SCIENTIFIC PROGRAMS AND ACTIVITIES

September  1, 2014

THE MATHEMATICS OF EXTREME SEA WAVES:
Tsunamis, Rogue Waves, And Flooding

June 13- 16, 2011
Hosted by Fields,
held at Wallberg Building (WB 116),184-200 College Street
University of Toronto

Organizing Committee:
W. Craig, D. Henderson, E. Pelinovsky & C. Sulem

Abstracts

Diego Arcas (NOAA)
Operational Aspects of Tsunami Modeling and Detection

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Onno Bokhove (Twente)
Makings Waves at Beaches

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John Dudley,
FEMTO-ST, Université de Franche Comté
Light on nonlinearity: what optics can reveal about the science of extreme ocean waves

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Denys Dutykh
, Université de Savoie-CNRS
Dispersive and non-dispersive wave runup and some related phenomena

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Isaak Fine
, Institute of Ocean Sciences, BC
The NEPTUNE Canada measurements of approaching tsunamis off the British Columbia coast: an opportunity for regional modelling and forecasting

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Johannes Gemmich
, University of Victoria
Dynamical and statistical explanations of rogue wave occurrence rates

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Diana Greenslade,
Bureau of Meteorology, Melbourne
Operational tsunami forecast and warning

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Christian Kharif
, IRPHE
Extreme sea wave modelling : Application to rogue waves

A series of experiments in deep water conducted in the Large Air-Sea Interactions Facility (LASIF-Marseille, France) showed that wind blowing over a short wave group due to the dispersive focusing of a longer frequency modulated wave train (chirped wave packet) may increase the time duration of the extreme wave event by delaying the defocusing stage. These experi-
ments have pointed out that the transfer of momentum and energy is strongly increased during extreme wave events. Starting from this fact, a series of nu- merical simulations has been performed using a pressure distribution over the steep crests given by the modified Jeffreys’sheltering theory. These numerical simulations corresponding to the dispersive focusing confirms the experimental results. Furthermore, it was shown numerically that during extreme wave events the wind-driven current could play a significant role in their persistence. For more detail see [1]. A similar investigation has been developed in
finite depth ([2]). Similarly to the deep water case, it was found that the wind blowing over a strongly modulated wave group due to the dispersive focusing of an initial long wave packet increases the duration and maximal amplitude of the steep wave event. In addition, steep wave events in shallow water are found to be less unstable to wind perturbation than in deep water. Numerical simulations showed that the wind speeds up the wave breaking and amplifies slightly the wave height.

References
[1] C. Kharif, JP Giovanangeli, J. Touboul, L. Grare \& E. Pelinovsky Influence of wind on extreme wave events : Experimental and numerical approaches J. Fluid Mech., 594 (2008), 209–247
[2] J. Chambarel, C. Kharif and O. Kimmoun, Generation of two-dimensional steep water waves on finite depth with and without wind, Eur. J. Mech. B/Fluids, 29 (2010), 132-142

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Emile Okal
, Northwestern
Tsunamis as normal modes of the Earth, and a venture into extracurricular geophysics

In a series of seminal papers, Ward [1980, 1981] has shown that tsunamis can be interpreted as a special branch of the normal modes (free oscillations) of a planet including an oceanic layer. This approach is particularly powerful as it expresses naturally the coupling between the solid Earth (where most tsunami sources are located) and the oceanic column, and in particular can handle directly any intermediate sedimentary structure. Routine algorithms used in classical seismological synthesis are seamlessly applicable to tsunami excitation. Normal mode theory is also extended effortlessly to higher frequencies outside the shallow water approximations, known to have a crucial effect on the final small scale of harbor response. On the other hand, its limitations stem from its inability to handle lateral heterogeneity.

Recently, and especially in the wake of the 2004 Sumatra tsunami, a number of fascinating observations were made on instruments not designed for that purpose: in most cases, they express subtle coupling between media of extremely different properties, such as the oceanic column, the solid Earth, or the atmosphere. They include recording of tsunamis by seismometers at land stations and on the ocean bottom, by hydrophones of the CTBTO, the definitive observation and explanation of tsunami shadows, tsunami signatures in the geomagnetic field, the generation of deep infrasound, and the perturbation of the ionosphere detected on GPS receiver arrays. In most cases, these phenomena are readily explained by the continuation (in a mathematical sense) of the tsunami eigenfunction outside of the water column; we will show that in many instances, the order of magnitude of the effect is well predicted by simple arguments derived under the normal mode approach.

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Miguel Onorato
, Università di Torino
Triggering breathers in currents

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Geir Pedersen
, Universitetet i Oslo
Topics related to tsunamis generated by rock slides

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Efim Pelinovsky
, Institute of Applied Physics, Russian Academy of Sciences
Rogue Waves in the Ocean; Facts, Theories and Modelling

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Harvey Segur
, University of Colorado
Tsunamis

This talk is intended to survey our current understanding of tsunamis. It answers four (or maybe five) basic questions. What is a tsunami? How do tsunamis work? Does soliton theory apply to tsunamis ? What can be done to protect people from the dangers of tsunamis? (If time permits: Why are some some tsunamis deadly and some benign?)

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Harry Yeh
, Oregon State
Solitary-Wave Amplification along a Vertical Wall: Theory and Experiment

When a solitary wave (a model of tsunami in the nearshore shallow water) impinges on a reflective vertical wall, it can take the formation of Mach reflection (a geometrically similar reflection from acoustics). The mathematical theory predicts that the amplification at the reflection is not twice, but four times the incident wave amplitude. Evidently, this has an important implication to engineering design practice. Our laboratory experiments verify detailed features of the Mach reflection phenomenon, whereas contradict the theory in terms of the maximum four-fold amplification: the maximum amplification observed in the laboratory was 2.92, instead. The reason for the discrepancy is discussed. In addition, we show that a tsunami along the reflective wall can reach higher than the maximum solitary wave height. Once the wave breaking happens along the wall, the substantial increase in water-surface slope results along the wave crest away from the wall.

 

 
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