Hidekazu Tsuji - Academia.edu (original) (raw)

Papers by Hidekazu Tsuji

Solitary waves are typical nonlinear long waves in the ocean. The two-dimensional interaction of ... more Solitary waves are typical nonlinear long waves in the ocean. The two-dimensional interaction of solitary waves has been shown to be essentially different from the one-dimensional case and can be related to generation of large amplitude waves (including ‘freak waves’). Concerning surface-water waves, Miles (1977) theoretically analyzed interaction of three solitary waves, which is called “resonant interaction” because of the relation among parameters of each wave. Weakly-nonlinear numerical study (Funakoshi, 1980) and fully-nonlinear one (Tanaka, 1993) both clarified the formation of large amplitude wave due to the interaction (“stem” wave) at the wall and its dependency of incident angle. For the case of internal waves, analyses using weakly nonlinear model equations (e.g. Tsuji and Oikawa, 2006) suggest also qualitatively similar results. Therefore, the aim of this study is to investigate the strongly nonlinear interaction of internal solitary waves; especially whether the resonan...

Eprint Arxiv Nlin 0702052, Feb 1, 2007

We consider a mechanism of generation of huge waves by multi-soliton resonant interactions. A non... more We consider a mechanism of generation of huge waves by multi-soliton resonant interactions. A non-stationary wave amplification phenomenon is found in some exact solutions of the Kadomtsev-Petviashvili (KP) equation. The mechanism proposed here explains the character of extreme waves and of those in Tsunami.

Journal of Japan Society of Civil Engineers, Ser. B2 (Coastal Engineering), 2010

Journal of Japan Society of Civil Engineers, Ser. B2 (Coastal Engineering), 2011

To clarify the resonance of fully-nonlinear internal solitary waves which is one of the reasons f... more To clarify the resonance of fully-nonlinear internal solitary waves which is one of the reasons for the occurrence of large amplitude internal waves, fully-nonlinear and strongly-dispersive internal wave equation model was applied, which attempted to investigate interaction of internal solitary waves in a two-dimensional plane. The 3 rd order theoretical solutions for internal waves in a two-layer system was used for the initial conditions and progress of internal solitary wave was confirmed. Seven different incident wave angles were given, in which 'stem' was confirmed to appear when incident wave angle is less than critical angle. As a result, it is found that the amplified internal wave amplitude becomes about three times as much as the original amplitude.

Coastal Engineering Proceedings, 2014

Wave Motion, 2005

It is shown that generation of the rogue waves in the ocean may be described in framework of non-... more It is shown that generation of the rogue waves in the ocean may be described in framework of non-linear two-dimensional shallow water theory where the simplest two-dimensional long wave non-linear model corresponds to the Kadomtsev-Petviashvili (KP) equation. Numerical solution of the KP equation is obtained to account for the formation of localized abnormally high amplitude wave due to a resonant superposition of two incidentally non-interacting long-crested waves. Peculiarities of the solution allow to explain rare and unexpected appearance of the rogue waves. However, our solution differs from the exact two-solitary wave solution of the KP equation used before for the rogue waves description.

Studies in Applied Mathematics, 2009

We study the maximum wave amplitude produced by line-soliton interactions of the Kadomtsev-Petvia... more We study the maximum wave amplitude produced by line-soliton interactions of the Kadomtsev-Petviashvili II (KPII) equation, and we discuss a mechanism of generation of large amplitude shallow water waves by multi-soliton interactions of KPII. We also describe a method to predict the possible maximum wave amplitude from asymptotic data. Finally, we report on numerical simulations of multi-soliton complexes of the KPII equation which verify the robustness of all types of soliton interactions and web-like structure.

Oblique interactions of weakly nonlinear long waves in dispersive systems

Fluid Dynamics Research, 2006

Studies on the oblique interactions of weakly nonlinear long waves in dispersive systems are surv... more Studies on the oblique interactions of weakly nonlinear long waves in dispersive systems are surveyed. We focus mainly our concentration on the two-dimensional interaction between solitary waves. Two-dimensional Benjamin–Ono (2DBO) equation, modified Kadomtsev–Petviashvili (MKP) equation and extended Kadomtsev–Petviashvili (EKP) equation as well as the Kadomtsev–Petviashvili (KP) equation are treated. It turns out that a large-amplitude wave can be generated due to the oblique interaction of two identical solitary waves in the 2DBO and the MKP equations as well as in the KP-II equation. Recent studies on exact solutions of the KP equation are also surveyed briefly.

