Numerical modeling of waves for a tsunami early warning system

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Numerical modeling of waves for a tsunami early warning system ∇h (gh∇hN)+ω 2 1 N = − cosh (ksh) fft(htt) (4.12) and the model results are compared with the reference solutions of the three dimensional model. η (m) η (m) 0.02 0 −0.02 0.02 0 −0.02 10 15 20 10 15 20 t(s) long landslide 0.02 0 −0.02 short landslide 0.02 0 −0.02 10 15 20 10 15 20 t(s) Figure 4.14: Comparison of the free surface elevation obtained from the three dimensional model (dashed red line) and from the long wave depth integrated model respectively using the frequency filter function (thick black line) and the landslide filter function (thin black line).The presented results are relative to the points A (left panels) and B (right panels) of figure 4.10. Figure 4.14 shows the water surface elevation at point A and B (left and right panels respectively); the top panels refer to the long landslide simulation, while the bottom panel to the short landslide one. With the red dashed lines the three dimensional results are represented, the black lines are relative to the solution of equation (4.11) (thick lines) and equation (4.12) (thin lines). The comparison shows that a smaller extension of the generation area involves, for the landslide filter, a stronger cut in all the frequencies of the wave amplitude. As it can be seen by the thin lines in the bottom panels, these ones do not produce reliable results. The application of the wave frequency filter function better estimates the first crest-trough wave. However some differences arise in the comparison with the three dimensional solutions. These are due to the long wave approximation of the Università degli Studi di Roma Tre - DSIC 59
Numerical modeling of waves for a tsunami early warning system depth integrated model, which provides a correct reproduction of landslide generated waves, only when the ratio h is small. Ls 4.3.2 Experiments on a plane slope Another set of numerical experiments is carried out reproducing the movement of a submerged landslide on a plane beach. In the sketch of figure 4.15 the numerical domain is represented, which is 10 m long and with a 1 : 3 slope; the landslide is also here a semi-ellipse, 4.21 m long and 0.1 m thick. The landslide suddenly starts to move after 10 s with a velocity of 1 m/s for 2 s and a total displacement of 2 m, as in the previous experiments. Figure 4.15: Sketch of the computational domain. Numerical simulations were run with both the depth integrated model and the three dimensional one. The depth integrated model is applied in a one-dimensional domain, representative of the free water surface. At the left boundary (x =0m) a reflecting boundary condition is imposed, by using a very small water depth (0.0001 m). At the right boundary, the water depth is equal to 3.3001 m and the waves are allowed to exit the domain, by applying the radiation condition (3.34). The numerical simulations reproduce a time series of 100 s, usingaΔt of 0.1 s, as in the previous experiments. The field equation is solved for same 200 angular frequencies, in the range of 2π · 10 −2 ≤ ω ≤ 2π · 2. The maximum distance between the computational Università degli Studi di Roma Tre - DSIC 60
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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 t
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and Numerical modeling of waves for
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Numerical modeling of waves for a tsunami early warning system

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