Practical Tsunami Numerical Simulation Model by Use of Non-Linear Dispersive Long Wave Theory

This study reveals the roles of the wave dispersion and nonlinear effects for the 2011 TohokuOki earthquake tsunami. We conducted tsunami simulations based on the nonlinear dispersive equations with a high-resolution source model. The simulations successfully reproduced the waveforms recorded in the offshore, deep sea, and focal areas. The calculated inundation area coincided well with the actual inundation for the Sendai Plain, which was the widest inundation area during this event. By conducting sets of simulations with different tsunami equations, we obtained the followings insights into the wave dispersion, nonlinear effects, and energy dissipation for this event. Although the wave dispersion was neglected in most studies, the maximum amplitude was significantly overestimated in the deep sea if the dispersion was not included. The waveform observed at the station with the largest tsunami height ($2 m) among the deep-ocean stations also verified the necessity of the dispersion. It is well known that the nonlinear effects play an important role for the propagation of a tsunami into bays and harbors. Additionally, nonlinear effects need to be considered to accurately model later waves, even for offshore stations. In particular, including nonlinear terms rather than the inundation was more important when precisely modeling the waves reflected from the coast.

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“…This study employs the nonlinear dispersive tsunami equations (NDS) with the x-y coordinates in the horizontal space [e.g., Iwase et al, 1998]: …”

Section: Nds Simulationmentioning

confidence: 99%

“…(1)-(3) is described in this appendix. The method used in this study follows the method that was described in Iwase et al [1998]. However, this study uses a vertically averaged horizontal velocity u and v to avoid numerical instability; the advective terms diverged at the very shallow sea if …”

Section: Appendix A: Finite-difference Scheme For Nonlinear Dispersivmentioning

confidence: 99%

Dispersion and nonlinear effects in the 2011 Tohoku‐Oki earthquake tsunami

et al. 2014

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“…Moreover, we considered cases in which the still-water depth h was 2000 m and the traveling velocity v p and duration τ of an atmospheric pressure wave were gh = 140 m/s and 300 s, respectively. When the wavelength of the atmospheric pressure wave, λ, was 30 km, the maximum water level η max at t = 340 s using the nonlinear shallow-water model was 0.034 m. Conversely, the corresponding value χ max obtained using the Boussinesq-type equations [25], which are described as Equations (A1) and (A2) in the Appendix A, was also 0.034 m at t = 340 s. Furthermore, when the wavelength of the atmospheric pressure wave, λ, was 20 km, the maximum water level η max was 0.051 m, and χ max was 0.045 m, at t = 340 s.…”

Section: Numerical Methods and Atmospheric Pressure Wave Modelmentioning

confidence: 94%

“…where η(x, t), Q(x, t), h(x, t), and p(x, t) are the water surface displacement, flow rate in the x-axis direction, still-water depth, and pressure on the water surface, respectively. Equations (A1) and (A2) were proposed and applied in [25], with reference to the dispersion term of [26], and also utilized by [27] to calculate transoceanic tsunamis. In Section 2, these equations were transformed to finite difference equations, as in [27], and solved numerically, where the grid size ∆x was 100 m and the time interval ∆t was 0.05 s.…”

Section: Appendix Amentioning

confidence: 99%

Tsunamis Generated and Amplified by Atmospheric Pressure Waves Due to an Eruption over Seabed Topography

Kakinuma

2022

Geosciences

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Numerical simulations were generated using a nonlinear shallow-water model of velocity potential to study the fundamental processes of tsunami generation and amplification by atmospheric pressure waves. When an atmospheric pressure wave catches up with an existing tsunami that is propagating as a free wave over an abrupt change in water depth, the amplified tsunami propagates in the shallower water. An existing tsunami propagating as a free wave over a sloping seabed is also amplified by being passed by atmospheric pressure waves. When atmospheric pressure waves travel over an abrupt change in water depth, the water surface profile of tsunamis in the shallower water depends on both the interval of the atmospheric pressure waves and the phase of the tsunami-generation process over the change in water depth. Moreover, when atmospheric pressure waves travel over an abrupt change in water depth, the tsunami amplitude in the shallower water increases, as the water depth of the shallower area is decreased and the Proudman resonance is further reduced. When an atmospheric pressure wave train with positive pressure travels over a sloping seabed, the amplification of tsunami crests propagating as free waves is controlled by leaving the forced water waves following the atmospheric pressure waves. Conversely, the amplitudes of tsunami troughs propagating as free waves increase.

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“…To reveal the overall trends of tsunamis that are generated in the Japan Sea, simulations of tsunami propagation based on the 60 sources identified by Ministry of Land, Infrastructure, Transport and Tourism (2014) were first conducted using the following linear Boussinesq theory (Goto 1991), using the (Saito et al 2014;Iwase, Mikami, and Goto 1998).…”

Section: Simulation Of the Propagation Of Japan Sea Tsunamismentioning

confidence: 99%

A numerical study on nearshore behavior of Japan Sea tsunamis using Green’s functions for Gaussian sources based on linear Boussinesq theory

Yamanaka

Sato

Shimozono

et al. 2019

Coastal Engineering Journal

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The aim of this study is to estimate how and what kinds of tsunamis are generated near shorelines in the Japan Sea, using earthquake tsunami sources proposed by the Japanese government. Tsunami propagation based on these sources was first simulated based on the linear Boussinesq theory for Miho Bay, where a historical tsunami inundated the shoreline.The results indicate that tsunami sources not only near the bay but also farther from the bay could generate significant tsunami fluctuations. Thus, the amplification of the latter tsunamis was examined using Fourier analysis. Tsunami waveforms in the bay periodically fluctuate with large amplitudes after the first wave. The Fourier analysis specified these periods to be 13-16 min, consistent with the estimated resonance periods of the bay. Therefore, it can be concluded that one of the factors responsible for the amplification of tsunamis in Miho Bay is the bay-scale resonance. To investigate why resonance occurs during tsunamis, a relationship between the tsunami source geometry and the generated tsunami was examined. This analysis indicates that specific tsunami sources located in critical areas could enhance the resonance in Miho Bay. ARTICLE HISTORY

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Practical Tsunami Numerical Simulation Model by Use of Non-Linear Dispersive Long Wave Theory

Cited by 13 publications

References 7 publications

Dispersion and nonlinear effects in the 2011 Tohoku‐Oki earthquake tsunami

Dispersion and nonlinear effects in the 2011 Tohoku‐Oki earthquake tsunami

Tsunamis Generated and Amplified by Atmospheric Pressure Waves Due to an Eruption over Seabed Topography

A numerical study on nearshore behavior of Japan Sea tsunamis using Green’s functions for Gaussian sources based on linear Boussinesq theory

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