A Particle-based Approach for Stochastic Modelling of Waves in the Near-shore Region

Processes occurring in the near-shore region operates on a small spatial and temporal scale. Simulations of these processes have long posed challenges for computational science, and to have accurate representations require a higher resolution. This results in computationally expensive models. This project aimed to investigate the possibility of a new stochastic model, simulate these processes with higher computational efficiency, and estimate the energy density and spectral properties of waves in the near-shore region. The gist of the particle model is to discretize the energy flux into several packets of finite energy, propagating in the domain, and governed by the equations derived from the wave dynamics. These particles correspond to a particular wave component at a particular location and, therefore, are defined by these wave properties. The equations of particle motion are derived from the wave dynamics by treating energy density as probability density and the energy balance equation as a Fokker-Planck equation while the energy dissipation is modelled with exponential decay of particle energy with a location-dependent rate. An iterative approach is taken to accommodate the dissipation processes resulting from the wave interactions. These particles were treated as independent to create prospects of asynchronous computation and providing the scope of computational optimization. The phenomena of shoaling, refraction, bottom friction, and depth-induced surf breaking are included in the implementation for both monochromatic waves and irregular waves described by a two-dimensional wave spectrum. The model is tested for its performance and accuracy by comparing with the estimations from other existing models. The ability to provide control over processes in computations made SWAN a perfect candidate as a benchmark. The results showed a high degree of accuracy on comparison while the computational time was of the same order or lower to that of the SWAN model for most of the cases with a great scope of improvement. It was also observed that high computational efficiency could be achieved by sacrificing little accuracy. Additional dominant processes were identified affecting the accuracy in certain conditions by comparing the model with lab measurement data. Non-linear wave-wave interactions play an important role in the evolution of the spectrum, while diffraction becomes dominant for the flow over a shoal in two-dimension. These processes are considered as future scope of the project. The results show that with a stochastic model, it is possible to simulate real-life situations and does need further development to include additional processes and make the model computationally robust.Applied Mathematic