An assessment of the roller approach for wave breaking in a hybrid finite-volume finite-difference Boussinesq-type model for the surf-zone

This paper investigates the application of the roller approach for breaking waves in a 10 hybrid finite volume finite-difference weakly-nonlinear Boussinesq-type model. The vorticity transport equation is employed to model the movement of vorticity through the fluid. This allows vertical profiles of horizontal velocity and undertow to be computed. Previous implementations of this method caused numerical dissipation that influenced the physical behaviour of the breaking process. The use of a hybrid scheme overcomes this issue as the need to filter flow variables in the surf-zone is removed. Greater numerical stability increases the flexibility of the calibration parameters, allowing finer control over the breaking process and a more detailed investigation of the underlying physics. The mechanism used to dissipate energy during breaking is derived from physical principles and the Boussinesq equations are retained throughout the breaking procedure, providing a realistic description of the hydrodynamics throughout the surf-zone. The dissipative performance of the proposed model is discussed and compared with other state-of-the-art approaches, proving the feasibility and value of using a rotational roller model with a finite-volume finite-difference scheme to model surf-zone hydrodynamics with a Boussinesqtype model. Tests involving waves breaking on a sloping beach are performed to validate against results from physical experiments, demonstrating the model to be capable of accurately resolving profiles of the free surface, velocity and undertow. The resulting new model overcomes many of the issues encountered by previous Boussinesq solvers based on the same approach and provides significant improvements in the accuracy of predictions of breaking wave processes. The proposed approach is very flexible and can be used in any hybrid finite-volume finite-difference weakly-nonlinear Boussinesq-type model. (C) 2018 Elsevier Ltd. All rights reserved.