Shoaling of Nonlinear Internal Waves on a Uniformly Sloping Beach

Yamashita, K.; Kakinuma, Taro; Nakayama, Keisuke

doi:10.9753/icce.v33.waves.72

Cited by 3 publications

(2 citation statements)

References 10 publications

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“…Numerical simulation of propagation of surface/internal solitary waves over a horizontal bottom has also been performed using the time-dependent numerical model (Yamashita et al, 2013). In the calculation process of wave propagation, the time development is carried out by applying implicit schemes similar to that of Nakayama and Kakinuma (2010).…”

Section: Propagation Of a Surface Solitary Wavementioning

confidence: 99%

Properties of Surface and Internal Solitary Waves

Yamashita

Kakinuma

2014

Int. Conf. Coastal. Eng.

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Numerical solutions of surface and internal solitary waves are obtained through a new method, where advection equations on physical quantities including surface/interface displacements and velocity potential are solved to find convergent solutions by applying the Newton-Raphson method. The nonlinear wave equations derived using a variational principle are adopted as the fundamental equations in the present study. Surface and internal solitary waves obtained through the proposed method are compared with the corresponding theoretical solutions, as well as numerical solutions of the Euler equations, to verify the accuracy of solutions through the proposed method especially for internal solitary waves of large amplitude progressing at a large celerity with a flattened wave profile. Properties of surface and internal solitary waves are discussed considering vertical distribution of horizontal and vertical velocity, as well as kinetic and potential energy. Numerical simulation using a time-dependent model has also been performed to represent propagation of surface and internal solitary waves with permanent waveforms.

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Section: Propagation Of a Surface Solitary Wavementioning

confidence: 99%

Properties of Surface and Internal Solitary Waves

Yamashita

Kakinuma

2014

Int. Conf. Coastal. Eng.

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“…Numerical simulation of tsunamis due to submarine volcanic eruption in Kagoshima Bay is performed using the shallow water version of the nonlinear wave model (Yamashita et al, 2013), where implicit schemes similar to that of Nakayama and Kakinuma (2010) are utilized to solve the fundamental equations. The seabed level in the bay is shown in Fig.…”

Section: Numerical Model and Calculation Conditionsmentioning

confidence: 99%

Tsunami Generation Due to Submarine Volcanic Eruptions With Phreatomagmatic Explosion or Caldera Subsidence

Kakinuma

Matsumoto

Yamashita

et al. 2014

Int. Conf. Coastal. Eng.

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An index of submarine volcanic explosivity concerning tsunami generation has been proposed on the basis of the relationship between phreatomagmatic explosion and resultant initial waveform of tsunamis. In the generation process of tsunamis due to phreatomagmatic explosion, the seawater touches magma of high temperature, after which the water evaporates in an instant with explosive increase of volume. We assume the value of this index specifically to simulate tsunamis caused by submarine volcanic eruption in Kagoshima Bay, where submarine explosion has been observed. Furthermore, tsunamis due to subsidence of a caldera near a volcanic mountain in the same bay are numerically simulated using an initial tsunami profile assumed without discussion about the emission process of magma out of a chamber through submarine volcanic eruption.

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Numerical Analyses of Internal Solitary Waves Propagating from Deep Water to Shallow Water

Yamashita¹,

Kakinuma²,

Kimura³

2014

Journal of Japan Society of Civil Engineers, Ser. B2 (Coastal E

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Internal solitary waves propagating from deep water to shallow water in a two-layer fluid are numerically simulated by solving the set of nonlinear equations in consideration of both strong nonlinearity and strong dispersion of waves. As an internal solitary wave travels from deep water to shallow water, almost all its wave energy is transmitted from the deep-to the shallow-water regions. A BO soliton propagates into a shallow-water region, generating KdV solitons, the characteristics of which depend on the positional relationship between the interface and the critical level. In the case where the static interface is below the critical level in a shallow-water region, disintegration of an internal solitary wave occurs remarkably, after which the available potential energy of the wave train becomes larger than its kinetic energy.

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Shoaling of Nonlinear Internal Waves on a Uniformly Sloping Beach

Cited by 3 publications

References 10 publications

Properties of Surface and Internal Solitary Waves

Properties of Surface and Internal Solitary Waves

Tsunami Generation Due to Submarine Volcanic Eruptions With Phreatomagmatic Explosion or Caldera Subsidence

Numerical Analyses of Internal Solitary Waves Propagating from Deep Water to Shallow Water

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