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Journal ArticleDOI

Propagation and breaking characteristics of solitons and N-wave in fresh water and brine

02 Feb 2017-Journal of Hydraulic Research (Taylor & Francis)-Vol. 55, Iss: 4, pp 557-572
Abstract: In this paper, the results of the study on the wave propagation and breaking of solitons and N-waves in fresh water and brine are reported. The experiments were performed in the twin flume facility at the Franzius Institute, Leibniz University of Hannover. Brine from Dead Sea was used for the study. The objective of the experimental study was to determine the flood safety levels along the banks of the Dead Sea and to arrive at the empirical equations for run-up. A weakly coupled numerical model based on the fully nonlinear potential flow and Navier–Stokes equation was used to validate the experimental results. The proposed numerical model is in good agreement with the present experimental results and the available analytical solutions for run-up estimation. The breaking N-waves were found to have a reduced run-up when compared to breaking solitons. The paper shows that the long wave propagation and run-up in both brine and water has similar characteristics.

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Topics: Breaking wave (56%), Wave propagation (52%)
Citations
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Journal ArticleDOI
15 Apr 2020-Ocean Engineering
Abstract: In the present paper, the hybrid numerical model (Sriram et al. (2014)) is used for the estimation of long wave run-up. The model is based on the strong coupling between the fully nonlinear potential flow theory (FNPT) at the far-field and Navier-Stokes (NS) equations in the nearshore. The simulations are carried out for the propagation and evolution of the tsunami-like waves, i.e., elongated single pulses having a realistic timescale. The model is validated from large scale experiments for the wave propagation as well as for run-up (Sriram et al., 2016). The numerical simulations are found to agree well with experiments. The model capability is shown for two different scenarios over a slope: (a) a rapidly rising tide including surging and spilling breaking and (b) undular bore formation and its plunging breaking on a beach. For the first case, the numerical model is also compared with the analytical estimates. The second case, undular bore breaking over a slope, shows the capability of the meshfree method and the requirements of the hybrid model. In many of the existing particle-based methods, dense distribution of particles is required to simulate the rapidly rising tide, which is not needed in the present model.

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6 citations



References
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Journal ArticleDOI
Costas E. Synolakis1Institutions (1)
Abstract: This is a study of the runup of solitary waves on plane beaches. An approximate theory is presented for non-breaking waves and an asymptotic result is derived for the maximum runup of solitary waves. A series of laboratory experiments is described to support the theory. It is shown that the linear theory predicts the maximum runup satisfactorily, and that the nonlinear theory describes the climb of solitary waves equally well. Different runup regimes are found to exist for the runup of breaking and non-breaking waves. A breaking criterion is derived for determining whether a solitary wave will break as it climbs up a sloping beach, and a different criterion is shown to apply for determining whether a wave will break during rundown. These results are used to explain some of the existing empirical runup relationships.

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811 citations


"Propagation and breaking characteri..." refers background or methods or result in this paper

  • ...In comparison, Synolakis (1986, 1987) had used the solitary wave model to estimate the run-up of long waves....

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  • ...(9) proposed by Synolakis (1987), the difference in coefficient of about 20% was observed from the present study....

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  • ...Similarly, Spielvogel (1976) and Synolakis (1986, 1987) extended the Carrier and Greenspan transformation to study the run-up of long waves over a slope....

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  • ...Empirical equations were proposed in Synolakis (1986, 1987) to estimate the run-up of breaking solitary waves on slopes....

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  • ...The experimentally obtained values were then compared with the empirical formula suggested by Synolakis (1987) for estimating the run-up of breaking solitary waves (Eq....

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Journal ArticleDOI
George F. Carrier1, H. P. Greenspan1Institutions (1)
Abstract: In this paper, we investigate the behaviour of a wave as it climbs a sloping beach. Explicit solutions of the equations of the non-linear inviscid shallow-water theory are obtained for several physically interesting wave-forms. In particular it is shown that waves can climb a sloping beach without breaking. Formulae for the motions of the instantaneous shoreline as well as the time histories of specific wave-forms are presented.

