Study of irregular wave run-up over fringing reefs based on a shock-capturing Boussinesq model

This paper presents the results of a parametric study of irregular wave run-up over fringing reefs using the shock-capturing Boussinesq wave model Funwave-TVD to better understand the role of fringing reefs in the mitigation of wave-driven flooding. Laboratory experiments were newly performed with a typical fringing reef profile and typical hydrodynamic conditions to validate the model. Experimental data shows irregular wave run-ups are dominated by the low-frequency motions and confirms the run-up resonant phenomenon over the back-reef slope, which has been revealed in previous numerical studies. It is demonstrated that irregular wave evolution and run-up over fringing reefs are reasonably reproduced by the present model with a proper grid size. However, the infragravity run-up height and highest 2% run-up height over the back-reef slope are under-predicted due to the underestimation of the infragravity wave height over the reef flat. The validated model was then utilized to model irregular wave transformations and run-ups under different conditions. Through a series of numerical experiments, the effects of key hydrodynamic and reef geometry parameters, including the reef flat width, water depth over the reef flat, fore-reef slope angle and back-reef slope angle, on the irregular wave run-up were investigated. Variations of spectral components of irregular wave run-ups were examined to better understand the physical process underlying the effect of each parameter.     

Flow fields in reflected waves at a sloped sea wall

Wave run-up, and flow visualization experiments were conducted with a 1:2 sloped sea wall model. The visualization experiments gave an overview of flow fields in reflected, non-breaking conditions. Maximum particle velocities were found to be significantly smaller than suggested in the literature. Downrush produced a fast sheet flow, extending down to the toe of the sea wall. This created a ‘reverse’ breaker during the retreat of the initially non-breaking wave, which explains the high-energy dissipation rates for non-breaking waves reported in the literature. Embankments may therefore be exposed to wave impact pressures in areas up to 1.18H₀ below MWL.     

Boussinesq-type modelling using an unstructured finite element technique

A model for solving the two-dimensional enhanced Boussinesq equations is presented. The model equations are discretised in space using an unstructured finite element technique. The standard Galerkin method with mixed interpolation is applied. The time discretisation is performed using an explicit three-step Taylor–Galerkin method. The model is extended to the surf and swash zone by inclusion of wave breaking and a moving boundary at the shoreline. Breaking is treated by an existing surface roller model, but a new procedure for the detection of the roller thickness is devised. The model is verified using four test cases and the results are compared with experimental data and results from an existing finite difference Boussinesq model.     

Reconstructing tsunami run-up from the characteristics of tsunami deposits on the Thai Andaman Coast

Tsunamis can leave deposits on the land surface they inundate. The characteristics of tsunami deposits can be used to calculate tsunami run-up height and velocity. This paper presents a reconstruction of tsunami run-up from tsunami deposit characteristics in a simple mathematical model. The model is modified and applied to reconstruct tsunami run-ups at Ao Kheuy beach and Khuk Khak beach, Phangnga province, Thailand. The input parameters are grain-size and maximum run-up distance of the sediment. The reconstructed run-up heights are 4.16–4.91 m at Ao Kheuy beach and 5.43–9.46 m at Khuk Khak beach. The estimated run-up velocities (maximum velocity) at the still water level are 12.78–19.21 m/s. In the area located 70–140 m inland to the end of run-up inundation, estimated mean run-up velocities decrease from approximately 1.93 m/s to 0 m/s. Reasonably good agreements are found between reconstructed and observed run-up heights. The tsunami run-up height and velocity can be used for risk assessment and coastal development programs in the tsunami affected area. The results show that the area from 0 to 140 m inland was flooded by high velocity run-ups and those run-up energies were dissipated mainly in this area. The area should be designated as either an area where settlement is not permitted or an area where effective protection is provided, for example with flood barriers or forest.     

Sumatra tsunami: lessons from modeling

The need for the combination of seismic data with real-time wave height information for an effective prediction of tsunami impact is emphasized in the paper. A preliminary, but comprehensive study of arrival times, wave heights and run-up values at a number of locations and tide gage stations throughout the Indian Ocean seaboard is presented. Open ocean wave height data from satellite observations are analyzed and used in the reconstruction of a tsunami source mechanism for the December 26, 2004 event. The reconstructed source is then used to numerically estimate tsunami impact along the Indian Ocean seaboard, including wave height, and arrival times at 12 tide gage stations, and inundation at 3 locations on the coast of India. The December 2004, as well as the March 28, 2005 tsunamis are investigated and their differences in terms of tsunami generation are analyzed and presented as a clear example of the need for both, seismic and real-time tsunami data for a reliable tsunami warning system in the Indian Ocean.     

