Tsunami runup on a sloping beach

Чугунов, В. А.; Fomin, Sergei; Noland, William; Sagdiev, Bayazit R.

doi:10.1002/cmm4.1081

Cited by 8 publications

(12 citation statements)

References 10 publications

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“…extending along the y axis infinitely far). In this case, as one can easily see, (7) takes the specifically simple form…”

Section: Introductionmentioning

confidence: 99%

“…Mathematically rigorous treatment of SWE including the well-posedness and exact solutions can be found in Dobrokhotov and Tirozzi [19], Dobrokhotov et al [17,18], Alekseenko et al [1] and references therein. It is worth mentioning that IVP for SWE have been treated in Chugunov et al [7,8] using a perturbation approach.…”

Section: Introductionmentioning

confidence: 99%

“…The latter is, in general, not explicit but can easily be done numerically without affecting the total accuracy, which remains O (ε) . In fact, we can call our method exact as the error it introduces can be made negligible comparing with the one inherited by the shallow water approximation leading to the very SWE (7). Loosely speaking, the idea behind our method is to replace the IVP we cannot solve with an equivalent one we can.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The Generalized Carrier–Greenspan Transform for the Shallow Water System with Arbitrary Initial and Boundary Conditions

et al. 2020

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We put forward a solution to the initial boundary value (IBV) problem for the nonlinear shallow water system in inclined channels of arbitrary cross section by means of the generalized Carrier-Greenspan hodograph transform (Rybkin et al. in J Fluid Mech, 748:416-432, 2014). Since the Carrier-Greenspan transform, while linearizing the shallow water system, seriously entangles the IBV in the hodograph plane, all previous solutions required some restrictive assumptions on the IBV conditions, e.g., zero initial velocity, smallness of boundary conditions. For arbitrary non-breaking initial conditions in the physical space, we present an explicit formula for equivalent IBV conditions in the hodograph plane, which can readily be treated by conventional methods. Our procedure, which we call the method of data projection, is based on the Taylor formula and allows us to reduce the transformed IBV data given on curves in the hodograph plane to the equivalent data on lines. Our method works equally well for any inclined bathymetry (not only plane beaches) and, moreover, is fully analytical for U-shaped bays. Numerical simulations show that our method is very robust and can be used to give express forecasting of tsunami wave inundation in narrow bays and fjords.

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“…extending along the y axis infinitely far). In this case, as one can easily see, (7) takes the specifically simple form…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

The Generalized Carrier–Greenspan Transform for the Shallow Water System with Arbitrary Initial and Boundary Conditions

et al. 2020

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“…As a result, several particular analytical solutions were obtained. Chugunov et al [11] effectively applied the approximate approach for solving exactly the same problem, with the same seafloor geometry as used in [3,4] (see Figure 1). In [11], it was shown that the approximate method works well and, therefore, can be potentially applied to the problems with more complex seafloor topography.…”

Section: Introductionmentioning

confidence: 99%

Quasi-Linear Model of Tsunami Run-Up on a Beach with a Seafloor Described by the Piecewise Continuous Function

2022

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The purpose of this paper is to propose the quasi-linear theory of tsunami run-up and run-down on a beach with complex bottom topography. We begin with the one-dimensional nonlinear shallow-water wave equations, which we consider over a beach of complex geometry that can be modeled by a piecewise continuous function, along with several natural initial and boundary conditions. The primary obstacle in solving this problem is the moving boundary associated with the shoreline motion. To avoid this difficulty, we replace the moving boundary with a stationary boundary by applying a transformation to the spatial variable of the computational domain. A characteristic feature of any tsunami problem is the smallness of the parameter ε=η0/h0, where η0 is the characteristic amplitude of the wave, and h0 is the characteristic depth of the ocean. The presence of this small parameter enables us to effectively linearize the problem by using the method of perturbations, which leads to an analytical solution via an integral transformation. This analytical solution assumes that there is no wave breaking. In light of this assumption, we introduce the wave no-breaking criterion and determine bounds for the applicability of our theory. The proposed model can be readily used to investigate the tsunami run-up and draw-down for different sea bottom profiles. The novel particular solution, when the seafloor is described by the piecewise linear function, is obtained, and the effects of the different beach profiles and initial wave locations are considered.

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“…Mathematically rigorous treatment of SWE including the well-posedness and exact solutions can be found in ; Dobrokhotov et al ( , 2013, Alekseenko et al (2017) and references therein. It is worth mentioning that IVP for SWE have been treated in Chugunov et al (2014Chugunov et al ( , 2020 using a perturbation approach.…”

Section: Introductionmentioning

confidence: 99%

The Generalized Carrier-Greenspan Transform for the shallow water system with arbitrary initial and boundary conditions

Rybkin,

Nicolsky,

Pelinovsky

et al. 2020

Preprint

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We put forward a solution to the initial boundary value (IBV) problem for the nonlinear shallow water system in inclined channels of arbitrary cross-section by means of the generalized Carrier-Greenspan hodograph transform (Rybkin et al., 2014). Since the Carrier-Greenspan transform, while linearizing the shallow water system, seriously entangles the IBV in the hodograph plane, all previous solutions required some restrictive assumptions on the IBV conditions, e.g., zero initial velocity, smallness of boundary conditions. For arbitrary non-breaking initial conditions in the physical space, we present an explicit formula for equivalent IBV conditions in the hodograph plane, which can readily be treated by conventional methods. Our procedure, which we call the method of data projection, is based on the Taylor formula and allows us to reduce the transformed IBV data given on curves in the hodograph plane to the equivalent data on lines. Our method works equally well for any inclined bathymetry (not only plane beaches)

show abstract

Tsunami runup on a sloping beach

Cited by 8 publications

References 10 publications

The Generalized Carrier–Greenspan Transform for the Shallow Water System with Arbitrary Initial and Boundary Conditions

The Generalized Carrier–Greenspan Transform for the Shallow Water System with Arbitrary Initial and Boundary Conditions

Quasi-Linear Model of Tsunami Run-Up on a Beach with a Seafloor Described by the Piecewise Continuous Function

The Generalized Carrier-Greenspan Transform for the shallow water system with arbitrary initial and boundary conditions

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