Two-dimensional horizontal (2DH) Boussinesq modelling of waves at the coast
Item statusRestricted Access
Embargo end date04/07/2019
Judge, Frances Mary
Understanding the behaviour of waves and their interaction with the coast is vital for marine engineers and maritime planners. As sea levels rise due to climate change, low-lying coastal areas and existing sea defences will become increasingly vulnerable to run-up and overtopping by large wave events. Accurate and effcient numerical models are essential tools for the assessment of such events and the impact they have on the coast so that effective coastal protection can be designed. This thesis presents a depth-integrated numerical solver with two horizontal dimensions for modelling waves in the coastal zone from intermediate depth to zero depth. Pre-breaking, the evolution of the water surface is calculated using the enhanced Boussinesq equation set of Madsen and Sorensen (1992). This equation set has improved dispersion characteristics over the classical Boussinesq equations, but with relatively few terms compared to models based on the Navier-Stokes equations, allowing for more effcient numerical modelling while maintaining suffcient accuracy. The equations are discretised using second-order finite differences and solved using the conjugate gradient method with fourth-order Runge-Kutta time stepping. Switching from the Boussinesq equation set to the shallow water equations allows shoaling waves to break, with the broken waves then propagating as bores. The shallow water equations are solved using a finite volume MUSCL-Hancock scheme with an HLLC approximate Riemann solver in order to resolve the behaviour of steep-fronted bores at the shore. The model incorporates a wetting and drying algorithm that models the moving wet/dry front. Waves are generated by a line of independently moving piston paddles, allowing full replication of laboratory experiments. A mapping technique is used in the region of the paddles to map the moving physical domain onto a fixed computational domain to facilitate the solution of the governing equations. Different aspects of the model are verified using standard benchmark tests. The complete model is then validated by comparing the numerical simulation of laboratory experiments with high quality experimental data from the UK Coastal Research Facility (UKCRF). The laboratory experiments simulated include the interaction of regular waves with sinusoidal and tri-cuspate beaches, and the interaction of both uni-directional and multi-directional focused wave groups with a plane beach. It is found that the model provides satisfactory wave phase resolution and reproduces most of the flow features of waves and currents in the shallow nearshore environment.