This is a study of the runup of solitary waves on plane beaches. An approximate theory is presented for non-breaking waves and an asymptotic result is derived for the maximum runup of solitary waves. A series of laboratory experiments is described to support the theory. It is shown that the linear theory predicts the maximum runup satisfactorily, and that the nonlinear theory describes the climb of solitary waves equally well. Different runup regimes are found to exist for the runup of breaking and non-breaking waves. A breaking criterion is derived for determining whether a solitary wave will break as it climbs up a sloping beach, and a different criterion is shown to apply for determining whether a wave will break during rundown. These results are used to explain some of the existing empirical runup relationships.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S002211208700329X

The runup of solitary waves

A numerical solution for the 2 + 1 (long-shore and onshore propagation directions and time) nonlinear shallow-water wave equations, without friction factors or artificial viscosity is presented. The models use a splitting method to generate two 1 + 1 propagation problems, one in the onshore and the other in long-shore direction. Both are solved in characteristic form using the method of characteristics. A shoreline algorithm is implemented, which is the generalization of the earlier 1 + 1 algorithm used in the code VTCS-2. The model is validated using large-scale laboratory data from solitary wave experiments attacking a conical island. The method is applied then to model the 1993 Okushiri, Japan, the 1994 Kuril Island, Russia, and the 1996 Chimbote, Peru tsunamis. It is found that the model can reproduce correctly overland flow and even extreme events such as the 30-m runup and the 20-m/s inundation velocities inferred during field surveys. The results suggest that bathymetric and topographic resolution ...

Numerical Modeling of Tidal Wave Runup

Landslide generated impulse waves were investigated in a two-dimensional physical laboratory model based on the generalized Froude similarity. The recorded wave profiles were extremely unsteady and nonlinear. Four wave types were determined: weakly nonlinear oscillatory wave, non-linear transition wave, solitary-like wave and dissipative transient bore. Most of the generated impulse waves were located in the intermediate water depth wave regime. Nevertheless the propagation velocity of the leading wave crest closely followed the theoretical approximations for a solitary wave. Between 4 and 50% of the kinetic slide impact energy propagated outward in the impulse wave train. The applicability ranges of the classical nonlinear wave theories to landslide generated impulse waves were determined. The main wave characteristics were related to the landslide parameters driving the entire wave generation process. The slide Froude number was identified as the dominant parameter. The physical model results were compared to the giant rockslide generated impulse wave which struck the shores of the Lituya Bay, Alaska, in 1958.

Near Field Characteristics of Landslide Generated Impulse Waves

This paper describes the formulation, verification, and validation of a depth-integrated, non-hydrostatic model with a semi-implicit, finite difference scheme. The formulation builds on the nonlinear shallow-water equations and utilizes a non-hydrostatic pressure term to describe weakly dispersive waves. A momentum-conserved advection scheme enables modeling of breaking waves without the aid of analytical solutions for bore approximation or empirical equations for energy dissipation. An upwind scheme extrapolates the free-surface elevation instead of the flow depth to provide the flux in the momentum and continuity equations. This greatly improves the model stability, which is essential for computation of energetic breaking waves and run-up. The computed results show very good agreement with laboratory data for wave propagation, transformation, breaking, and run-up. Since the numerical scheme to the momentum and continuity equations remains explicit, the implicit non-hydrostatic solution is directly applicable to existing nonlinear shallow-water models. Copyright © 2008 John Wiley & Sons, Ltd.

Depth‐integrated, non‐hydrostatic model for wave breaking and run‐up

Tsunami science has evolved differently from research on other extreme natural hazards, primarily because of the unavailability until recently of instrumental recordings of tsunamis in the open ocean. Here, the progress towards developing tsunami inundation modelling tools for use in inundation forecasting is discussed historically from the perspective of hydrodynamics. The state-of-knowledge before the 26 December 2004 tsunami is described. Remaining aspects for future research are identified. One, validated inundation models need to be further developed through benchmark testing and instrumental tsunameter measurements and standards for operational codes need to be established. Two, a methodology is needed to better quantify short-duration impact forces on structures. Three, the mapping of vulnerable continental margins to identify unrecognized hazards must proceed expeditiously, along with palaeotsunami research to establish repeat intervals. Four, the development of better coupling between deforming seafloor motions and model initialization needs further refinement. Five, in an era of global citizenship, more comprehensive educational efforts on tsunami hazard mitigation are necessary worldwide.

Tsunami science before and beyond Boxing Day 2004

/pdf/laboratory-investigation-of-the-vertical-rise-of-solitary-32nenoyxif.pdf

Jay V. Hall

Papers

Laboratory investigation of the vertical rise of solitary waves on impermeable slopes

Beach Rehabilitation by Fill and Nourishment