Effective coastal boundary conditions for tsunami simulations (original) (raw)

Abstract

This dissertation has been approved by: prof. dr. ir. E. W. C. van Groesen prof. dr. ir. O. Bokhove this thesis is dedicated to my mother and the memory of my father to my husband Contents Summary ix Samenvatting xi xii CONTENTS water en in tweede instantie niet-lineaire vergelijkingen voor ondiep water. De lineaire benadering wordt gestart met het eenvoudigste geval, dat is een vlakke bathymetrie met een vaste wand als randvoorwaarde. Verder is een langzaam variërende bathymetrie beschouwd. De analytische oplossing is gebaseerd op lineaire ondiep water theorie en de Wentzel-Kramer-Brillouin benadering, evenals uitbreidingen voor het dispersieve Boussinesq model. Vervolgens worden in de lineaire benadering de waterdiepten aan de kust benaderd door een strand met een constante gemiddelde helling. De oploophoogten aan de kust en de reflectie veroorzaakt door de helling worden vervolgens gemodelleerd op basis van nietlineaire ondiep water theorie over hellende bathymetrie. De koppeling tussen de numerieke en analytische dynamiek in de twee gebieden wordt behandeld met behulp variatieprincipes, wat bij benadering leidt tot behoud van de totale energie in beide gebieden. De numerieke oplossing in het simulatiegebied is gebaseerd op een variationele eindige elementenmethode. Verificaties van de effectieve randvoorwaarde techniek en implementatie worden gedaan in een reeks van numerieke testcases van toenemende complexiteit, waaronder een geval verwant aan tsunami-oploop naar de kustlijn op Atjeh, Sumatra, Indonesie. Bij vergelijking blijkt dat de effectieve randvoorwaarde methode een goede voorspelling geeft van zowel de golf die aankomt bij de kustlijn alsmede van de golfreflectie, terwijl deze methode uitsluitend is gebaseerd op de informatie van het golfsignaal bij dit zeewaartse grenspunt. De rekentijden die nodig zijn in simulaties met behulp van de effectieve randvoorwaarde tonen een reductie ten opzichte van tijden die nodig zijn voor overeenkomstige volledige numerieke simulaties. CHAPTER 1 Introduction 1.1 Motivation The word tsunami is a Japanese word, represented by two characters: tsu, meaning, harbor, and nami, meaning, wave. Tsunami is defined as a set of ocean waves with very long wavelengths (typically hundreds of kilometres) and relatively small amplitude (a metre or so is typical), so that it often passes by ships in the deep ocean without anyone on board even noticing. The cause of a tsunami is any large, sudden disturbance of the sea-surface, such as an underwater earthquake, landslide, or volcanic eruption. More rarely, a tsunami can be generated by a giant meteor impact with the ocean. About 80 percent of tsunamis happen within the Pacific Ocean's "Ring of Fire", which is an active geological area where tectonic shifts make volcanoes and earthquakes common. Historical data of tsunamis record that since 1850 tsunamis have killed more than 420,000 people and caused billions of dollars of damage to coastal structures and habitats [Bernard and Robinson, 2009]. Knowing no international boundaries across the sea, tsunami propagation is a problem with global dimensions and ranks high on the scale of natural disasters. Most of the casualties were caused by local tsunamis that occur about once per year somewhere in the world. The December 26, 2004 Indian Ocean Tsunami (IOT) with a Moment magnitude (Mw) of 9.2 was likely the most devastating tsunami in recorded history, causing over 200,000 fatalities within a few hours in 27 countries across the entire Indian Ocean basin, with tens of thousands reported missing and over one million left homeless [

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