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678 citations


"Propagation and breaking characteri..." refers background or methods in this paper

  • ...Similarly, Spielvogel (1976) and Synolakis (1986, 1987) extended the Carrier and Greenspan transformation to study the run-up of long waves over a slope. In Carrier and Greenspan (1958), an initial shape of the wave was assumed with a zero initial velocity and the propagation and run-up was estimated. Spielvogel (1976) used an inverse problem to estimate the wave shape based by using the run-up estimates as the initial condition. In comparison, Synolakis (1986, 1987) had used the solitary wave model to estimate the run-up of long waves. Didenkulova and Pelinovsky (2008) had also tried to study the influence of incident waveform on run-up of long waves. Another approach to using the classical shallow water equation for studying the run-up of non-breaking solitary waves on a plane slope can be found in Li and Raichlen (2001). The Boussinesq equation is another popular model used in the study of long wave propagation. Torsvik and Liu (2007), Liu, Simarro, Vandever, and Orifila (2006) and Orifila, Simarro, and Liu (2007) are primarily based on this model. In the formulations, the effects of bottom friction and viscosity are incorporated and tested for their effects during long wave propagation. In order to generate these long waves in the experiments, Schimmels, Sriram, and Didenkulova (2016) revisited the traditional method to generate a tsunami in laboratory scale using a classical wave maker....

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  • ...Similarly, Spielvogel (1976) and Synolakis (1986, 1987) extended the Carrier and Greenspan transformation to study the run-up of long waves over a slope. In Carrier and Greenspan (1958), an initial shape of the wave was assumed with a zero initial velocity and the propagation and run-up was estimated. Spielvogel (1976) used an inverse problem to estimate the wave shape based by using the run-up estimates as the initial condition. In comparison, Synolakis (1986, 1987) had used the solitary wave model to estimate the run-up of long waves. Didenkulova and Pelinovsky (2008) had also tried to study the influence of incident waveform on run-up of long waves. Another approach to using the classical shallow water equation for studying the run-up of non-breaking solitary waves on a plane slope can be found in Li and Raichlen (2001). The Boussinesq equation is another popular model used in the study of long wave propagation. Torsvik and Liu (2007), Liu, Simarro, Vandever, and Orifila (2006) and Orifila, Simarro, and Liu (2007) are primarily based on this model. In the formulations, the effects of bottom friction and viscosity are incorporated and tested for their effects during long wave propagation. In order to generate these long waves in the experiments, Schimmels, Sriram, and Didenkulova (2016) revisited the traditional method to generate a tsunami in laboratory scale using a classical wave maker. The paper discussed the requirements and limitations in performing such a study in a large wave flume. Sriram, Didenkulova, Sergeeva, and Schimmels (2016) used this method to study the evolution and run-up of long waves in the large wave flume (GWK) at the Forschungszentrum Küste (FZK)....

    [...]

  • ...Similarly, Spielvogel (1976) and Synolakis (1986, 1987) extended the Carrier and Greenspan transformation to study the run-up of long waves over a slope. In Carrier and Greenspan (1958), an initial shape of the wave was assumed with a zero initial velocity and the propagation and run-up was estimated. Spielvogel (1976) used an inverse problem to estimate the wave shape based by using the run-up estimates as the initial condition. In comparison, Synolakis (1986, 1987) had used the solitary wave model to estimate the run-up of long waves. Didenkulova and Pelinovsky (2008) had also tried to study the influence of incident waveform on run-up of long waves....

    [...]

  • ...Similarly, Spielvogel (1976) and Synolakis (1986, 1987) extended the Carrier and Greenspan transformation to study the run-up of long waves over a slope. In Carrier and Greenspan (1958), an initial shape of the wave was assumed with a zero initial velocity and the propagation and run-up was estimated....

    [...]

  • ...Similarly, Spielvogel (1976) and Synolakis (1986, 1987) extended the Carrier and Greenspan transformation to study the run-up of long waves over a slope. In Carrier and Greenspan (1958), an initial shape of the wave was assumed with a zero initial velocity and the propagation and run-up was estimated. Spielvogel (1976) used an inverse problem to estimate the wave shape based by using the run-up estimates as the initial condition....

    [...]


01 Jan 2007-

322 citations


"Propagation and breaking characteri..." refers methods in this paper

  • ...All the results provided in the publications described above as well as in the empirical relationships proposed in Hughes (2004) and in manuals like the Shore Protection Manual (1984) and EuroTop manual (Pullen et al., 2007) were based on laboratory tests conducted in fresh water....

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DissertationDOI
01 Nov 1978-
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.

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301 citations


Additional excerpts

  • ...Goring (1979) performed experiments to study the propagation of long waves onto a shelf....

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Journal ArticleDOI

279 citations


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