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Journal ArticleDOI

NWF: Propagation of Tsunami and its Interaction with Continental Shelf and Vertical Wall

30 Jun 2006-Marine Geodesy (Taylor & Francis Group)-Vol. 29, Iss: 3, pp 201-221
TL;DR: In this paper, the authors simulated tsunamis represented as solitary waves using the fully nonlinear free surface waves based on Finite Element method developed by Sriram et al. (2006) and established the split up of solitary wave while it propagates over the uneven bottom topography.
Abstract: In this article, tsunamis represented as solitary waves was simulated using the fully nonlinear free surface waves based on Finite Element method developed by Sriram et al. (2006). The split up of solitary wave while it propagates over the uneven bottom topography is successfully established. Wave transmission and reflection over a vertical step introduced in the bottom topography is in good agreement with the experimental results from Seabra-Santos et al. (1987). The wave transformation over a continental shelf with different smooth slopes reveals that the solitary wave reflection increases while the continental slope varies from flat to steep. The interaction of the solitary wave with a vertical wall for different wave steepness has been analysed. The reflected shape of the profile is in good agreement with the observation made by Fenton and Rienecker (1982) and an increase in wave celerity is observed.
Citations
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Journal ArticleDOI
TL;DR: Schimmels et al. as mentioned in this paper studied the propagation and run-up of long tsunami-like waves in the 300m long Large Wave Flume (GWK), Hannover, Germany and analyzed the feasibility of experiments on tsunami runup in large facilities.

31 citations

Journal ArticleDOI
TL;DR: In this paper, smoothed particle hydrodynamics (SPH) has been shown to be useful to study the propagation of nonlinear water waves generated in a numerical flume, and an explicit dynamic free surface boundary condition has been imposed in the SPH model for steady long time simulation.

19 citations

Journal ArticleDOI
TL;DR: In this paper, an attempt is made to understand the effect of continental slope on the transmission, propagation and run-up of a tsunami, and to get a preliminary understanding, a one-dimensional numerical model study is carried out using shallow water equations.
Abstract: Frequent tsunamis across the globe have devastated the coasts and led to significant loss of life and property. This calls for a better understanding and estimation of the tsunami characteristics. Considering the scale of the problem, numerical modelling is the most suitable method for tsunami simulation and understanding. Most tsunamis are long-period wave and governed by shallow water equations. Although tsunami is expected to initiate in the deeper waters with very less height, it may have significant amplification while traversing over the slopes. In this study, an attempt is made to understand the effect of continental slope on the transmission, propagation and run-up of tsunami. This study provides better understanding of the physical process through computation of tsunami run-up height and arrival time. To carry out this investigation and to get a preliminary understanding, a one-dimensional numerical model study is carried out using shallow water equations. These equations are solved using Crank–N...

5 citations


Cites background from "NWF: Propagation of Tsunami and its..."

  • ...Tsunami is a shallow water wave, which undergoes deformation due to nearshore bathymetry reducing its speed, resulting in increase in wave height in the process of their propagation (Kowalik et al., 2006; Sriram et al., 2006)....

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Journal ArticleDOI
TL;DR: In this article, the finite element method is used in the domain for the estimation of the velocity potential, while, a cubic spline approximation is used to recover the velocity, and further modification is carried out for the velocity recovery by using least square method to overcome the difficulties in the simulation of steep waves.

5 citations

Journal ArticleDOI
TL;DR: In this paper, a numerical model study is carried out using shallow water equations that are solved using Crank-Nicolson finite difference approximation method on a staggered grid, where a rectangular solitary wave is considered to propagate over typical continental slopes and nearshore profiles available along the Indian coast.

