Costas E. Synolakis

The runup of solitary waves

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.

Runup of solitary waves on a circular island

This is a study of the interactions of solitary waves climbing up a circular island. A series of large-scale laboratory experiments with waves of different incident height-to-depth ratios and different crest lengths is described. Detailed two-dimensional run-up height measurements and time histories of surface elevations around the island are presented. A numerical model based on the two-dimensional shallow-water wave equations including runup calculations was developed. Numerical model predictions agreed very well with the laboratory data and the model was used to study wave trapping and the effect of slope. Under certain conditions, enhanced runup and wave trapping on the lee side of the island were observed, suggesting a possible explanation for the devastation reported by field surveys in Babi Island off Flores, Indonesia, and in Okushiri Island, Japan.

Tsunami: The Underrated Hazard

Tsunami: the Underrated Hazard, by Edward Bryant, would appear to be a welcome addition to the scholarly tsunami literature. No book on tsunamis has the broad perspective of this work. The book looks attractive, with many high-quality photographs. It looks comprehensive, with discussions of tsunami hydrodynamics, tsunami effects on coastal landscapes, and causes of tsunamis (earthquakes, landslides, volcanic eruptions, meteorite impacts). It looks practical, with a section on risk and mitigation. It also looks entertaining, with an opening chapter on tsunami legends and a closing chapter presenting fanciful descriptions of imagined events. Appearances are deceiving, though. Any initial enthusiasm for the work evaporates on even casual reading. The book is so flawed by errors, omissions, confusion, and unsupported conjecture that we cannot recommend it to anyone.

The slump origin of the 1998 Papua New Guinea Tsunami

The origin of the Papua New Guinea tsunami that killed over 2100 people on 17 July 1998 has remained controversial, as dislocation sources based on the parent earthquake fail to model its extreme run–up amplitude. The generation of tsunamis by submarine mass failure had been considered a rare phenomenon which had aroused virtually no attention in terms of tsunami hazard mitigation. We report on recently acquired high–resolution seismic reflection data which yield new images of a large underwater slump, coincident with photographic and bathymetric evidence of the same feature, suspected of having generated the tsunami. T–phase records from an unblocked hydrophone at Wake Island provide new evidence for the timing of the slump. By merging geological data with hydrodynamic modelling, we reproduce the observed tsunami amplitude and timing in a manner consistent with eyewitness accounts. Submarine mass failure is predicted based on fundamental geological and geotechnical information.

Tsunami science before and beyond Boxing Day 2004.

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.

The run-up of N-waves on sloping beaches

Anecdotal reports of tsunamis climbing up coastlines have often described the shoreline receding significantly before the tsunami waves run-up on the beach. These waves are caused by tsunamigenic earthquakes close to the shoreline, when the generated wave does not have sufficient propagation distance to evolve into leading-elevation waves or a series of solitary waves. Yet all previous run-up investigations have modelled periodic waves or solitary waves which initially only run-up on the beach. In our studies of these initially receding shorelines, we have found a class of N-shaped waves with very interesting and counterintuitive behaviour which may lead to a new paradigm for the studies of tsunami run-up. We will use a first-order theory and we will derive asymptotic results for the maximum run-up within the validity of the theory for different types of N-waves. We have observed that leading depression N-waves run-up higher than leading elevation N-waves, suggesting that perhaps the solitary wave model may not be adequate for predicting an upper limit for the run-up of near-shore generated tsunamis.

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 104 m long, 3.7 m wide and 4.6 m 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.

Laboratory experiments of tsunami runup on a circular island

Laboratory experiments of a 7.2-m-diameter conical island were conducted to study three-dimensional tsunami runup. The 62.5-cm tall island had 1 on 4 side slopes and was positioned in the center of a 30-m-wide by 25-m-long flat-bottom basin. Solitary waves with height-to-depth ratios ranging from 0.05 to 0.20 and “source” lengths ranging from 0.30 to 7.14 island diameters were tested in water depths of 32 and 42 cm. Twenty-seven capacitance wave gages were used to measure surface wave elevations at incident and four radial transects on the island slope. Maximum vertical runup measurements were made at 20 locations around the perimeter of the island using rod and transit. A new runup gage was located on the back or lee side of the island to record runup time series.

Extreme inundation flows during the Hokkaido-Nansei-Oki Tsunami

The tsunami generated by the July 12, 1993 Hokkaido-Nansei-Oki Mw=7.8 earthquake produced in Japan the worst local tsunami-related death toll in fifty years, with estimated 10–18m/sec overland flow velocities and 30m runup. These extreme values are the largest recorded in Japan this century and are among the highest ever documented for non-landslide generated tsunamis. We model this event to confirm the estimated overland flow velocities, and we find that, given reasonable ground deformation data, current state-of-the-art shallow-water wave models can predict tsunami inundation correctly including extreme runup, current velocities and overland flow. We find that even small local topographic structures affect the runup to first-order, and that the resolution of the bathymetric data is more important than the grid resolution. Our results qualitatively suggest that—for this event—coastal inundation is more correlated with inundation velocities than with inundation heights, explaining also why threshold-type modeling has substantially underpredicted coastal inundation for this and other recent events.

Long wave runup on piecewise linear topographies

We study long-wave evolution and runup on piecewise linear one- and two-dimensional bathymetries analytically and experimentally with the objective of understanding certain coastal effects of tidal waves. We develop a general solution method for determining the amplification factor of different ocean topographies consisting of linearly varying and constant-depth segments to study how spectral distributions evolve over bathymetry, and apply our results to study the evolution of solitary waves. We find asymptotic results which suggest that solitary waves often interact with piecewise linear topographies in a counter-intuitive manner. We compare our analytical predictions with numerical results, with results from a new set of laboratory experiments from a physical model of Revere Beach, and also with the data on wave runup around an idealized conical island. We find good agreement between our theory and the laboratory results for the time histories of free-surface elevations and for the maximum runup heights. Our results suggest that, at least for simple piecewise linear topographies, analytical methods can be used to calculate effectively some important physical parameters in long-wave runup. Also, by underscoring the effects of the topographic slope at the shoreline, this analysis qualitatively suggests why sometimes predictions of field-applicable numerical models differ substantially from observations of tsunami runup.