A Hydrodynamics Perspective for the 2004 Megatsunami

The megatsunami of 26 December 2004 was the first tsunami with transoceanic impact since the 1960 Great Chilean and 1964 Great Alaskan tsunamis. Because of the distribution of deaths among a large portion of the nations of the world, the 2004 Boxing Day tsunami is the first universal natural disaster of modern times. For the purpose of adequate mitigation of future tsunamis, it is important to understand which factors control most critically the final characteristics of the flooding, namely runup and inundation. Their successful modeling requires not only a credible database of inundation parameters, against which models can be tested through numerical simulation of the generation, propagation to the local shores, and final interaction of the tsunami with the target beaches, but also in situ observations that help identify unusual impact and previously unrecognized or controversial flow patterns. Here, I comment on the hydrodynamic lessons -mostly relearned- and describe remaining challenges

The runup of long waves

This is a study of the fundamental physical processes of the runup of long waves with the objective to understand some coastal effects of tsunamis. The runup of nonbreaking long waves on plane beaches is studied and an exact solution is developed for the runup of solitary waves. The maximum runup predicted by this solution is compared to laboratory data from this and other investigations and it is found to be in good agreement. A runup transducer was developed and deployed in the laboratory to provide data for the shape of the runup tongue. The exact solution is shown to model the details of the climb of the wave satisfactorily. The runup of breaking long waves on plane beaches is investigated in the laboratory by studying different long waves and bores of [mite volume. The runup is shown to be a function of a momentum scale determined from the generation characteristics of the incoming wave. The runup number is introduced and it is demonstrated that it models the runup process adequately. It is also observed that arbitrary long waves have runup numbers smaller than, or at most equal to, the runup number of breaking solitary waves, suggesting that on a given plane beach breaking solitary waves run-up further than other long waves with similar generation characteristics. An exact result is established for the force on an accelerating plate in a fluid with a free surface. The result is used to explain some of the results of this study and other results on the hydrodynamic forces on moving partitions. A technique is developed to generate arbitrary, long, continuously evolving waves at any desired location in a laboratory model. The technique is applied in the laboratory and it is shown to be successful in reproducing complex waveforms

Runup and rundown generated by three-dimensional sliding masses

To study the waves and runup/rundown generated by a sliding mass, a numerical simulation model, based on the large-eddy-simulation (LES) approach, was developed. The Smagorinsky subgrid scale model was employed to provide turbulence dissipation and the volume of fluid (VOF) method was used to track the free surface and shoreline movements. A numerical algorithm for describing the motion of the sliding mass was also implemented. To validate the numerical model, we conducted a set of large-scale experiments in a wave tank of 104m long, 3.7m wide and 4.6m deep with a plane slope (1:2) located at one end of the tank. A freely sliding wedge with two orientations and a hemisphere were used to represent landslides. Their initial positions ranged from totally aerial to fully submerged, and the slide mass was also varied over a wide range. The slides were instrumented to provide position and velocity time histories. The time-histories of water surface and the runup at a number of locations were measured. Comparisons between the numerical results and experimental data are presented only for wedge shape slides. Very good agreement is shown for the time histories of runup and generated waves. The detailed three-dimensional complex flow patterns, free surface and shoreline deformations are further illustrated by the numerical results. The maximum runup heights are presented as a function of the initial elevation and the specific weight of the slide. The effects of the wave tank width on the maximum runup are also discussed

A modified Galerkin/finite element method for the numerical solution of the Serre-Green-Naghdi system

A new modified Galerkin / Finite Element Method is proposed for the numerical solution of the fully nonlinear shallow water wave equations. The new numerical method allows the use of low-order Lagrange finite element spaces, despite the fact that the system contains third order spatial partial derivatives for the depth averaged velocity of the fluid. After studying the efficacy and the conservation properties of the new numerical method, we proceed with the validation of the new numerical model and boundary conditions by comparing the numerical solutions with laboratory experiments and with available theoretical asymptotic results

Influence of sedimentary layering on tsunami generation

The present article is devoted to the influence of sediment layers on the process of tsunami generation. The main scope here is to demonstrate and especially quantify the effect of sedimentation on vertical displacements of the seabed due to an underwater earthquake. The fault is modelled as a Volterra-type dislocation in an elastic half-space. The elastodynamics equations are integrated with a finite element method. A comparison between two cases is performed. The first one corresponds to the classical situation of an elastic homogeneous and isotropic half-space, which is traditionally used for the generation of tsunamis. The second test case takes into account the presence of a sediment layer separating the oceanic column from the hard rock. Some important differences are revealed. We conjecture that deformations in the generation region may be amplified by sedimentary deposits, at least for some parameter values. The mechanism of amplification is studied through careful numerical simulations.Comment: 17 pages, 12 figures. Revised version for Computer Methods in Applied Mechanics and Engineering. Other author's papers can be downloaded from http://www.lama.univ-savoie.fr/~dutykh

Late Holocene uplift of Rhodes, Greece: evidence for a large tsunamigenic earthquake and the implications for the tectonics of the eastern Hellenic Trench System

