Fundamentals of nonlinear wave-particle interactions are studied experimentally in a Hele-Shaw configuration with wave breaking and a dynamic bed. To design this configuration, we determine, mathematically, the gap width which allows inertial flows to survive the viscous damping due to the side walls. Damped wave sloshing experiments compared with simulations confirm that width-averaged potential-flow models with linear momen- 2A n t h o n y T h o r n t o n e t a l .tum damping are adequately capturing the large scale nonlinear wave motion. Subsequently, we show that the four types of wave breaking observed at realworld beaches also emerge on Hele-Shaw laboratory beaches, albeit in idealized forms. Finally, an experimental parameter study is undertaken to quantify the formation of quasi-steady beach morphologies due to nonlinear, breaking waves: berm or dune, beach and bar formation are all classified. Our research reveals that the Hele-Shaw beach configuration allows a wealth of experimental and modelling extensions, including benchmarking of forecast models used in the coastal engineering practice, especially for shingle beaches.

We explore extreme nonlinear water-wave amplification in a contraction or, analogously, wave amplification in crossing seas. The latter case can lead to extreme or rogue-wave formation at sea. First, amplification of a solitary-water-wave compound running into a contraction is disseminated experimentally, for small-scale and larger wavetanks. Maximum amplification in our bore-soliton-splash observed is circa tenfold. Subsequently, nonlinear and numerical modelling approaches are developed and validated for amplifying, contracting waves. Amplification phenomena observed have led us to develop a novel wave-energy device with wave amplification in a contraction used to enhance wave-buoy motion and magnetically-induced energy generation. An experimental proof-of-principle shows that our wave-energy device works. Furthermore, we develop a monolithic, mathematical model of wave hydrodynamics, buoy motion and electric power generation by magnetic induction, satisfying one grand variational principle in its conservative limit. Dissipative features, electrical wire resistance and nonlinear LED-loads, are added a posteriori. Preliminary simulations of our simplified (linear) wave-energy model are encouraging. Further highlights discussed are: exact modelling of crossing seas with Kadomtsev-Petviashvili's equation, bore-soliton-splash' relevance to devastating Tohoku tsunami run-up in 2011, nonlinear wave-energy optimisation and a steel-soliton-splash artwork. (Note that this is a non-peer reviewed preprint submitted to EarthArXiv.)

We explore extreme nonlinear water-wave amplification in a contraction or, analogously, wave amplification in crossing seas. The latter case can lead to extreme or rogue-wave formation at sea. First, amplification of a solitary-water-wave compound running into a contraction is disseminated experimentally in a wave tank. Maximum amplification in our bore-soliton-splash observed is circa tenfold. Subsequently, we summarise some nonlinear and numerical modelling approaches, validated for amplifying, contracting waves. These amplification phenomena observed have led us to develop a novel wave-energy device with wave amplification in a contraction used to enhance wave-activated buoy motion and magnetically induced energy generation. An experimental proof-of-principle shows that our wave-energy device works. Most importantly, we develop a novel wave-to-wire mathematical model of the combined wave hydrodynamics, wave-activated buoy motion and electric power generation by magnetic induction, from first principles, satisfying one grand variational principle in its conservative limit. Wave and buoy dynamics are coupled via a Lagrange multiplier, which boundary value at the waterline is in a subtle way solved explicitly by imposing incompressibility in a weak sense. Dissipative features, such as electrical wire resistance and nonlinear LED loads, are added a posteriori. New is also the intricate and compatible finite-element space-time discretisation of the linearised dynamics, guaranteeing numerical stability and the correct energy transfer between the three subsystems. Preliminary simulations of our simplified and linearised wave-energy model are encouraging and involve a first study of the resonant behaviour and parameter dependence of the device.

The primary evolution of beaches by wave action takes place during storms. Beach evolution by non-linear breaking waves is 3D, multi-scale, and involves particle-wave interactions. We will show how a novel, three-phase extension to the classic "Hele-Shaw" laboratory experiment is designed to create beach morphologies with breaking waves in a quasi-2D setting. Idealized beaches emerge in tens of minutes due to several types of breaking waves, with about 1s periods. The thin Hele-Shaw cell simplifies the inherent complexity of three-phase dynamics by reducing the turbulence. Given the interest in the Hele-Shaw table-top demonstrations at ICCE2014, we will also discuss how different versions of the Hele-Shaw cell have been constructed. Construction can be inexpensive thus yielding an accessible and flexible coastal engineering demonstration as well as research tool. Beach evolution is sufficiently fast and can start very far from equilibrium, allowing an unusually large dynamical range to be investigated.

Wetropolis is a transportable "table-top" demonstration model with extreme rainfall and flooding events. It is a conceptual model with random rainfall, river flow, a flood plain, an upland reservoir, a porous moor, representing the upper catchment and visualising groundwater flow, and a city which can flood following extreme rainfall. Its aim is to let the viewer experience extreme rainfall and flood events in a physical model on reduced spatial and temporal scales. In addition, it conveys concepts of flood storage and control, via manual intervention. To guide the building of an operational Wetropolis, we have explored its spatial and temporal dimensions first in a simplified mathematical design. We explain this mathematical model in detail since it was a crucial step in Wetropolis' design and it is of scientific interest from a hydrodynamic modelling perspective. The key novelty is the supply of rainfall every Wetropolis day (unit ${\rm wd}$), variable temporally and spatially in terms of both the amount of rain and the rainfall location. The joint probabilities (rain amount times rain location) are determined daily as one of 16 possible outcomes from two asymmetric Galton boards, in which steel balls fall down every wd, with the most extreme rainfall event involving 90% rainfall on both moor and reservoir. This occurs with a probability of circa 3% and -by design- can cause severe floods in the city. This randomised rainfall has a Wetropolis' return period of 6:06min, short enough to wait for but sufficiently "extreme'' or long to get slightly irritated as a viewer. While Wetropolis should be experienced live, here we provide a photographic overview. To date, Wetropolis has been showcased to over 200 flood victims at workshops and exhibitions on recent UK floods, as well as to flood practitioners and scientists at various workshops. To enhance Wetropolis' reach, we analyse and report here how both the general public and professionals interacted with Wetropolis. We conclude with a discussion on some ongoing design changes, including how people can experience natural flood management in a revised Wetropolis design, before highlighting how the "Wetropolis experience" can stimulate new approaches in hydrological modelling, flood mitigation and control in science, education and water management. (Note that this is non-peer reviewed preprint submitted to EarthArXiv.)