Narrow Results

The nonlinear shallow water equations and Boussinesq equations have been widely used for analyzing the solitary wave runup phenomenon. In order to quantitatively assess the merits and limitations of these two approaches, a shock-capturing scheme has been applied to numerically solve both sets of equations for predicting the runup processes over plane beaches. The analytical and experimental data available in the literature have been used as references in the assessment. In this study, the uniform sloping beach is preceded by a length of flat seafloor. When incident solitary waves are specified close to the slope, the two approaches are found to produce almost identical results for nonbreaking waves. For breaking waves, the Boussinesq equations give a better representation of the wave evolution prior to the breaking point, whereas they overestimate the short undulations accompanying the breaking process. If incoming solitary waves need to travel a long distance over a flat bed before reaching the slope, the shallow water equations cannot capture the correct waveform transformation, and the predicted runup depends heavily on the length of the flat-bed section. As this length approaches zero, however, the shallow water equations somehow give roughly the same maximum runup heights as those predicted by the Boussinesq model. The bed friction has little effect on the runup for small waves, but becomes important for large waves. The roughness coefficient needs to be calibrated to reproduce the measured runup heights of breaking waves.

A methodology combining the offshore tsunami calculated by using numerical reciprocal Green's function (RGF) and the runup flow field calculated by using an analytical Green's function (AGF) is proposed to quickly estimate a tsunami hazard.

For a vulnerable city, the RGF is computed previously via linear shallow water equations over real bathymetry and the offshore tsunami can be obtained promptly once the initial rupture is known. A transformation from time to space is then applied to obtain an equivalent waveform. With an integral with the AGF, derived by Carrier et al. [2003] based on 1D fully nonlinear shallow water equations over a uniform constant slope, the runup flow field is calculated. Thus, besides saving computation time and reducing the memory requirement, the desired initial condition for the AGF can also be generate by RGF. In this approach, the max wave height and the inundation distance are estimated very quickly and can be applied to broadcast an early warning of tsunami.

To verify the method, data obtained during the 2004 Indian Ocean Tsunami from Sri Lanka and Phuket, Thailand is applied. The offshore condition is first verified by comparing with the record at Maldives. The accuracy of RGF is also tested. Then, by taking the nearshore shelf slope as the constant bottom slope for the analytical solution, the max tsunami height agrees reasonably well with the in-situ measurement. Therefore, this method is a useful tool for tsunami early warning by quickly estimating if the max wave height is higher than the seawall or the breakwater. The max inundation distance calculated by the analytic integral solution also has reasonable agreement with the field survey, but the value from the in-situ investigation scatters widely, which suggests that the detailed local topography plays an important role. A different method for the determination of the bottom slope is also tested and the result shows that the slope should be based on the bathymetry nearshore.

The characteristics of flow fields for a complete evolution of the non-breaking solitary wave, having a wave-height to water-depth ratio of 0.363 and propagating over a 1:5 sloping bottom, are investigated experimentally. This study mainly focuses on the occurrences of both flow separation on the boundary layer under an adverse pressure gradient and subsequent hydraulic jump with the abrupt rising of free surface during rundown motion of the shoaling wave, together with emphasis on the evolution of vortex structures underlying the separated shear layer and hydraulic jump. A flow visualization technique with particle trajectory method and a high-speed particle image velocimetry (HSPIV) system with a high-speed digital camera were used. Based on the instantaneous flow images visualized and/or the ensemble-averaged velocity fields measured, the following interesting features, which are unknown up-to-date, are presented and discussed in this study: (1) Flow bifurcation occurring on both offshore and onshore sides of the explicit demarcation curve and the stagnation point during runup motion; (2) The dependence of the diffuser-like flow field, being changed from the supercritical flow in the shallower region to the subcritical flow in the deeper counterpart, on the Froude number during the early and middle stages of rundown motion; (3) The positions and times for the occurrences of the incipient flow separation and the sudden rising of free surface of the hydraulic jump; (4) The associated movement and evolution of vortex structures under the separated shear layer, the hydraulic jump and/or the high-speed external main stream of the retreated flow; and (5) The entrainment of air bubbles from the free surface into the external main stream of the retreated flow.

Understanding the runup and inundation of long waves on coasts is of great importance for coastal community as flooding hazards are closely related to safety issues. For many years, solitary and solitary-like waves are frequently considered as a surrogate of extremely long waves for estimating runup and inundation. Since scaling issues are of concern when extending to real-world conditions, large-scale experiments for solitary waves on uniform beaches are reviewed and additional experiments for solitary waves on composite slopes are performed in this study. As such, those experimental data obtained from large-scale physical modeling can be used to validate numerical models and then to extend the range of parameters in terms of wave conditions and slope geometries which cannot be straightforwardly achieved in large-scale experimental works. Considering the computational efficiency, an open-source non-hydrostatic wave-flow model SWASH is used herein. Detailed model-data comparisons in terms of free surface elevation time series and maximum runup heights are carried out for long waves running up and down on beaches with different slope gradients to ensure the accuracy of the SWASH model for such applications. Finally, a simple method for estimating maximum shoreline excursion for solitary waves on a particularly designed composite slope is provided.