Journal ArticleDOI
Tsunami run-up and draw-down on a plane beach
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In this article, the authors evaluated tsunami run-up and draw-down motions on a uniformly sloping beach based on fully nonlinear shallow-water wave theory and found that the maximum flow velocity occurs at the moving shoreline and the maximum momentum flux occurs in the vicinity of the extreme drawdown location.Abstract:
Tsunami run-up and draw-down motions on a uniformly sloping beach are evaluated based on fully nonlinear shallow-water wave theory. The nonlinear equations of mass conservation and linear momentum are first transformed to a single linear hyperbolic equation. To solve the problem with arbitrary initial conditions, we apply the Fourier–Bessel transform, and inversion of the transform leads to the Green function representation. The solutions in the physical time and space domains are then obtained by numerical integration. With this semi-analytic solution technique, several examples of tsunami run-up and draw-down motions are presented. In particular, detailed shoreline motion, velocity field, and inundation depth on the shore are closely examined. It was found that the maximum flow velocity occurs at the moving shoreline and the maximum momentum flux occurs in the vicinity of the extreme draw-down location. The direction of both the maximum flow velocity and the maximum momentum flux depend on the initial waveform: it is in the inshore direction when the initial waveform is predominantly depression and in the offshore direction when the initial waves have a dominant elevation characteristic.read more
Citations
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SWASH: An operational public domain code for simulating wave fields and rapidly varied flows in coastal waters
TL;DR: In this article, a computational procedure has been developed for simulating non-hydrostatic, free-surface, rotational flows in one and two horizontal dimensions using SWASH.
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On the solitary wave paradigm for tsunamis
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Tsunami modelling with adaptively refined finite volume methods
TL;DR: These issues are discussed in the context of Riemann-solver-based finite volume methods for tsunami modelling in a ‘wellbalanced’ manner and also apply to a variety of other geophysical flows.
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Tsunami science before and beyond Boxing Day 2004
TL;DR: The progress towards developing tsunami inundation modelling tools for use in inundation forecasting is discussed historically from the perspective of hydrodynamics, and the state-of-knowledge before the 26 December 2004 tsunami is described.
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Validation and Verification of Tsunami Numerical Models
Costas E. Synolakis,Eddie N. Bernard,Vasily V. Titov,Vasily V. Titov,Utku Kânoğlu,Frank I. Gonzalez +5 more
TL;DR: Analytical, laboratory, and field benchmark tests with which tsunami numerical models can be validated and verified are discussed.
References
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Journal ArticleDOI
The runup of solitary waves
TL;DR: In this article, an approximate theory is presented for non-breaking waves and an asymptotic result is derived for the maximum runup of solitary waves on plane beaches, and a series of laboratory experiments is described to support the theory.
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Handbook of Mathematical Functions, with Formulas, Graphs, and Mathematical Tables
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Water waves of finite amplitude on a sloping beach
TL;DR: In this paper, the authors investigated the behavior of a wave as it climbs a sloping beach and obtained explicit solutions of the equations of the non-linear inviscid shallow-water theory for several physically interesting wave-forms.
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The run-up of N-waves on sloping beaches
TL;DR: In this paper, the authors used a first-order theory and derived asymptotic results for the maximum run-up within the validity of the theory for different types of N -waves.
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Exact analytical solutions of nonlinear problems of tsunami wave run-up on slopes with different profiles
Efim Pelinovsky,R. Kh. Mazova +1 more
TL;DR: In this paper, a stage-by-stage approach for finding run-up characteristics is formulated: the linear calculation of shoreline oscillations and the subsequent non-linear transformation of the solution according to the Riemann method.