Numerical modeling of waves for a tsunami early warning system

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Numerical modeling of waves for a tsunami early warning system Figure 1.2: Different types of impulse waves defined as function of the landslide volume, represented by the dimensionless parameter λ/d, andthe landslide velocity, represented by the Froud number Fr (picture taken from Noda, 1970). open sea, and the second panel (B) of Figure 1.3 shows an intermediate case. The situation sketched in the panel A, is the limit of a case where the far field does not exist, that one on the panel C, shows a case where the near field is small compared to the far field, the intermediate situation (panel B) consist of near field and far field of comparable extents. So it is important to consider which could be the dominant aspects of the phenomenon before modeling subaerial landslide generated waves. 1.2 Aims and structure of the present work In the recent past the research interest on tsunamis has risen enormously, due to the threat of the inundation consequences on coastal zone. Mathematical theory and physical model experiments have been implemented in order to get more insight about the physical processes and to plan defence strategies aimed to mitigate the effects of these events. The present work aims at developing a new numerical model and methodology to simulate the generation and propagation of tsunamis. The model is based on the mild Università degli Studi di Roma Tre - DSIC 7
Numerical modeling of waves for a tsunami early warning system Figure 1.3: Three different main cases defined as a function of the ratio between the volume of the landslide and that of the water body. slope equation (MSE hereinafter), originally developed by Berkhoff (1972), which is able to reproduce small amplitude transient waves, because is linear, and to properly simulate the full frequency dispersion of the waves. The numerical technique makes use of the Fourier Tranform (with respect to the time) of the wave equation in order to obtain an elliptic equation for each component of the wave spectrum, which are solved using a numerical finite element method. Solving the mild slope equation in the frequency domain potentially allows the solution of all the wave frequency components, which can be then superimposed, due to the linerity of the equations, to obtain the time domain solution. The innovative feature of the model is in the computational procedure, more than in the model equations, which makes it suitable for the use in tsunami early warning system (TEWS). As it will be shown the model can be applied in real time. This is possible because the computational procedure is split into two parts. One is computationally expensive, and has to be carried out when preparing the system; the other one is very fast, and can be carried out in real time as the tsunami event takes place. The present document is structured in 5 chapters. In the first one the topics and the aims of the work are already outlined. Chapter 2 provides an overview of the mathematical water wave theories, with particular attention to those used to model tsunamis and to the recent works on this topic. In Chapter 3 the model equations are derived and the numerical model is described. Chapter 4 presents the model applications and shows the Università degli Studi di Roma Tre - DSIC 8
Page 1 and 2: Università degli studi ROMA TRE Ph
Page 3 and 4: To my father Michele, my mother Ant
Page 6 and 7: Abstract A numerical model based on
Page 8 and 9: Sommario Un modello numerico basato
Page 10 and 11: Contents 1 Introduction 3 1.1 Tsuna
Page 12 and 13: List of Figures 1.1 Principal phase
Page 14 and 15: xiii 4.13 Panels a and b: absolute
Page 16 and 17: 4.32 Comparison of the free surface
Page 18 and 19: xvii 5.8 Numerical results of the S
Page 20: List of Tables 4.1 Radial and Angul
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aFourier filter functions aFourier
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Numerical modeling of waves for a t
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half an hour. ηS12(m) ηS7(m) ηS1
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ηS6(m) ηS9(m) Numerical modeling
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ηS15(m) ηS24(m) ηS16(m) −0.01
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η(m) η(m) η(m) 50 0 Numerical mo
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Numerical modeling of waves for a tsunami early warning system

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