Tsunami deposits in the geological record

A review is presented here of tsunami deposits in the geological record. It begins with a discussion of the relationships between the processes of tsunami generation and propagation and the sedimentary responses. This is followed by a consideration of the sedimentary processes associated with the passage of tsunami waves across coastlines. Attention is also given to the sedimentary processes associated with tsunami-triggered gravity backwash flows and comparisons are made with turbidity current action. We observe that despite sedimentary evidence for recent tsunamiites, geological research on ancient tsunamis has not identified stratigraphic units associated with onshore tsunami sedimentation. Equally, it is noted that nearly all published studies of sedimentary processes associated with modern tsunamis have not considered patterns of sediment transport and deposition in the offshore zone.     

Tsunami generation,propagation, and run-up with a high-order Boussinesq model

In this work we extend a high-order Boussinesq-type (finite difference) model, capable of simulating waves out to wavenumber times depth kh < 25, to include a moving sea-bed, for the simulation of earthquake- and landslide-induced tsunamis. The extension is straight forward, requiring only an additional term within the kinematic bottom condition. As first test cases we simulate linear and nonlinear surface waves generated from both positive and negative impulsive bottom movements. The computed results compare well against earlier theoretical, numerical, and experimental values. Additionally, we show that the long-time (fully nonlinear) evolution of waves resulting from an upthrusted bottom can eventually result in true solitary waves, consistent with theoretical predictions. It is stressed, however, that the nonlinearity used far exceeds that typical of geophysical tsunamis in the open ocean. The Boussinesq-type model is then used to simulate numerous tsunami-type events generated from submerged landslides, in both one and two horizontal dimensions. The results again compare well against previous experiments and/or numerical simulations. The new extension compliments recently developed run-up capabilities within this approach, and as demonstrated, the model can therefore treat tsunami events from their initial generation, through their later propagation, and final run-up phases. The developed model is shown to maintain reasonable computational efficiency, and is therefore attractive for the simulation of such events, especially in cases where dispersion is important.     

Simulation of nonlinear wave run-up with a high-order Boussinesq model

This paper considers the numerical simulation of nonlinear wave run-up within a highly accurate Boussinesq-type model. Moving wet–dry boundary algorithms based on so-called extrapolating boundary techniques are utilized, and a new variant of this approach is proposed in two horizontal dimensions. As validation, computed results involving the nonlinear run-up of periodic as well as transient waves on a sloping beach are considered in a single horizontal dimension, demonstrating excellent agreement with analytical solutions for both the free surface and horizontal velocity. In two horizontal dimensions cases involving long wave resonance in a parabolic basin, solitary wave evolution in a triangular channel, and solitary wave run-up on a circular conical island are considered. In each case the computed results compare well against available analytical solutions or experimental measurements. The ability to accurately simulate a moving wet–dry boundary is of considerable practical importance within coastal engineering, and the extension described in this work significantly improves the nearshore versatility of the present high-order Boussinesq approach.     

Modelling of run up of steep non-breaking waves

A Navier–Stokes solver is used to examine steep waves as they run up a steep beach (10.54°). The volume of fluid method (VOF) is used to model the free surface. Comparison with experimental results shows reasonable overall agreement in the prediction of the free-surface, velocities and accelerations within the flow. A spurious feature at the free-surface was found which does reduce the quality of the results. For a steep wave we see the transition from a steep wave front to a smooth run-up tongue at the beach that is in qualitative agreement with experiment.     

Propagation and run-up of nearshore tsunamis with HLLC approximate Riemann solver

A numerical model describing the propagation and run-up process of nearshore tsunamis in the vicinity of shorelines is developed based on an approximate Riemann solver. The governing equations of the model are the nonlinear shallow-water equations. The governing equations are discretized explicitly by using a finite volume method. The nonlinear terms in the momentum equations are solved with the Harten-Lax-van Leer-Contact (HLLC) approximate Riemann solver. The developed model is first applied to prediction of water motions in a parabolic basin, and propagation and subsequent run-up process of nearshore tsunamis around a circular island. Computed results are then compared with available analytical solutions and laboratory measurements. Very reasonable agreements are observed.