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E305: A Dune Roundabout: Undulations and Bedforms in a 1D Annulus: (Lead Supervisor: Nathalie Vriend, Department of Mathematics and Theoretical Physics)

*Please note this project is fully funded by Schlumberger Gould Research, Cambridge*

Supervisors: Nathalie Vriend (DAMTP), and Sean Lovett (Schlumberger Gould Research, Cambridge)

Importance of the area of research:

Mobile sediment transport influences flooding thresholds, coastal boundaries and shipping lines with major environmental and economic consequences. After the 2011 Japan earthquake, tsunamis dramatically changed the seafloor in Japan's coastal areas, forming new underwater dunes and influencing the marine ecosystem. Mouths of major rivers or tidal currents through narrow orifices---such as the Golden Gate Bridge strait---can create underwater sand waves as well and change drastically over short times. Oilfield applications of bedform dynamics include the cross-flow past subsea pipelines or tiebacks, and particle bed flow in pipes or annuli.

Although their prominence in our natural world is known, there are many open questions related to the mathematical modelling and physical description of these bedforms of different size and shape. What happens if these bedforms encounter obstacles (e.g. pipes) on a seabed? This project aims to thoroughly investigate the structure and migration of underwater bedforms.

Project summary:

What is the effect of external forcing (river inflows, tidal cycles and storms) or obstacles on the morphology, structure and migration speed of underwater bedforms? In this project the student investigates the formation and migration of underwater one-dimensional bedforms in a novel experimental set-up at DAMTP and, potentially, in a meso-scale industrial flow loop at Schlumberger Gould Research in Cambridge. Due to the continuous interaction with the water and air phase, the bedforms evolve their shape, height and wavelength depending on external influences. Experiments and modelling aim to determine the physical behaviour of evolving annular bedforms.

What the student will do:

The student will use a novel thin annular Taylor-Couette geometry on a turn-table to create a 1D aqueous periodic system. First, the long-term behaviour of bedform evolution is investigated with different initial conditions. Next, the forcing on the system will be varied, with a continuously increasing velocity, step-size increases or out-of-phase alternating velocities (mimicking tidal flow). Thirdly, an array of objects of different orientation, size and submersion will be inserted in the channel to study aspects of coastal/beach erosion and design optimisation. Is it possible to design a structure that stabilises a seabed or guarantees its cleaning?

The mathematical component of this work includes the construction of a model for initiation and selection of waveforms in a 1D circular and periodic geometry. Furthermore, a mathematical analysis of the long-term, steady behaviour should include both a stability analysis for the initiation phase and mass and momentum conservation arguments for the interaction between neighbouring bedforms.

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.


Barnard, P. L., Hanes, D.M., Rubin D.M. & Kvitek R.G., 2006. Giant sand waves at the mouth of San Francisco Bay. Eos Transactions of the American Geophysical Union, vol. 87, pp.285,289.

Ashley, G.M., 1990. Classification of large-scale subaqueous bedforms: a new look at an old problem. J Sed Petr, vol 60, pp.160-172.

Betat, A., Kruelle, C.A., Frette, V., Rehberg, I. 2002. Long-time behaviour of sand ripples induced by water shear flow, Eur Phys J E Soft Matter, vol 8, pp.465-476.

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