Statistical estimates of characteristics of long-wave run-up on a beach

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.

Section: Introductionmentioning

confidence: 99%

“…The connection of the run-up parameters at the nonlinear stage with the linear field at a fixed point is described either in a parametric form or implicitly in the nonlinear equation (Didenkulova et al, 2010). This does not allow for using the standard methods of random processes.…”

Section: Introductionmentioning

confidence: 99%

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

Гурбатов

Pelinovsky

2019

“…We focused our attention on wave run-up prediction; wave run-up prediction is required in most coastal vulnerability and risk evaluation projects (Didenkulova and Pelinovsky, 2008;Didenkulova et al, 2010). Wave run-up (Ru) is defined as "the landward extent of wave uprush measured vertically from the still water level" (Melby et al, 2012).…”

Section: Introductionmentioning

confidence: 99%

Wave run-up prediction and observation in a micro-tidal beach

Luccio

Benassai

Budillon

et al. 2018

Abstract. Extreme weather events bear a significant impact on coastal human activities and on the related economy. Forecasting and hindcasting the action of sea storms on piers, coastal structures and beaches is an important tool to mitigate their effects. To this end, with particular regard to low coasts and beaches, we have developed a computational model chain based partly on open-access models and partly on an ad-hoc-developed numerical calculator to evaluate beach wave run-up levels and flooding. The offshore wave simulations are carried out with a version of the WaveWatch III model, implemented by CCMMMA (Campania Centre for Marine and Atmospheric Monitoring and Modelling – University of Naples Parthenope), validated with remote-sensing data. The waves thus computed are in turn used as initial conditions for the run-up calculations, carried out with various empirical formulations; the results were finally validated by a set of specially conceived video-camera-based experiments on a micro-tidal beach located on the Ligurian Sea. Statistical parameters are provided on the agreement between the computed and observed values. It appears that, while the system is a useful tool to properly simulate beach flooding during a storm, empirical run-up formulas, when used in a coastal vulnerability context, have to be carefully chosen, applied and managed, particularly on gravel beaches.

“…It is important to mention that the run-up height is higher if a periodic incident wave is cnoidal or a nonlinearly deformed wave compared with a simple sine wave of the same amplitude and period. Some results are obtained for irregular incident waves modeled by the Fourier superposition of the sine waves with random phases (Didenkulova et al, 2010(Didenkulova et al, , 2011 or the random set of solitons (Brocchini and Gentile, 2001).…”

mentioning

confidence: 99%

Resonance phenomena at the long wave run-up on the coast

Ezersky

Tiguercha

Pelinovsky

2013

Abstract. Run-up of long waves on a beach consisting of three pieces of constant but different slopes is studied. Linear shallow-water theory is used for incoming impulse evolution, and nonlinear corrections are obtained for the run-up stage. It is demonstrated that bottom profile influences the run-up characteristics and can lead to resonance effects: increase of wave height, particle velocity, and number of oscillations. Simple parameterization of tsunami source through an earthquake magnitude is used to calculate the run-up height versus earthquake magnitude. It is shown that resonance effects lead to the sufficient increase of run-up heights for the weakest earthquakes, and a tsunami wave does not break on chosen bottom relief if the earthquake magnitude does not exceed 7.8.