Patrick J. Lynett

A numerical study of submarine-landslide-generated waves and run-up

A mathematical model is derived to describe the generation and propagation of water waves by a submarine landslide. The model consists of a depth–integrated continuity equation and momentum equations, in which the ground movement is the forcing function. These equations include full nonlinear, but weak frequency–dispersion, effects. The model is capable of describing wave propagation from relatively deep water to shallow water. Simplified models for waves generated by small seafloor displacement or creeping ground movement are also presented. A numerical algorithm is developed for the general fully nonlinear model. Comparisons are made with a boundary integral equation method model, and a deep–water limit for the depth–integrated model is determined in terms of a characteristic side length of the submarine mass. The importance of nonlinearity and frequency dispersion in the wave–generation region and on the shoreline movement is discussed.

A two-layer approach to wave modelling

A set of model equations for water–wave propagation is derived by piecewise integration of the primitive equations of motion through two arbitrary layers. Within each layer, an independent velocity profile is derived. With two separate velocity profiles, matched at the interface of the two layers, the resulting set of equations has three free parameters, allowing for an optimization with known analytical properties of water waves. The optimized model equations show good linear wave characteristics up to kh ≈ 6, while the second–order nonlinear behaviour is captured to kh ≈ 6 as well. A numerical algorithm for solving the model equations is developed and tested against one– and two–horizontal–dimension cases. Agreement with laboratory data is excellent.

Modeling of storm-induced coastal flooding for emergency management

This paper describes a model package that simulates coastal flooding resulting from storm surge and waves generated by tropical cyclones. The package consists of four component models implemented at three levels of nested geographic regions, namely, ocean, coastal, and nearshore. The operation is automated through a preprocessor that prepares the computational grids and input atmospheric conditions and manages the data transfer between components. The third generation spectral wave model WAM and a nonlinear long-wave model calculate respectively the wave conditions and storm surge over the ocean region. The simulation results define the water levels and boundary conditions for the model SWAN to transform the storm waves in coastal regions. The storm surge and local tides define the water level in each nearshore region, where a Boussinesq model uses the wave spectra output from SWAN to simulate the surf-zone processes and runup along the coastline. The package is applied to hindcast the coastal flooding caused by Hurricanes Iwa and Iniki, which hit the Hawaiian Island of Kauai in 1982 and 1992, respectively. The model results indicate good agreement with the storm-water levels and overwash debris lines recorded during and after the events, demonstrating the capability of the model package as a forecast tool for emergency management.

Analytical solutions for forced long waves on a sloping beach

∂t 2 for x> 0, in which Y (x, t )d enotes an unknown variable, f (x, t )a prescribed forcing function and b a positive constant. This equation has been used to describe landslide- generated tsunamis and also long waves induced by moving atmospheric pressure distributions. We discuss particular and general solutions. We then compare our results with numerical solutions of the same equation and with the corresponding solutions of the nonlinear depth-integrated equations and discuss them in terms of landslide-generated tsunamis.

A two-dimensional, depth-integrated model for internal wave propagation over variable bathymetry

Based on assumptions of an inviscid fluid and weakly rotational flow, a set of depth-averaged governing equations are developed to model long internal waves in two horizontal dimensions. These waves are assumed to be weakly nonlinear and weakly dispersive, existing in a two-layer system with a small density difference between the layers. No restriction is placed on the bathymetry or the dominant wave propagation direction. A high-order, finite difference numerical algorithm is developed, formally accurate to (�x) 4 in space and (�t) 4 in time. The model is checked with known analytical solutions and experimental data. Real bathymetry case studies are also performed, including simulations of internal waves evolving in the Strait of Gibraltar and near the island of Dongsha in the China Sea. Numerical results show strong similarities to satellite images taken over the same locations.

