Smoothed particle hydrodynamics (SPH) modelling of nearshore breaking waves.

Abstract

Breaking waves drive sediment transport in the nearshore zone of coastal regions and directly govern beach transformation. Accurate coastal modelling of breaking waves is essential to predict sediment transport accurately. Efficient and sustainable management of natural coastal systems and urban coastal developments relies on accurate sediment transport predictions. This study proposes a mesh-free, Lagrangian, smoothed particle hydrodynamics (SPH) model to simulate nearshore breaking waves in two-dimensions. This study emphasises using SPH to evaluate the wave field parameters (local velocities, vorticities, and shear stresses) that can be used to predict coastal phenomena, namely sediment transport in nearshore, wave-driven environments. This study showed that a two-dimensional SPH model could replicate the free surface of nearshore breaking waves and accurately predict the flow characteristics beneath breaking waves. However, the accuracy of the results can vary depending on the position of the breaking wave in the surf zone. Furthermore, SPH applications must choose between accuracy and computational efficiency. The key SPH calibration parameters identified were the artificial viscosity coefficient (α), the dimensionless smoothing length ratio (hSPH/dp), and the particle resolution (H/dp). Extensive comparative analysis was performed between simulated results and measured data to obtain suitable parameter values for a plunging solitary wave. A suitable choice of α=0.1, hSPH/dp=3, and H/dp=90 were selected based on the results. Furthermore, the results suggested that a suitable choice of model parameters depends on the viscosity treatment method (artificial/sub-particle scale viscosity approach) and the type of wave breaking simulated (plunging/spilling). Thus, α=0.1, hSPH/dp=3, and H/dp=90 were only deemed suitable when the standard SPH artificial viscosity approach is used to simulate breaking plunging and spilling waves on beach slopes milder than 1/10. The model sensitivity to α, hSPH/dp, and H/dp was also investigated based on the numerical wave energy dissipation and simulated wave surface of a plunging solitary wave in the space and time domain. When α was above or below the ideal value of 0.1 for a given hSPH/dp and H/dp, the numerical wave energy dissipation and wave height at breaking did not match the measured data. The choice of α was strongly related to H/dp, and a reduced α became more appropriate for a lower H/dp. The results also showed that the model was less sensitive to hSPH than the choice of α and H/dp in terms of the model performance. However, when hSPH/dp was less than 1, for any given α and H/dp, the numerical wave energy dissipation and wave height at breaking were under-predicted. The choice of H/dp was of principal importance and influenced the choice of the other model parameters. When H/dp was below the ideal value of 90, for any given α and hSPH/dp, the numerical wave energy dissipation and wave height at breaking did not match the measured data. Additionally, the breaking wave shape was poorly simulated. However, H/dp=90 becomes computationally expensive when simulating breaking waves in large numerical domains or with relative wave heights significantly less than 0.6. Hence, the available computing power limits the choice of H/dp. The performance of a two-dimensional SPH model was assessed by analysing the simulated flow field under several breaking waves. The local velocities, vorticities, and bed shear stresses were evaluated beneath two plunging solitary waves and a spilling solitary wave. Generally, the characteristics of the simulated flow field were fairly accurate during wave shoaling and wave breaking, less accurate during wave run-up, and inaccurate during wave run-down. The results also hinted at obliquely descending eddies occurring under the breaking plunging waves. However, the three-dimensional eddy structure beneath the breaking waves could not be investigated due to the limited two-dimensional nature of the model setup used in this study. A well-calibrated SPH wave and hydrodynamic model is an important coastal engineering tool. Thus, this study can serve as a physically based framework for using a two-dimensional SPH model to investigate coastal engineering problems that include wave-structure interactions, wave-run up on beach slopes and sediment transport in the surf zone over a wide range of scales and wave conditions.