Numerical modeling of waves for a tsunami early warning system

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ηS6(m) ηS9(m) Numerical modeling of waves for a tsunami early warning system 0.01 0.005 0 −0.005 −0.01 0.01 0.005 0 −0.005 −0.01 15 20 25 30 35 40 15 20 25 30 35 40 t(s) ηS13(m) 0.01 0.005 0 −0.005 −0.01 15 20 25 30 35 40 t(s) Figure 4.39: Comparison of the free surface elevations at the back field gauges position, measured (red dashed line) and obtained from the numerical model (black solid line). The numerical results are achieved imposing a forcing source term in the MSE. 4.6 Matching of elliptic and parabolic MSE - Numerical experiments As already introduced the solution of the fully elliptic mild-slope equation for a large number of wave frequencies, is computationally very expensive, and until now has limited the application of the model over relatively small geographical areas, typically of the order of 100 km 2 (Bellotti et al., 2008). Thus the further reduction of the computational costs and the model application extension to larger geographical areas (thousand of km 2 )canbe achieved by solving the parabolic approximation of the MSE. It is here shown a simple numerical experiment which aims at validating the numerical model when it solves the elliptic MSE over a restricted domain and the parabolic MSE over a bounding larger domain. The experiment consists on choosing an hypotethical tsunami scenario domain, which covers the generation area and a large propagation field, and split the domain in two parts, one close to the source (near field), the other far from it (far field). In the near field is solved the elliptic MSE (equation 3.29 or 3.48), at the boundary of matching with the far field domain the solution is saved and it is given as input condition to the model which solves the parabolic MSE (3.57) in the far field. Since here Università degli Studi di Roma Tre - DSIC 85
Numerical modeling of waves for a tsunami early warning system a validation test is shown, the elliptict MSE is solved in the whole domain (near and far filed), thus its solution is taken as the reference one. Figure 4.40: Layout of the numerical experiment aimed at validating the matching between the solution of the elliptic and parabolic MSE The layout of the chosen numerical domain is shown in Figure 4.40. The upper sketch reproduce a planimetric view of the circular domain, where the dashed circumference is the boundary of matching between the so called near and far field. In the lower sketch a vertical section of the domain (not in scale) can be viewed and the domain dimensions are explicitly written. The generation mechanism is supposed to occur at the coast of a conical island, posed in the center of the numerical domain, as if it would represent a landslide sliding on a flank of the island and impacting the water surface. However no particular interest is given to the generation mechanism since the aim of the present experiment is to test the far field tsunami propagation. The boundary matching is posed at a distance from the generation area which is far enough to allows the generated waves (with a specified frequency) cross it everywhere perpendicularly. In the far field the parabolic MSE is solved in cylindrical coordinates (see equation B.36 in the appendix B.3). A system of reference centered in the middle of the island and covering the domain Università degli Studi di Roma Tre - DSIC 86
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Università degli studi ROMA TRE Ph
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To my father Michele, my mother Ant
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Abstract A numerical model based on
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Sommario Un modello numerico basato
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Contents 1 Introduction 3 1.1 Tsuna
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List of Figures 1.1 Principal phase
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xiii 4.13 Panels a and b: absolute
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4.32 Comparison of the free surface
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xvii 5.8 Numerical results of the S
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List of Tables 4.1 Radial and Angul
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Numerical modeling of waves for a tsunami early warning system

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