Against this background, results obtained in the two research stream are as follows:
Extreme waves:
- Models for the interactions between waves and currents with constant vorticity have been derived in detail based on variational and Hamiltonian analysis, including a description of how a variational, finite-element potential-flow wavetank can be extended to include constant-vorticity currents in a two-dimensional vertical plane.
- A numerical wavetank has been (re)defined based on discretising the relevant Luke's variational principle (VP) in space and time.
- Coordinate transformations and dynamic mesh motions have been explored since these lead to an implementational innovation with potential high gains in computational efficiency, of which the main exploration is reported elsewhere (in the other subproject).
- A series of benchmark problems has been investigated, including various improvements, with enhanced performance, to the numerical formulation and its associated code.
- New test cases concerning short-crested waves have been defined in detail, which includes a novel analysis of exact solutions of the Kadomtsev-Petviashvilli (KP) equation; such exact solutions have defined the initial conditions for simulations within the numerical potential-flow wavetank. These finings were published in two publications in the journal Water Waves.
- A robust wavebreaking parameterisation based on diffusivity has been analysed; it has led to a preliminary investigation of a potentially new alternative based on augmented Hamiltonian dynamics. In addition, we have refined coupled potential-flow and shallow-water model, the latter at the beach where wavebreaking is occurring.
Wave-Turbine Impact:
- With reference to wave-impact on a wind-turbine mast modelled as a hyperelastic beam, the theoretical and numerical formulation of the coupled dynamics of water waves and beam motion have been investigated using variational principles (VPs). Due to the complexities involved, and for didactic training purposes, the methodology has been developed by considering a hierarchy of increasingly-complex dynamical problems, as follows.
- The VP of the nonlinear hyperelastic beam was investigated in separation, including some preliminary numerical tests.
-A first theoretical formulation, based on the relevant VP, was made of the coupled dynamics.
- A digression was made investigating the generation of water waves by a waveflap. Its numerical formulation requires a coordinate transformation and its discretisation is related to that for the coupled wave-beam problem. It results in a final time-discrete VP directly of use for a numerical discretisation. This was published in a first refereed (OMAE) conference proceeding.
- Full theoretical and numerical formulations are considered of the coupled problem, again using VPs, in which various computational-grid-transformation strategies are explored.
- Novel FSI experiments were designed and performed at MARIn. Results were presented in a second, refereed OMAE proceeding, on GitHub as well as a larger archived report.
- Using bespoke MARIN software, first validation of the nbew data set were made, for which a conference paper has been submitted to the ASME conference.
The above haw culminated in the delivery and validation, to MARIN and maritime-engineering consulting, of numerical wavetanks and new datasets for advanced computer modelling of extreme waves at sea and wave-impact on offshore wind-turbine masts. all tools have been made available in public repositories, to attract academic attention and usage in related research sectors.
