This article describes a one-dimensional numerical model of a shallow-water flume with an in-built piston paddle moving boundary wavemaker. The model is based on a set of enhanced Boussinesq equations and the nonlinear shallow water equations. Wave breaking is described approximately, by locally switching to the nonlinear shallow water equations when a critical wave steepness is reached. The moving shoreline is calculated as part of the solution. The piston paddle wavemaker operates on a movable grid, which is Lagrangian on the paddle face and Eulerian away from the paddle. The governing equations are, however, evolved on a fixed mapped grid, and the newly calculated solution is transformed back onto the moving grid via a domain mapping technique. Validation test results are compared against analytical solutions, confirming correct discretisation of the governing equations, wave generation via the numerical paddle, and movement of the wet/dry front. Simulations are presented that reproduce laboratory experiments of wave runup on a plane beach and wave overtopping of a laboratory seawall, involving solitary waves and compact wave groups. In practice, the numerical model is suitable for simulating the propagation of weakly dispersive waves and can additionally model any associated inundation, overtopping or inland flooding within the same simulation.

Wave loading on marine structures is the major external force to be considered in the design of such structures. The accurate prediction of the nonlinear high-order components of the wave loading has been an unresolved challenging problem. In this paper, the nonlinear harmonic components of hydrodynamic forces on a bottom-mounted vertical cylinder are investigated experimentally. A large number of experiments were conducted in the Danish Hydraulic Institute shallow water wave basin on the cylinder, both on a flat bed and a sloping bed, as part of a European collaborative research project. High-quality data sets for focused wave groups have been collected for a wide range of wave conditions. The high-order harmonic force components are separated by applying the 'phase-inversion' method to the measured force time histories for a crest focused wave group and the same wave group inverted. This separation method is found to work well even for locally violent nearly-breaking waves formed from bidirectional wave pairs. It is also found that the nth-harmonic force scales with the nth power of the envelope of both the linear undisturbed free-surface elevation and the linear force component in both time variation and amplitude. This allows estimation of the higher-order harmonic shapes and time histories from knowledge of the linear component alone. The experiments also show that the harmonic structure of the wave loading on the cylinder is virtually unaltered by the introduction of a sloping bed, depending only on the local wave properties at the cylinder. Furthermore, our new experimental results reveal that for certain wave cases the linear loading is actually less than 40 % of the total wave loading and the † Email addresses for correspondence: lifen.chen@uwa.edu.au, chenlifen239@163.com, J.Zang@bath.ac.uk Nonlinear forces on a column 43 high-order harmonics contribute more than 60 % of the loading. The significance of this striking new result is that it reveals the importance of high-order nonlinear wave loading on offshore structures and means that such loading should be considered in their design.

Insight is provided into focused wave group runup on a plane beach by means of laboratory wave flume experiments and numerical simulations. A focused wave group is presented as an alternative to an empirical description of the wave conditions leading to extreme runup. Secondorder correction to the laboratory wavemaker generation signal is observed to remove about 60% of the sub-harmonic error wave that would otherwise contaminate coastal response experiments. Laboratory measurements of the wave runup time history are obtained using inclined resistancetype wires and copper strips attached to the beach surface. The numerical wave runup model is based on hybrid Boussinesq-Nonlinear Shallow Water equations, empirical parameters for wave breaking and bed friction, and a wetting and drying algorithm. After calibration against experimental runup data, the numerical model reproduces satisfactorily the propagation, shoaling and runup of focused wave groups over the entire length of the wave flume. Results from a comprehensive parametric study show that both measured and predicted maximum runup elevations exhibit strong dependence on the linear focus amplitude of the wave group (linked to its probability of occurrence), the focus location, and the phase of the wave group at focus. The results also demonstrate that extreme runup events owing to focused wave incidence cannot be characterised using spectral parameters alone. The optimal band of focus locations shifts onshore as linear focus amplitude of the incident wave group increases. Optimisation of phase and focus location leads to a maximum runup elevation at each linear amplitude, and, when generated using second-order corrected paddle signals, the maximum runup appears to approach saturation

Focused wave groups offer a means for coastal engineers to determine extreme run-up and overtopping events. Numerical predictions and laboratory measurements are presented for NewWave-type focused wave groups generated by a piston-type paddle generator, and interacting with a plane beach and a seawall in a wave basin. The numerical wave tank is based on the Boussinesq equations for non-breaking waves, and the non-linear shallow water equations for broken waves. Good agreement is achieved between the numerical predictions and laboratory measurements of free surface elevation, run-up distances and overtopping volumes for the test cases driven by linear paddle signals. Errors in run-up distance and overtopping volume are then assessed by repeating the test cases using second-order accurate wave generation signals. Focused wave groups generated using first-order wave-maker theory are found to be substantially contaminated by a preceding long error wave, resulting in erroneously enhanced run-up distances and overtopping volumes. Thus, the use of secondorder wave-maker theory for wave group run-up and overtopping experiments is instead recommended.

Wave energy converters and other offshore structures may exhibit instability, in which one mode of motion is excited parametrically by motion in another. Here, theoretical results for the transverse motion instability (large sway oscillations perpendicular to the incident wave direction) of a submerged wave energy converter buoy are compared to an extensive experimental dataset. The device is axi-symmetric (resembling a truncated vertical cylinder) and is taut-moored via a single tether. The system is approximately a damped elastic pendulum. Assuming linear hydrodynamics, but retaining nonlinear tether geometry, governing equations are derived in six degrees of freedom. The natural frequencies in surge/sway (the pendulum frequency), heave (the springing motion frequency) and pitch/roll are derived from the linearized equations. When terms of second order in the buoy motions are retained, the sway equation can be written as a Mathieu equation. Careful analysis of 80 regular wave tests reveals a good agreement with the predictions of sub-harmonic (period-doubling) sway instability using the Mathieu equation stability diagram. As wave energy converters operate in real seas, a large number of irregular wave runs is also analysed. The measurements broadly agree with a criterion (derived elsewhere) for determining the presence of the instability in irregular waves, which depends on the level of damping and the amount of parametric excitation at twice the natural frequency.