2 citations

References
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Journal ArticleDOI
TL;DR: In this article, a head-on collision between two solitary waves on the surface of an inviscid homogeneous fluid was considered, and a perturbation method was used to calculate the effects of the collision.
Abstract: We consider a head-on collision between two solitary waves on the surface of an inviscid homogeneous fluid. A perturbation method which in principle can generate an asymptotic series of all orders, is used to calculate the effects of the collision. We find that the waves emerging from (i.e. long after) the collision preserve their original identities to the third order of accuracy we have calculated. However a collision does leave imprints on the colliding waves with phase shifts and shedding of secondary waves. Each secondary wave group trails behind its primary, a solitary wave. The amplitude of the wave group diminishes in time because of dispersion. We have also calculated the maximum run-up amplitude of two colliding waves. The result checks with existing experiments.

326 citations

DissertationDOI
01 Nov 1978
TL;DR: In this paper, a numerical method of solving the Boussinesq equations for constant depth using finite element techniques is presented, which is extended to the case of an arbitrary variation in depth (i.e., gradually to abruptly varying depth).
Abstract: The various aspects of the propagation of long waves onto a shelf (i.e., reflection, transmission and propagation on the shelf) are examined experimentally and theoretically. The results are applied to tsunamis propagating onto the continental shelf. A numerical method of solving the one-dimensional Boussinesq equations for constant depth using finite element techniques is presented. The method is extended to the case of an arbitrary variation in depth (i.e., gradually to abruptly varying depth) in the direction of wave propagation. The scheme is applied to the propagation of solitary waves over a slope onto a shelf and is confirmed by experiments. A theory is developed for the generation in the laboratory of long waves of permanent form, i.e., solitary and cnoidal waves. The theory, which incorporates the nonlinear aspects of the problem, applies to wave generators which consist of a vertical plate which moves horizontally. Experiments have been conducted and the results agree well with the generation theory. In addition, these results are used to compare the shape, celerity and damping characteristics of the generated waves with the long wave theories. The solution of the linear nondispersive theory for harmonic waves of a single frequency propagating over a slope onto a shelf is extended to the case of solitary waves. Comparisons of this analysis with the nonlinear dispersive theory and experiments are presented. Comparisons of experiments with solitary and cnoidal waves with the predictions of the various theories indicate that, apart from propagation, the reflection of waves from a change in depth is a linear process except in extreme cases. However, the transmission and the propagation of both the transmitted and the reflected waves in general are nonlinear processes. Exceptions are waves with heights which are very small compared to the depth. For these waves, the entire process of propagation onto a shelf in the vicinity of the shelf is linear . Tsunamis propagating from the deep ocean onto the continental shelf probably fall in this class.

310 citations


"NWF: Propagation of Tsunami and its..." refers background or methods in this paper

  • ...The simulation of solitary waves by prescribing the ‘piston’ wave maker motion is determined from the first order Boussinesq wave theory used by Goring (1979)....

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  • ...Goring (1979) carried out a study on the long wave propagation over a continental shelf, in which the tsunami wave was theoretically and experimentally represented by solitary and cnoidal waves. Murty (1979) has shown that the energy released by the moving submarine land mass by an earthquake can be modeled as a solitary wave....

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  • ...Goring (1979) carried out a study on the long wave propagation over a continental shelf, in which the tsunami wave was theoretically and experimentally represented by solitary and cnoidal waves....

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  • ...The simulation of solitary waves by prescribing the ‘piston’ wave maker motion is determined from the first order Boussinesq wave theory used by Goring (1979). The velocity of the wave maker is given by,...

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Journal ArticleDOI
TL;DR: In this article, the nonlinear properties of finite-amplitude water waves are modelled by a numerical method based on the Marker and Cell technique, which is shown to be a valid tool for analyzing incompressible flows with a free surface under transient conditions.

