Numerical modeling of waves for a tsunami early warning system

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Numerical modeling of waves for a tsunami early warning system for the tsunami propagation and inundation. TOPICS uses curve fits of numerical results from a fully nonliner potential flow model to provide approximate landslide tsunami sources for tsunami propagation models, based on marine geology data and interpretations. While the simulation of tsunami propagation and inundation is carried out with the long wave propagation model FUNWAVE, which is based on fully nonlinear Boussinesq equations, with an extended dispersion equation, in the sense that ist matches the linear dispersion relationship for deep water waves. They incuded a breaker model in FUNWAVE in order to simulate inundation of dry land. In their work, Grilli et al. (2005) performed numerical and experimental models of tsunami generated by landslide slumps and slides. Not taking into account the wave frequency dispersion can be even worse in the cases of landslide generated tsunamis, because the landslide, moving further in deeper water, still generates waves, which are generally shorter relatively to the water depth. Lynett & Liu (2002) developed a mathematical model to describe the generation and propagation of submarine landslide generated water waves. Their model consist of a depth integrated continuity equation and momentum equations which include full nonlinear, but weakly frequency dispersion effects. They pointed out two main differences between the tsunami generation mechanism of a submarine landslide and a submarine earthquake. First the duration of a landslide is much longer, indeed the time history of the seafloor movement will affect the characteristic of the generated wave, and can not be considered just as an initial impulsive condition. Second, the typical wavelength of the tsunami generated by landslide is shorter, therefore, the frequency dispersion could be important even in the wave generation region. In their model equations the ground movement is the forcing function, they have therefore developed a new version of the BTE, starting from bottom boundary conditions that take into account the seafloor deformations given by the landslide. They have obtained model equations that naturally incorporate the effect of the moving bottom and are able to satisfactorily reproduce the frequency dispersion of the waves. They also suggest that the effects of the moving bottom on the surface waves depend on the wave frequency. Sammarco & Renzi (2008) developed an analytical two-horizontal dimension model to analyze the different physical features of landslideinduced tsunamis along a straight coast. Their model is based on the forced linear long-wave equation of motion (LSWE). In particular they noticed that after a short transient immediately following the landslide generation, the Università degli Studi di Roma Tre - DSIC 19
Numerical modeling of waves for a tsunami early warning system wave motion starts to be trapped at the shoreline and finally only transient long-shore traveling edge waves are present. Longer waves travel faster and are followed by a tail of shorter waves, while new crests are created. Unlike transient waves generated and propagating in water of constant depth, for landslide-induced tsunamis along a sloping beach the larger waves are not in the front of the wave train, but are shifted toward the middle of it. Experimental comparison shows the validity of the model in reproducing the physical behavior of the system. Their close analysis on the trapped waves of landslide tsunamis along a straight beach is in the following compared with the model presented in this document. The MSE has been originally developed by Berkhoff (1972) for purely harmonic waves, and due to its elliptic nature it was able of providing the steady-state wave field. The MSE is a depth integrated equation that, whitin appropriate boundary conditions, describes the waves propagation over mildly slope sea bottom. It is derived from the adimensional problem (2.7) by assuming ɛ
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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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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η (m) η (m) η (m) η (m) 20 0
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and Numerical modeling of waves for
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