Two- and three-dimensional computation of solitary wave runup on non-plane beach

Choi, Byung Ho; Pelinovsky, Efim; Kim, D. C.; Didenkulova, Ira; Woo, Seung‐Buhm

doi:10.5194/npg-15-489-2008

Cited by 54 publications

(37 citation statements)

References 27 publications

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“…This technique has remained popular ever since and had a resurge after the formula for solitary wave run-up was published by Synolakis (1987). However, the technique is limited to hydrostatic equations and, save for a few exceptions (Kânoǧlu and Synolakis, 1998;Choi et al, 2008;Didenkulova and Pelinovsky, 2009) to plane slopes as well. Moreover, non-linear specifications of initial conditions are cumbersome due to the transformation technique, while the transformation back to the physical plane generally requires numerical integration.…”

Section: Run-up Modeling With Depth Integrated Equationsmentioning

confidence: 99%

Simulating run-up on steep slopes with operational Boussinesq models; capabilities, spurious effects and instabilities

Løvholt

Lynett

Pedersen

2013

Nonlin. Processes Geophys.

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Tsunamis induced by rock slides plunging into fjords constitute a severe threat to local coastal communities. The rock slide impact may give rise to highly non-linear waves in the near field, and because the wave lengths are relatively short, frequency dispersion comes into play. Fjord systems are rugged with steep slopes, and modeling non-linear dispersive waves in this environment with simultaneous run-up is demanding. We have run an operational Boussinesq-type TVD (total variation diminishing) model using different run-up formulations. Two different tests are considered, inundation on steep slopes and propagation in a trapezoidal channel. In addition, a set of Lagrangian models serves as reference models. Demanding test cases with solitary waves with amplitudes ranging from 0.1 to 0.5 were applied, and slopes were ranging from 10 to 50°. Different run-up formulations yielded clearly different accuracy and stability, and only some provided similar accuracy as the reference models. The test cases revealed that the model was prone to instabilities for large non-linearity and fine resolution. Some of the instabilities were linked with false breaking during the first positive inundation, which was not observed for the reference models. None of the models were able to handle the bore forming during drawdown, however. The instabilities are linked to short-crested undulations on the grid scale, and appear on fine resolution during inundation. As a consequence, convergence was not always obtained. It is reason to believe that the instability may be a general problem for Boussinesq models in fjords

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Section: Run-up Modeling With Depth Integrated Equationsmentioning

confidence: 99%

Simulating run-up on steep slopes with operational Boussinesq models; capabilities, spurious effects and instabilities

Løvholt

Lynett

Pedersen

2013

Nonlin. Processes Geophys.

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“…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%

“…The runup height discussed above is computed in the framework of the linear theory. At the same time in the case of the parabolic bay with linearly inclined bottom profile in longitudinal direction it is possible to find the solution of the nonlinear problem using the Legendre transformation (19)-(22) (see Zahibo et al, 2006;Choi et al, 2008 …”

Section: Runup Of Tsunami Waves In U-shaped Bays Of "Non-reflecting" mentioning

confidence: 99%

“…Meanwhile for certain bathymetry configurations the wave can propagate without internal reflection even in the cases, when the depth varies strongly along the wave path. Such effects have been studied early for 1D wave propagation (Clements and Rogers, 1975;Didenkulova et al, 2008; and recently for channels of a parabolic cross-section . With an application to a tsunami problem it means that destructive tsunami wave can propagate over large distances without reflection and transfers all its energy to the coast that leads to an abnormal wave amplification and runup.…”

Section: Introductionmentioning

confidence: 99%

“…At the same time approximation of a rectangular cross-section does not correspond to natural narrow bays, which bottom configuration varies in both longitudinal and transversal directions. The runup of long nonlinear waves in narrow basins of special geometries is analyzed in Choi et al, 2008).…”

Section: Introductionmentioning

confidence: 99%

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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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Long Wave Runup in Asymmetric Bays and in Fjords With Two Separate Heads

et al. 2018

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Modeling of tsunamis in glacial fjords prompts us to evaluate applicability of the cross‐sectionally averaged nonlinear shallow water equations to model propagation and runup of long waves in asymmetrical bays and also in fjords with two heads. We utilize the Tuck‐Hwang transformation, initially introduced for the plane beaches and currently generalized for bays with arbitrary cross section, to transform the nonlinear governing equations into a linear equation. The solution of the linearized equation describing the runup at the shore line is computed by taking into account the incident wave at the toe of the last sloping segment. We verify our predictions against direct numerical simulation of the 2‐D shallow water equations and show that our solution is valid both for bays with an asymmetric L‐shaped cross section, and for fjords with two heads—bays with a W‐shaped cross section.

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Two- and three-dimensional computation of solitary wave runup on non-plane beach

Cited by 54 publications

References 27 publications

Simulating run-up on steep slopes with operational Boussinesq models; capabilities, spurious effects and instabilities

Simulating run-up on steep slopes with operational Boussinesq models; capabilities, spurious effects and instabilities

Runup of Tsunami Waves in U-Shaped Bays

Long Wave Runup in Asymmetric Bays and in Fjords With Two Separate Heads

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