Solitary Wave Runup on Plane Slopes

Li, Ying; Raichlen, Fredric

doi:10.1061/(asce)0733-950x(2001)127:1(33)

Cited by 113 publications

(75 citation statements)

References 12 publications

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“…In the nonlinear theory the same effects can be found for a particular case of the linearly inclined bay with a parabolic cross-section m = 2 ). The solution of the nonlinear problem in this case can be obtained with the use of the Legendre (hodograph) transformation, which has been very popular for long wave runup on a plane beach (Carrier and Greenspan, 1958;Pedersen and Gjevik, 1983;Synolakis, 1987;Tadepalli and Synolakis, 1996;Li, 2000;Li and Raichlen, 2001;Carrier et al, 2003;Kânoğlu, 2004;Tinti and Tonini, 2005;Kânoğlu and Synolakis, 2006;Didenkulova et al, 2006;2008a;Antuono and Brocchini, 2007;Pritchard and Dickinson, 2007) and is valid for non-breaking waves. In this case the nonlinear system (3) can be reduced to the linear equation (Choi et al, 2008; …”

Section: Traveling Waves In U-shaped Bays With a Arbitrary Varying Dementioning

confidence: 99%

Runup of Tsunami Waves in U-Shaped Bays

Didenkulova

Pelinovsky

2010

Pure Appl. Geophys.

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The problem of tsunami wave shoaling and runup in U-shaped bays (such as fjords) and underwater canyons is studied in the framework of shallow water theory. The wave shoaling in bays, when the depth varies smoothly along the channel axis, is studied with the use of asymptotic approach. In this case a weak reflection provides significant shoaling effects. The existence of traveling (progressive) waves, propagating in bays, when the water depth changes significantly along the channel axis, is studied. It is shown that traveling waves do exist for certain bay bathymetry configurations and may propagate over large distances without reflection.The tsunami runup in such bays is significantly larger than for a plane beach.

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Section: Traveling Waves In U-shaped Bays With a Arbitrary Varying Dementioning

confidence: 99%

Runup of Tsunami Waves in U-Shaped Bays

Didenkulova

Pelinovsky

2010

Pure Appl. Geophys.

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“…The dash-dotted line shown separates non-breaking from breaking wave run-up; this has been evaluated using the analysis presented by Synolakis (1986). (The maximum run-up for non-breaking solitary waves was calculated from the nonlinear theory of Li & Raichlen (2001), and that for breaking solitary wave was obtained from the WENO numerical model described herein.) It can be seen in figure 13 that the variation of the maximum run-up with the angle of the slope relative to horizontal is different for non-breaking solitary waves and breaking solitary waves.…”

Section: Shoreline Movement and Maximum Run-upmentioning

confidence: 99%

Non-breaking and breaking solitary wave run-up

2002

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The run-up of non-breaking and breaking solitary waves on a uniform plane beach connected to a constant-depth wave tank was investigated experimentally and numerically. If only the general characteristics of the run-up process and the maximum run-up are of interest, for the case of a breaking wave the post-breaking condition can be simplified and represented as a propagating bore. A numerical model using this bore structure to treat the process of wave breaking and subsequent shoreward propagation was developed. The nonlinear shallow water equations (NLSW) were solved using the weighted essentially non-oscillatory (WENO) shock capturing scheme employed in gas dynamics. Wave breaking and post-breaking propagation are handled automatically by this scheme and ad hoc terms are not required. A computational domain mapping technique was used to model the shoreline movement. This numerical scheme was found to provide a relatively simple and reasonably good prediction of various aspects of the run-up process. The energy dissipation associated with wave breaking of solitary wave run-up (excluding the effects of bottom friction) was also estimated using the results from the numerical model.

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“…It is claimed that the linear and nonlinear theories predict the same maximal values for the run-up height if the incident wave is determined far from the shore (Synolakis, 1987). In contrast, Li and Raichlen (2001) show that there is a difference in the maximum run-up prediction between linear and nonlinear theory. In addition to calculating only the maximum run-up height as in Choi's method, our EBC also includes the calculation of reflected waves.…”

Section: Introductionmentioning

confidence: 58%

“…The asymptotic solution of this system of equations for wave propagation over sloping bathymetry has been given for several initial-value problems using a hodograph transformation (Carrier and Greenspan, 1958;Synolakis, 1987;Pelinovsky and Mazova, 1992;Carrier et al, 2003;Kânoglu, 2004), and also for the boundary-value problem (Antuono and Brocchini, 2007;Li and Raichlen, 2001;Madsen and Schaffer, 2010) that will be used in this article. Since the system is hyperbolic, it has the following characteristic forms:…”

Section: Characteristic Formmentioning

confidence: 99%

Effective coastal boundary conditions for tsunami wave run-up over sloping bathymetry

Bokhove

Groesen

2014

Nonlin. Processes Geophys.

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Abstract. An effective boundary condition (EBC) is introduced as a novel technique for predicting tsunami wave runup along the coast, and offshore wave reflections. Numerical modeling of tsunami propagation in the coastal zone has been a daunting task, since high accuracy is needed to capture aspects of wave propagation in the shallower areas. For example, there are complicated interactions between incoming and reflected waves due to the bathymetry and intrinsically nonlinear phenomena of wave propagation. If a fixed wall boundary condition is used at a certain shallow depth contour, the reflection properties can be unrealistic. To alleviate this, we explore a so-called effective boundary condition, developed here in one spatial dimension. From the deep ocean to a seaward boundary, i.e., in the simulation area, we model wave propagation numerically over real bathymetry using either the linear dispersive variational Boussinesq or the shallow water equations. We measure the incoming wave at this seaward boundary, and model the wave dynamics towards the shoreline analytically, based on nonlinear shallow water theory over bathymetry with a constant slope. We calculate the run-up heights at the shore and the reflection caused by the slope. The reflected wave is then influxed back into the simulation area using the EBC. The coupling between the numerical and analytic dynamics in the two areas is handled using variational principles, which leads to (approximate) conservation of the overall energy in both areas. We verify our approach in a series of numerical test cases of increasing complexity, including a case akin to tsunami propagation to the coastline at Aceh, Sumatra, Indonesia.

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Solitary Wave Runup on Plane Slopes

Cited by 113 publications

References 12 publications

Runup of Tsunami Waves in U-Shaped Bays

Runup of Tsunami Waves in U-Shaped Bays

Non-breaking and breaking solitary wave run-up

Effective coastal boundary conditions for tsunami wave run-up over sloping bathymetry

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