Run-up of long solitary waves of different polarities on a plane beach

Didenkulova, Ira; Pelinovsky, Efim; Didenkulov, Oleg

doi:10.1134/s000143381405003x

Cited by 12 publications

(2 citation statements)

References 19 publications

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“…In this paper, we study this effect both analytically and numerically. Analytically, we apply the methodology developed in (Didenkulova 2009;Didenkulova et al 2014), where we consider the processes of wave propagation in the basin of constant depth and the following wave run-up on a plane beach independently, not taking into account the point of merging of these two bathymetries. Numerically, we solve the nonlinear shallow water equations.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear deformation and run-up of single tsunami waves of positive polarity: numerical simulations and analytical predictions

Abdalazeez¹,

Didenkulova²,

Dutykh³

2019

Preprint

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The estimate of individual wave run-up is especially important for tsunami warning and risk assessment as it allows to evaluate the inundation area. Here as a model of tsunami we use the long single wave of positive polarity. The period of such wave is rather long which makes it different from the famous Korteweg-de Vries soliton. This wave nonlinearly deforms during its propagation in the ocean, what results in a steep wave front formation. Situations, when waves approach the coast with a steep front are often observed during large tsunamis, e.g. 2004 Indian Ocean and 2011 Tohoku tsunamis. Here we study the nonlinear deformation and run-up of long single waves of positive polarity in the conjoined water basin, which consists of the constant depth section and a plane beach. The work is performed numerically and analytically in the framework of the nonlinear shallow water theory. Analytically, wave propagation along the constant depth section and its run-up on a beach are considered independently without taking into account wave interaction with the toe of the bottom slope. The propagation along the bottom of constant depth is described by Riemann wave, while the waverun-up on a plane beach is calculated using rigorous analytical solutions of the nonlinear shallow water theory following the Carrier-Greenspan approach. Numerically, we use the finite volume method with the second order UNO2 reconstruction in space and the third order Runge-Kutta scheme with locally adaptive time steps. During wave propagation along the constant depth section, the wave becomes asymmetric with a steep wave front. Shown, that the maximum run-up height depends on the front steepness of the incoming wave approaching the toe of the bottom slope. The corresponding formula for maximum run-up height, which takes into account the wave front steepness, is proposed.

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Section: Introductionmentioning

confidence: 99%

Nonlinear deformation and run-up of single tsunami waves of positive polarity: numerical simulations and analytical predictions

Abdalazeez¹,

Didenkulova²,

Dutykh³

2019

Preprint

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“…This scenario is common in the analysis based on nondispersive shallow-water propagation in wave systems led by a wave of depression. Such systems are particularly prone to the formation of steep slopes and high velocities (Didenkulova et al, 2014). This is a probable reason why ship-induced depression waves often play an unexpectedly large role in sediment resuspension (Rapaglia et al, 2011;Gelinas et al, 2013;Göransson et al, 2014).…”

mentioning

confidence: 99%

Numerical simulation of the propagation of ship-induced Riemann waves of depression into the Venice Lagoon

Rodin¹,

Soomere²,

Parnell³

et al. 2015

Proc. Estonian Acad. Sci.

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Large in situ measured ship-induced depression waves (Bernoulli wakes) in the Malamocco-Marghera industrial channel of the Venice Lagoon are interpreted as long-living strongly nonlinear Riemann (simple) waves of depression. The properties of these depressions are numerically replicated using nonlinear shallow water theory and the CLAWPACK software. The further behaviour of measured depressions is analysed by means of replicating the vessel-induced disturbances with the propagation of initially smooth free waves. It is demonstrated that vessel-driven depressions of substantial height (> 0.3 m) often propagate for more than 1 km from the navigation channel into areas of the lagoon of approximately 2 m water depth. As a depression wave propagates into the lagoon, its front slope becomes gradually less steep, but the rear slope preserves an extremely steep bore-like appearance and the amplitude becomes almost independent of the initial properties of the disturbance. Analysis suggests that even modest ships in terms of their size, sailing speed, and blocking coefficient may generate deep depressions that travel as compact and steep entities resembling asymmetric solitary waves over substantial distances into shallow water adjacent to navigation channels. Their impact may substantially increase the environmental impact of ship wakes in this and similar water bodies.

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Numerical Study for Run-Up of Breaking Waves of Different Polarities on a Sloping Beach

Rodin

Didenkulova

Pelinovsky

2015

Extreme Ocean Waves

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Run-up of long solitary waves of different polarities on a plane beach

Cited by 12 publications

References 19 publications

Nonlinear deformation and run-up of single tsunami waves of positive polarity: numerical simulations and analytical predictions

Nonlinear deformation and run-up of single tsunami waves of positive polarity: numerical simulations and analytical predictions

Numerical simulation of the propagation of ship-induced Riemann waves of depression into the Venice Lagoon

Numerical Study for Run-Up of Breaking Waves of Different Polarities on a Sloping Beach

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