Fluid Dynamics Research, 2001

Oblique interaction of internal solitary waves in a two-layer uid system with inÿnite depth is st... more Oblique interaction of internal solitary waves in a two-layer uid system with inÿnite depth is studied. Two-dimensional Benjamin-Ono (BO) equation is solved numerically to investigate the strong interactions of the non-linear long waves whose propagation directions are very close to each other. Computations of time development are performed for two initial settings: the ÿrst one is superposition of two BO solitons with the same amplitude and with di erent propagation directions, and the second one is an oblique re ection of a BO soliton at a vertical wall. It is observed that the Mach re ection does occur for small incident angles and for some incident angles very large stem waves are generated.

Two-dimensional interactions of solitons in a two-layer fluid of finite depth

Fluid Dynamics Research, 2010

Two-dimensional (2D) interactions of two interfacial solitons in a two-layer fluid of finite dept... more Two-dimensional (2D) interactions of two interfacial solitons in a two-layer fluid of finite depth are investigated under the assumption of a small but finite amplitude. When the angle between the wave normals of two solitons is not small, it is shown by a perturbation method that in the lowest order of approximation the solution is a superposition of two intermediate long wave (ILW) solitons and in the next order of approximation the effect of the interaction appears as position phase shifts and as an increase in amplitude at the interaction center of two solitons. When is small, it is shown that the interaction is described approximately by a nonlinear integro-partial differential equation that we call the two-dimensional ILW (2DILW) equation. By solving it numerically for a V-shaped initial wave that is an appropriate initial value for the oblique reflection of a soliton due to a rigid wall, it is shown that for a relatively large angle of incidence i the reflection is regular, but for a relatively small i the reflection is not regular and a new wave called stem is generated. The results are also compared with those of the Kadomtsev?Petviashvili (KP) equation and of the two-dimensional Benjamin?Ono (2DBO) equation.

Numerical and experimental verification of a theoretical model of ripple formation in ice growth under supercooled water film flow

Fluid Dynamics Research, 2009

Journal of Physics A: Mathematical and Theoretical, 2009

We consider the initial value problems of the Kadomtsev-Petviashvili (KP) equation for symmetric ... more We consider the initial value problems of the Kadomtsev-Petviashvili (KP) equation for symmetric V-shape initial waves consisting of two semi-infinite line solitons with the same amplitude. Numerical simulations show that the solutions of the initial value problem approach asymptotically to certain exact solutions of the KP equation found recently in [1]. We then use a chord diagram to explain the asymptotic result. We also demonstrate a real experiment of shallow water wave which may represent the solution discussed in this Letter.

European Journal of Mechanics - B/Fluids, 2018

The oblique reflection of an incident internal solitary wave is investigated using a fully-nonlin... more The oblique reflection of an incident internal solitary wave is investigated using a fully-nonlinear and strongly-dispersive internal wave model. The 3 rd order theoretical solution for an internal solitary wave in a two-layer system is used for the incident solitary wave. Two different incident wave amplitude cases are investigated, in which nine and eleven different incident angles are used for the small and large incident amplitude cases respectively. Under both amplitudes, at least for the cases investigated here, relatively smaller incident angles result in Mach reflection while relatively larger incident angles result in regular reflection. Under Mach-like reflection generation of a 'stem' is observed for a certain range of incident angles, in addition to the reflected wave. The stem is found to have, in a certain sense, the characteristics of an internal solitary wave, though the maximum stem wave amplitude is less than four times as large as the original incident internal solitary wave. The stem length is confirmed to increase faster for the larger incident wave amplitude. The maximum amplification factor for the small incident wave is the same as in previous studies. However, the maximum amplification factor for the large incident wave is less than that for the small wave. The results of these calculations are compared with those of the corresponding KP theory and it is found that a lower amplification factor may be a significant characteristic of internal solitary waves.

Little is known about morphological instability of a solidification front during the crystal grow... more Little is known about morphological instability of a solidification front during the crystal growth of a thin film of flowing supercooled liquid with a free surface: for example, the ring-like ripples on the surface of icicles. The length scale of the ripples is nearly 1 cm. Two theoretical models for the ripple formation mechanism have been proposed. However, these models lead to quite different results because of differences in the boundary conditions at the solid-liquid interface and liquid-air surface. The validity of the assumption used in the two models is numerically investigated and some of the theoretical predictions are compared with experiments.