296 citations


"NWF: Propagation of Tsunami and its..." refers background or methods in this paper

  • ...Recently, studies have been reported on the interaction of solitary waves with the submerged rectangular obstacle by Chang et al. (2001), Tang and Chang (1998), and Lin (2004). For proper modeling of the wave transformation over a submerged obstacle, the wave breaking and vortex evolution should be incorporated in the numerical model as quoted by Lin (2004). In addition, the solitary wave propagation over an uneven topography has been dealt analytically by Grimshaw (1970) and Johnson (1973), and its disintegration into two or more solitons over varying depth has been studied using KdV type equation by Pudjaprasetya et al. (1999). Fully nonlinear models based on BEM has been reported by Van Daalen et al....

    [...]

  • ...The results on the study of solitary wave interaction with the vertical wall through experiments of Maxworthy (1976), analytical works of Byatt-Smith (1971), and Su and Mirie (1980), numerical works of Chan and Street (1970), Fenton and Rienecker (1982), and Maiti and Sen (1999) have been reported....

    [...]

  • ...Recently, studies have been reported on the interaction of solitary waves with the submerged rectangular obstacle by Chang et al. (2001), Tang and Chang (1998), and Lin (2004)....

    [...]

  • ...Recently, studies have been reported on the interaction of solitary waves with the submerged rectangular obstacle by Chang et al. (2001), Tang and Chang (1998), and Lin (2004). For proper modeling of the wave transformation over a submerged obstacle, the wave breaking and vortex evolution should be incorporated in the numerical model as quoted by Lin (2004)....

    [...]

  • ...Recently, studies have been reported on the interaction of solitary waves with the submerged rectangular obstacle by Chang et al. (2001), Tang and Chang (1998), and Lin (2004). For proper modeling of the wave transformation over a submerged obstacle, the wave breaking and vortex evolution should be incorporated in the numerical model as quoted by Lin (2004). In addition, the solitary wave propagation over an uneven topography has been dealt analytically by Grimshaw (1970) and Johnson (1973), and its disintegration into two or more solitons over varying depth has been studied using KdV type equation by Pudjaprasetya et al. (1999). Fully nonlinear models based on BEM has been reported by Van Daalen et al. (1997) for the disintegration of solitons....

    [...]

01 Apr 1979
TL;DR: In this paper, a head-on collision between two solitary waves on the surface of an inviscid homogeneous fluid was considered, and a perturbation method was used to calculate the effects of the collision.
Abstract: We consider a head-on collision between two solitary waves on the surface of an inviscid homogeneous fluid. A perturbation method which in principle can generate an asymptotic series of all orders, is used to calculate the effects of the collision. We find that the waves emerging from (i.e. long after) the collision preserve their original identities to the third order of accuracy we have calculated. However a collision does leave imprints on the colliding waves with phase shifts and shedding of secondary waves. Each secondary wave group trails behind its primary, a solitary wave. The amplitude of the wave group diminishes in time because of dispersion. We have also calculated the maximum run-up amplitude of two colliding waves. The result checks with existing experiments.

293 citations

Journal ArticleDOI
TL;DR: In this article, an asymptotic solution of these equations is obtained which describes a slowly varying solitary wave; also differential equations for the slow variations of the parameters describing the solitary wave are derived, and solved in the case when the solitary waves evolves from a region of uniform depth.
Abstract: Equations are derived for two-dimensional long waves of small, but finite, amplitude in water of variable depth, analogous to those derived by Boussinesq for water of constant depth. When the depth is slowly varying compared to the length of the wave, an asymptotic solution of these equations is obtained which describes a slowly varying solitary wave; also differential equations for the slow variations of the parameters describing the solitary wave are derived, and solved in the case when the solitary wave evolves from a region of uniform depth. For small amplitudes it is found that the wave amplitude varies inversely as the depth.

241 citations


"NWF: Propagation of Tsunami and its..." refers background in this paper

  • ...In addition, the solitary wave propagation over an uneven topography has been dealt analytically by Grimshaw (1970) and Johnson (1973), and its disintegration into two or more solitons over varying depth has been studied using KdV type equation by Pudjaprasetya et al. (1999)....

    [...]