Benchmark Modelling of Breaking 1D Waves and Dynamic Shingle Beaches Prof. Onno Bokhove (School of Maths), Prof. Jeff Peakall (School of Earth & Environment)

Full details with project descriptions - and how to apply at: http://www.maths.leeds.ac.uk/postgraduate-research.html

Benchmark Modelling of Breaking 1D Waves and Dynamic Shingle Beaches with Prof. Onno Bokhove (SoM), Prof. Jeff Peakall (SEE)
Contact email: [Email Address Removed]

The proposed research concerns modelling of beach evolution due to breaking waves. Mathematical and numerical modelling of particle transport (morpho-dynamics) caused by breaking waves is computationally and theoretically difficult. To inspire new insights, in both laboratory and mathematical modelling proposed, a “slice of beach” is used to squeeze the complexities into a quasi-two-dimensional world. In the laboratory configuration, this slice is placed between two glass plates, to create a so-called Hele-Shaw beach, investigated here for an increasing range of gap widths. It is a three-phase extension of the classical experiment by Hele-Shaw put on its side with an open top, bed particles and a water-air interface. The advantages of this Hele-Shaw set-up are the great visibility of the dynamics, that turbulence has been greatly reduced so one can focus mainly on the issue of wave breaking induced bed transport, and the potential for validation of numerical models. The key characteristic of our Hele-Shaw beach experiment is that particle, wave and water motions can be measured and analysed thoroughly in the entire domain. This allows closure relations for fluid-particle interactions to be measured directly for the development and validation of the mathematical models. A hierarchy of models will be developed and investigated, from depth-averaged to multiphase models, based on these measurements. The Hele-Shaw beaches are most similar to gravel beaches. Hence, we will compare them against profiles of natural shingle beaches, and in large-scale wave tanks such as the one used by Dr. Keith Powell and co-workers at HR Wallingford.

The design of Hele-Shaw beach dynamics is based on asymptotic analysis and on extensive computer simulations of shallow water flows. The proposed laboratory component of the work concerns the accurate measurements of wave and particle motions, in a continuous or heterogeneous manner in space- and time such as to resolve the stress relations for particle entrainment and deposition. The proposed modelling part of the work will involve depth- and/or wave-averaged models as well as multiphase mixture theory for mathematical closures of wave-particle interactions under breaking waves. The holistic but simplified Hele-Shaw beach environment is valuable as it circumvents some of the complexities involved at natural beaches. Finally, the complementary research expertise of Bokhove and Peakall will engender new breakthroughs that could contribute meaningfully to the existing body of knowledge for both coastal and civil engineering.