Numerical modeling of waves for a tsunami early warning system

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Numerical modeling of waves for a tsunami early warning system source term in the MSE (‘direct’ procedure). 4.5.1 Waves generation with the ‘indirect’ procedure Here is presented the numerical model applied following the ‘indirect’ procedure to estimate the waves source term. The idea is to see how the model calculates the tsunami, when a registration is available to determine the waves source. As it will be discussed, the tsunami forecast depends on the position of the wave registration available. In particular the laboratory measurements at two different gauges are tested as they would be the real registration of a tsunami wave. These two gauges are respectively the 12S and the 15S, one located close to the generation area, the other far away of it. The different tsunami fields calculated are discussed in the following. When building a tsunami early warning system is important to determine a priori where to locate the monitoring instruments, because the measurements are a key input parameter for the forecasting model. This implies the knowledge of the tsunamogenic source position, that in most of the cases is easy to hypothesize realistically. Knowing the landslide width and its motion from the physical experiments, it is possible to define the arc of the shoreline where the landslide impacts the water. Therefore a wave maker condition (3.38), which moves that boundary with a generic velocity is here imposed and the problem is solved for all the wave frequencies. The solution of the water surface elevation, N ′ (x, y, ω), in the frequency domain is saved at the positions of all the wave gauges. The apices means that the solution is obtained for a unitary source term. In order to estimate the wave field due to the landslide movement, use is made of the physical registration of the water surface elevation time series at one point, i.e. gauge position. The simulation reproduces a time series of 50 s, usingaΔt of 0.01 s, thus corresponding to 5,000 time steps and equal number of wave frequencies to solve. In order to save computational costs, it is verified that the wave energy is mostly concentrated in the range of frequencies of 0.02 ≤ f ≤ 2 Hz, thus just 100 frequencies are solved. The numerical simulation has been carried out using triangular linear elements. The maximum elements size is set as 0.05 m, as one tenth of the shortest wave length simulated, since a resolution of 10 nodes per wave length is required. The resulting Degrees of Freedom are 80,970 for a computational time of about 20 s on a AMD Opteron 246 2GHz computer equipped with 4GB of RAM. Since the elliptic MSE is solved in the present simulation for 100 wave frequencies, the total computational time is about Università degli Studi di Roma Tre - DSIC 73
half an hour. ηS12(m) ηS7(m) ηS10(m) Numerical modeling of waves for a tsunami early warning system 0.02 0.01 0 −0.01 −0.02 12 14 16 18 20 22 0.02 0.01 0 −0.01 −0.02 12 14 16 18 20 22 0.02 0.01 0 −0.01 −0.02 12 14 16 18 20 22 t(s) ηS20(m) ηS11(m) 0.02 0.01 0 −0.01 −0.02 12 14 16 18 20 22 0.02 0.01 0 −0.01 −0.02 12 14 16 18 20 22 t(s) Figure 4.27: Comparison of the free surface elevations at the near field gauges position, measured (red dashed line) and obtained from the numerical model (black solid line). The numerical results are achieved by using the registration of the free surface elevation at the gauge 15S to estimate the wave source term. The first comparison results (figures 4.27, 4.28 and 4.29) refer to the numerical computations obtained by using the registration at the sea level gauge 15S to ‘indirectly’ estimate the source term and consequently solve the wave field. In particular the figures refer only to the water surface elevation time series at the 13 sea level gauges (see table 4.1). A distinction is made between 5 gauges (12S, 20S, 7S, 11S and 10S) which are located in front of the landslide movement and close to the island; 5 other gauges (15S, 22S, 24S, 19S and 16S) placed far from the island, all in the off-shore region, i.e. water depth of 0.80 m; and the last 3 gauges (6S, 13S and 9S) located at the rear side of the island with respect to the landslide movement. The figures 4.27, 4.28 and 4.29 refer respectively to these three groups of sea level gauges. In all the following figures the red dashed lines represent the experimental Università degli Studi di Roma Tre - DSIC 74
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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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