Sandy signs of a tsunami's onshore depth and speed

Tsunamis rank among the most devastating and unpredictable natural hazards to affect coastal areas. Just 3 years ago, in December 2004, the Indian Ocean tsunami caused more than 225,000 deaths. Like many extreme events, however, destructive tsunamis strike rarely enough that written records span too little time to quantify tsunami hazard and risk. Tsunami deposits preserved in the geologic record have been used to extend the record of tsunami occurrence but not the magnitude of past events. To quantify tsunami hazard further, we asked the following question: Can ancient deposits also provide guidance on the expectable water depths and speeds for future tsunamis?

Seasonal Dynamics of a Microtidal Pocket Beach with Posidonia oceanica Seabeds (Mallorca, Spain)

Abstract In this work, we analyze the seasonal evolution of a Mediterranean pocket beach and its response to different storm episodes. Magalluf, an intermediate medium sand beach located in the Bay of Palma (Balearic Islands) was monitored by topographic levelling during 14 months. Near the beach, a Posidonia oceanica meadow covers most of the seabed and appears to influence the cross-shore beach adjustment. The low variability observed during the sampling period was perturbed by two storm events that caused significant beach evolution and sediment transport. The first storm gave rise to waves from the SE, significant height = 2.4 m, cross-shore sediment transport and along-shore net sediment exchange that resulted in decreased dry beach extension to a minimum. The second storm was characterized by strong northeasterly winds and generated a set-up of 0.5 m and a nearshore drift reversal that redistributed sediment from the berm crest to the beach face, thereby increasing beach extension. Results from numerical simulations of wave propagation show the circulation patterns during both events and their influence on the beach morphology. In general terms, the beach exhibited a homeostatic behaviour characteristic of an equilibrium system.

Assessment of the tsunami‐induced current hazard

The occurrence of tsunami damage is not limited to events causing coastal inundation. Even without flooding, maritime assets are vulnerable to significant damage from strong currents and associated drag forces. While such impacts have been observed in the past, they have not been well studied in any context. Nearshore tsunami currents are governed by nonlinear and turbulent physics and often have large spatial and temporal variability making high-fidelity modeling particularly challenging. Furthermore, measured data for the validation of numerical simulations is limited, with few quality data sets appearing after recent tsunami events. In this paper, we present a systematic approach for the interpretation of measured tsunami-induced current impacts as well as a validation approach for simulation tools. The methods and results provided here lay the foundation for much needed efforts to assess tsunami hazards in ports and harbors.

Turbulent mixing and passive scalar transport in shallow flows

A depth-integrated model including subgrid scale mixing effects for turbulent transport by long waves and currents is presented. A fully nonlinear, depth-integrated set of equations for weakly dispersive and rotational flow is derived by the long wave perturbation approach. The same approach is applied to derive a depth-integrated scalar transport model which can accommodate small vertical variation of a weakly unsteady scalar. The proposed equations are solved by a fourth-order accurate finite volume method. The depth-integrated flow and transport models are applied to typical problems which have different mixing mechanisms. From the simulations, several important conclusions are obtained. (i) From simulation of a mixing layer generated by internal transverse shear, it is revealed that the dispersive stress implemented with a stochastic backscatter model (BSM) can play an important role for energy transfer in a shallow mixing layer. (ii) From a comparison of the characteristic width of a scalar plume in ...

Dispersive and Nonhydrostatic Pressure Effects at the Front of Surge

Undular bores and shocks generated by dam-break flows or tsunamis are examined considering nonhydrostatic pressure and dispersive effects in one- and two-horizontal-dimensional space. The fully nonlinear Boussinesq-type equations based on a weakly nonhydrostatic pressure assumption are chosen as the governing equations. The equation set is solved by a fourth-order accurate finite-volume method with an approximate Riemann solver. Several typical benchmark problems such as dam-break flows and tsunami wave fission are tested in one- and two-horizontal-dimensional space. The computed results by the Boussinesq-type model are at least as accurate as the results by the hydrostatic shallow water equations. This is particularly evident near the steep front of the wave, where frequency dispersion can play an important role. The magnitude of this nonhydrostatic pressure and dispersive effect near the front is quantified, and the engineering implications of neglecting these physics, as would be done through the use of a hydrostatic model, are discussed.