highly detailed simulation of flow fields, with strong variation in space and time, and correspondingly a highly detailed prediction of tracer transport. However there is still an important need for measures that provide an overall quantitative description of the transport properties of these flows. (For example, how does one decide whether a simulation of transport from a particular model provides a ‘good' or a ‘bad' representation of reality?) Also there is a need to find simplified models of transport that might be applied to practical problems without the enormous computational cost of a full simulation of the atmospheric or oceanic flow.

Project summary:

The project will examine the use of new mathematical methods for quantifying transport in atmosphere and ocean. The methods can be used to identify regions of space, which may depend on time, for which ‘transport out' or ‘transport in' is relatively infrequent. This can, for example, provide a ‘transition matrix' representation of the overall transport by calculating the rates at which fluid moves from any such region to any other. The specific question to be addressed is how do these new methods, which require calculation of fluid particle trajectories from a specified flow field provided from observational estimates or from a model, relate to those which have been used previously, which require the simulation of a tracer field.  The new methods seem most promising for oceanic flows and these will be the main focus.

What the student will do:

The student will review in detail the tracer-based methods (principally the calculation of ‘effective diffusivity') and the new trajectory-based methods. Theoretical ideas from dynamical systems will be exploited to establish the precise relation between the different methods. Both the principles underlying the methods and the computational resources required to apply them will be of interest. Calculations using the different methods, starting with idealized velocity fields and then moving on to velocity fields from ocean observational data and from ocean models, will be used to evaluate the strengths and weaknesses of the different methods, with particular attention to the computational expense required to provide reliable quantification of the transport properties of different flows. The viability of a  ‘transition matrix' model of oceanic transport, particularly for the Southern Ocean, will be assessed and compared against other simplified models of transport, e.g those based on diffusivities.

Please contact the lead supervisor directly for further information relating to what the successful applicant will be expected to do, training to be provided, and any specific educational background requirements.


Froyland G 2013 An analytic framework for identifying finite-time coherent sets in time-dependent dynamical systems Physica D 250 1-19.

Shuckburgh, E. F., Haynes, P. H., 2003: Diagnosing transport and mixing using a tracer-based coordinate system, Phys. Fluids, 15, 3342-3357.

Froyland, G, Stuart, R.M., and van Sebille, E., 2014: How well-connected is the surface of the global ocean?;Chaos, 24, 033126 (2014); doi: 10.1063/1.4892530

Follow this link to find out about applying for this project.

Other projects available from the Lead Supervisor can be viewed here.

There is currently no content classified with this term.