Model Skill and Sensitivity for Simulating Wave Processes on Coral Reefs Using a Shock-Capturing Green-Naghdi Solver

Abstract

Wave flume data from published benchmark experiments were used to extensively evaluate numerical model skill and sensitivity for applying a shock-capturing Green-Naghdi (GN) model to simulate nonlinear wave transformation processes on complex coral reefs. Boussinesq-type models that utilise nonlinear shallow water equations (NSWEs) to represent wave breaking and dissipation hold significant potential for understanding coastal hazards associated with global environmental change and sealevel rise. These fully nonlinear phase-resolving models typically require a threshold condition to switch from dispersive equations to shock-capturing NSWEs in areas of active wave breaking. However, limited information exits regarding how this splitting approach influences the behaviour of different surf-zone processes that contribute to wave runup and inundation on coral reefs. This paper presents a comprehensive analysis of model sensitivity to explore how input parameters that control wave breaking and dissipation influence the behaviour of sea-swell (SS) waves, infragravity (IG) waves, wave setup, runup and solitary waves on coral reefs. Results show that each wave process exhibits unique sensitivity to the free-surface slope threshold (B) that is used to represent areas of active wave breaking by locally switching from the weakly-dispersive GN equations to the shock-capturing NSWEs. However, accurate representation of all wave processes can be achieved if the wave-face steepens to at least 35 degrees (B ≥ 0.7) before breaking is initiated. Results from this research support and encourage the use of nonlinear phase-resolving wave models as tools for academic research, coastal management, coastal engineering and hazard forecasting on atoll and fringing reef environments.

Predicting wave overtopping thresholds on coral reef-island shorelines with future sea-level rise

“…Previous attempts to understand the physical drivers of future wave overtopping on reef coastlines focus on single case study islands 8 , 17 , 24 , 25 that are not globally applicable, neglect overtopping magnitudes 26 or use simplified hydrodynamic models that do not resolve nonlinear surf-zone processes 17 , 27 , 28 . Our research advances previous work by applying a comprehensively evaluated physics-based numerical model 20 , 29 to directly simulate wave overtopping motions resulting from incident wave dissipation and nonlinear surf-zone processes. Our approach builds on previous studies that utilised a wide range of idealised bathymetries and wave conditions to investigate the impacts of SLR on reef coastlines 26 – 28 , 30 .…”

“…A shock-capturing nonlinear shallow water solution is applied in areas of wave breaking and runup to ensure areas of rapid dissipation are handled with stability and accuracy 34 , 35 . The phase-resolving model we apply here has been comprehensively evaluated for accurately simulating wave dissipation, infragravity wave behaviour, wave setup, runup and overtopping on coral reef environments, using field data 20 and wave flume 29 experiments. The documented open-source model is available online 36 , with existing literature providing more information on the numerical scheme 34 and its application to simulate waves on coral reefs 20 , 25 .…”

Coastal flooding and mean sea-level rise allowances in atoll island

“…Our work builds upon prior hydrodynamic modelling studies using non-hydrostatic models such as Basilisk or Swash that have demonstrated the capacity to capture wave dynamics in coral reefs 21 , 30 – 32 , including validation with field observations 33 . Given a fixed reef morphology and offshore swells, the wave setup during swell events is projected to decrease for higher mean sea-levels according to simulations, which is consistent with observations showing that the wave setup is lower at high tides than at low-tides 34 , 35 .…”

Coastal flooding and mean sea-level rise allowances in atoll island

“…The application of the method to other coral reef atolls in different regions is straightforward, simple and fast, allowing to anticipate the concomitant impacts of mean sea-level rise and waves and to assist broad-scale coastal management. Our work builds upon prior hydrodynamic modelling studies using non-hydrostatic models such as Basilisk or Swash that have demonstrated the capacity to capture wave dynamics in coral reefs 21,[30][31][32] , including validation with field observations 33 . Given a fixed reef morphology and offshore swells, the wave setup during swell events is projected to decrease for higher mean sea-levels according to simulations, which is consistent with observations showing that the wave setup is lower at high tides than at low-tides 34,35 .…”