Run-Up of Long Waves in Piecewise Sloping U-Shaped Bays

Anderson, Donald G.; Harris, M. W.; Hartle, Harrison; Nicolsky, Dmitry; Pelinovsky, Efim; Raz, Amir; Rybkin, Alexei

doi:10.1007/s00024-017-1476-3

Cited by 17 publications

(31 citation statements)

References 25 publications

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“…Following the approach used by Synolakis () and Anderson et al (), we assume that in offshore segment the incoming wave height and velocity are small compared to the bay depth, such that

η ≪ h_{0}

and

u ≪ \sqrt{g h_{0}}

. Under this assumption, higher order terms in the SWEs can be neglected, and the wave is governed by the linear SWEs in Region 1.…”

Section: The Cross‐sectionally Averaged Shallow Water Equationsmentioning

confidence: 99%

“…To transform equation to the linear SWEs, we use the linear CG transform (Anderson et al, ; Massel & Pelinovsky, ). The linear CG transform is given by

\begin{array}{l} left & λ = - g α \tilde{t}, & \tilde{u} = \frac{1}{F (σ)} {normalΦ}_{σ}, \\ left & \tilde{η} = \frac{{normalΦ}_{λ}}{2 g}, & σ = \int_{0}^{\tilde{H}} \sqrt{\frac{g}{S false(\overset{H'}{true} false)} \frac{d S false(\overset{H'}{true} false)}{d \overset{H'}{true}}} d \overset{true\sim}{H'}, \end{array}

where

\tilde{H} = h (\tilde{x}) = α \tilde{x}

.…”

Section: Generalization Of the Tuck‐hwang Transformationmentioning

confidence: 99%

“…An incoming solitary wave centered at x = x 1 is given by (Anderson et al, )

η_{0} (x) = A {sech}^{2} true(\frac{x - x_{1}}{L} true),

where A is the amplitude of the wave and L is a characteristic length. We computed the runup of an incoming solitary wave centered at

x_{1} = 70

m, with an amplitude A = 0.01 m and characteristic length of L = 11.547 m. Both the bay and solitary wave characteristics were chosen to be consistent with Synolakis () and Anderson et al (). We note that these parameters can be scaled by a factor of ten to model a realistic long wave in one of the fjords in Alaska (Anderson et al, ).…”

Section: Validation Of the Csa Swes To Model Runup Of Long Wavesmentioning

confidence: 99%

“…Analytical solutions to the wave profile runup have also been found in more complex bathymetries using the CSA SWEs, for parabolic bays (Didenkulova & Pelinovsky, ) and more generally in U‐shaped and V‐shaped bays (Anderson et al, ; Didenkulova & Pelinovsky, ; Garayshin et al, ; Rybkin et al, ). Preliminary results by Harris et al (), Garayshin et al (), and Anderson et al () show that the runup at the head of the U‐shaped bay computed by the 2‐D SWEs equations and that computed by the CSA SWEs are comparable in height and timing. A limitation of the previously mentioned results for the U‐shaped bays is the symmetric and simple nature of the cross sections of the bathymetries under consideration.…”

Section: Introductionmentioning

confidence: 99%

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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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“…Following the approach used by Synolakis () and Anderson et al (), we assume that in offshore segment the incoming wave height and velocity are small compared to the bay depth, such that

η ≪ h_{0}

and

u ≪ \sqrt{g h_{0}}

. Under this assumption, higher order terms in the SWEs can be neglected, and the wave is governed by the linear SWEs in Region 1.…”

Section: The Cross‐sectionally Averaged Shallow Water Equationsmentioning

confidence: 99%

“…To transform equation to the linear SWEs, we use the linear CG transform (Anderson et al, ; Massel & Pelinovsky, ). The linear CG transform is given by

\begin{array}{l} left & λ = - g α \tilde{t}, & \tilde{u} = \frac{1}{F (σ)} {normalΦ}_{σ}, \\ left & \tilde{η} = \frac{{normalΦ}_{λ}}{2 g}, & σ = \int_{0}^{\tilde{H}} \sqrt{\frac{g}{S false(\overset{H'}{true} false)} \frac{d S false(\overset{H'}{true} false)}{d \overset{H'}{true}}} d \overset{true\sim}{H'}, \end{array}

where

\tilde{H} = h (\tilde{x}) = α \tilde{x}

.…”

Section: Generalization Of the Tuck‐hwang Transformationmentioning

confidence: 99%

“…An incoming solitary wave centered at x = x 1 is given by (Anderson et al, )

η_{0} (x) = A {sech}^{2} true(\frac{x - x_{1}}{L} true),

where A is the amplitude of the wave and L is a characteristic length. We computed the runup of an incoming solitary wave centered at

x_{1} = 70

Section: Validation Of the Csa Swes To Model Runup Of Long Wavesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

et al. 2018

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show abstract

“…Tsunami propagation and runup modelling in bays present difficult challenges. Anderson et al (2017) develop an analytical method to calculate the propagation and runup of long waves in U-shaped bays with piecewise linear slopes, using the Carrier-Greenspan transform. Aydin and Kânoglu (2017) also present new analytical results, in this case for runup on a linear sloping beach under general initial conditions.…”

Section: Tsunami Hydrodynamics and Modellingmentioning

confidence: 99%

Introduction to “Global Tsunami Science: Past and Future, Volume II”

Rabinovich

Fritz

Tanioka

et al. 2017

Pure Appl. Geophys.

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Abstract-Twenty-two papers on the study of tsunamis are included in Volume II of the PAGEOPH topical issue ''Global Tsunami Science: Past and Future''. Volume I of this topical issue was published as PAGEOPH, vol. 173, No. 12, 2016 (Eds., E. L. Geist, H. M. Fritz, A. B. Rabinovich, and Y. Tanioka). Three papers in Volume II focus on details of the 2011 and 2016 tsunamigenerating earthquakes offshore of Tohoku, Japan. The next six papers describe important case studies and observations of recent and historical events. Four papers related to tsunami hazard assessment are followed by three papers on tsunami hydrodynamics and numerical modelling. Three papers discuss problems of tsunami warning and real-time forecasting. The final set of three papers importantly investigates tsunamis generated by non-seismic sources: volcanic explosions, landslides, and meteorological disturbances. Collectively, this volume highlights contemporary trends in global tsunami research, both fundamental and applied toward hazard assessment and mitigation.

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New Analytical Solution for Nonlinear Shallow Water-Wave Equations

Aydın

Kânoğlu

2017

Pure Appl. Geophys.

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Run-Up of Long Waves in Piecewise Sloping U-Shaped Bays

Cited by 17 publications

References 25 publications

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

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

Introduction to “Global Tsunami Science: Past and Future, Volume II”

New Analytical Solution for Nonlinear Shallow Water-Wave Equations

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