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

Raz, Amir; Nicolsky, Dmitry; Rybkin, Alexei; Pelinovsky, Efim

doi:10.1002/2017jc013100

Cited by 11 publications

(13 citation statements)

References 31 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It is determined only by the particle acceleration value on the shoreline, but it is not determined separately by the shoreline displacement or its velocity. The similar Carrier-Greenspan transformation is obtained for waves in narrow-inclined channels, fjords, and bays (Rybkin et al, 2014;Pedersen, 2016;Anderson et al, 2017;Raz et al, 2018); only the wave equation (Eq. 4) and relations (Eqs.…”

Section: Basic Equations and Transformationsmentioning

confidence: 57%

“…The latter means the presence of steep fronts (the gradient catastrophe) within the hyperbolic shallow-water equation framework. The Carrier-Greenspan transformation was further generalized for the case of waves in an inclined channel of an arbitrary variable cross section (Rybkin et al, 2014;Pedersen, 2016;Shimozono, 2016;Anderson et al, 2017;Raz et al, 2018). In a number of practical cases, its use proves to be more efficient than the direct numerical computation within the 2-D shallow-water equation framework (Harris et al, 2015(Harris et al, , 2016.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Probabilistic characteristics of narrow-band long-wave run-up onshore

Гурбатов

Pelinovsky

2019

Nat. Hazards Earth Syst. Sci.

Self Cite

View full text Add to dashboard Cite

The run-up of random long-wave ensemble (swell, storm surge, and tsunami) on the constant-slope beach is studied in the framework of the nonlinear shallow-water theory in the approximation of non-breaking waves. If the incident wave approaches the shore from the deepest water, run-up characteristics can be found in two stages: in the first stage, linear equations are solved and the wave characteristics at the fixed (undisturbed) shoreline are found, and in the second stage the nonlinear dynamics of the moving shoreline is studied by means of the Riemann (nonlinear) transformation of linear solutions. In this paper, detailed results are obtained for quasi-harmonic (narrow-band) waves with random amplitude and phase. It is shown that the probabilistic characteristics of the run-up extremes can be found from the linear theory, while the same ones of the moving shoreline are from the nonlinear theory. The role of wave-breaking due to large-amplitude outliers is discussed, so that it becomes necessary to consider wave ensembles with non-Gaussian statistics within the framework of the analytical theory of nonbreaking waves. The basic formulas for calculating the probabilistic characteristics of the moving shoreline and its velocity through the incident wave characteristics are given. They can be used for estimates of the flooding zone characteristics in marine natural hazards.

show abstract

Section: Basic Equations and Transformationsmentioning

confidence: 57%

Section: Introductionmentioning

confidence: 99%

Probabilistic characteristics of narrow-band long-wave run-up onshore

Гурбатов

Pelinovsky

2019

Nat. Hazards Earth Syst. Sci.

Self Cite

View full text Add to dashboard Cite

show abstract

“…More recently, the CG transform was generalized to inclined bathymetries of arbitrary cross section [34]. In Raz et al [33], we finally show that the very same substitution (10a)-(10b) brings (1) to the linear system…”

Section: Introductionmentioning

confidence: 52%

“…For all other shapes (14) can effectively be solved and analyzed numerically. See Harris et al [21,22] and Raz et al [33] where detailed analysis is done for trapezoidal, L, W, and other shapes. We also refer to Anderson et al [2] for some extensions to piece-wise inclined power bays.…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2020

Self Cite

View full text Add to dashboard Cite

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.

show abstract

“…However, pointed out that the solitons are inappropriate for describing the real tsunami and proposed to use waves of longer duration than solitons and downscaled records of real tsunami. Schimmels et al (2016) and Sriram et al (2016) generated such long waves in the Large Wave Flume of Hanover (GWK FZK) using the piston type of wave maker, while McGovern et al (2018) did it using the pneumatic wave generator.…”

Section: Introductionmentioning

confidence: 99%

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

Abdalazeez

Didenkulova

Dutykh

2019

Nat. Hazards Earth Syst. Sci.

View full text Add to dashboard Cite

Abstract. The estimate of an individual wave run-up is especially important for tsunami warning and risk assessment, as it allows for evaluating the inundation area. Here, as a model of tsunamis, we use the long single wave of positive polarity. The period of such a 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, which results in a steep wave front formation. Situations in which waves approach the coast with a steep front are often observed during large tsunamis, e.g. the 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 the Riemann wave, while the wave run-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. It is 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.

show abstract

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

Cited by 11 publications

References 31 publications

Probabilistic characteristics of narrow-band long-wave run-up onshore

Probabilistic characteristics of narrow-band long-wave run-up onshore

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

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

Contact Info

Product

Resources

About