Several large earthquakes in the Hellenic subduction zone have been documented in historical records from around the eastern Mediterranean, but the relative seismic quiescence of the region over the period of instrumental observation means that the exact locations of these earthquakes and their tectonic significance are not known. We present AMS radiocarbon dates from uplifted late Holocene palaeoshorelines from the island of Rhodes, showing that uplift is most consistent with a single large (MW ≥ 7:7) reverse-faulting earthquake between about 2000 BC and 200 BC. Analysis of the uplift treating the earthquake as a dislocation in an elastic half space shows a predominantly a reverse-faulting event with a slip vector oblique to the direction of convergence between Rhodes and Nubia. We suggest that the fault responsible for the uplift dips at an angle of 30-60° above the more gently-dipping oblique subduction interface. The highly oblique convergence across the eastern Hellenic plate boundary zone appears to be partitioned into reverse slip on faults that strike parallel to the boundary and strike-parallel or oblique slip on the subduction interface. Hydrodynamical simulation of tsunami propagation from a range of tectonically plausible sources suggests that earthquakes on the fault uplifting Rhodes represent a significant tsunami hazard for Rhodes and SW Turkey, and also possibly for Cyprus and the Nile Delta.AH is supported by a Shell Studentship. This study forms part of the NERC- and ESRC-funded project "Earthquakes Without Frontiers".This is the final version of the article. It first appeared from Oxford University Press via http://dx.doi.org/10.1093/gji/ggv30

Tsunami generation by dynamic displacement of sea bed due to dip-slip faulting

In classical tsunami-generation techniques, one neglects the dynamic sea bed displacement resulting from fracturing of a seismic fault. The present study takes into account these dynamic effects. Earth's crust is assumed to be a Kelvin-Voigt material. The seismic source is assumed to be a dislocation in a viscoelastic medium. The fluid motion is described by the classical nonlinear shallow water equations (NSWE) with time-dependent bathymetry. The viscoelastodynamic equations are solved by a finite-element method and the NSWE by a finite-volume scheme. A comparison between static and dynamic tsunami-generation approaches is performed. The results of the numerical computations show differences between the two approaches and the dynamic effects could explain the complicated shapes of tsunami wave trains.Comment: 16 pages, 10 figures, Accepted to Mathematics and Computers in Simulation. Other author's papers can be downloaded at http://www.cmla.ens-cachan.fr/~dutyk

Late Holocene uplift of Rhodes, Greece: evidence for a large tsunamigenic earthquake and the implications for the tectonics of the eastern Hellenic Trench System

Several large earthquakes in the Hellenic subduction zone have been documented in historical records from around the eastern Mediterranean, but the relative seismic quiescence of the region over the period of instrumental observation means that the exact locations of these earthquakes and their tectonic significance are not known. We present AMS radiocarbon dates from uplifted late Holocene palæoshorelines from the island of Rhodes, showing that uplift is most consistent with a single large (MW ≥ 7.7) reverse-faulting earthquake between about 2000 BC and 200 BC. Analysis of the uplift treating the earthquake as a dislocation in an elastic half-space shows a predominantly reverse-faulting event with a slip vector oblique to the direction of convergence between Rhodes and Nubia. We suggest that the fault responsible for the uplift dips at an angle of 30–60° above the more gently dipping oblique subduction interface. The highly oblique convergence across the eastern Hellenic plate boundary zone appears to be partitioned into reverse slip on faults that strike parallel to the boundary and strike-parallel or oblique slip on the subduction interface. Hydrodynamical simulation of tsunami propagation from a range of tectonically plausible sources suggests that earthquakes on the fault uplifting Rhodes represent a significant tsunami hazard for Rhodes and SW Turkey, and also possibly for Cyprus and the Nile Delta

Practical use of variational principles for modeling water waves

This paper describes a method for deriving approximate equations for irrotational water waves. The method is based on a 'relaxed' variational principle, i.e., on a Lagrangian involving as many variables as possible. This formulation is particularly suitable for the construction of approximate water wave models, since it allows more freedom while preserving the variational structure. The advantages of this relaxed formulation are illustrated with various examples in shallow and deep waters, as well as arbitrary depths. Using subordinate constraints (e.g., irrotationality or free surface impermeability) in various combinations, several model equations are derived, some being well-known, other being new. The models obtained are studied analytically and exact travelling wave solutions are constructed when possible.Comment: 30 pages, 1 figure, 62 references. Other author's papers can be downloaded at http://www.denys-dutykh.com

Finite volume schemes for dispersive wave propagation and runup

Finite volume schemes are commonly used to construct approximate solutions to conservation laws. In this study we extend the framework of the finite volume methods to dispersive water wave models, in particular to Boussinesq type systems. We focus mainly on the application of the method to bidirectional nonlinear, dispersive wave propagation in one space dimension. Special emphasis is given to important nonlinear phenomena such as solitary waves interactions, dispersive shock wave formation and the runup of breaking and non-breaking long waves.Comment: 41 pafes, 20 figures. Other author's papers can be downloaded at http://www.lama.univ-savoie.fr/~dutykh