scholarly journals ARE SOLITARY WAVES THE LIMITING WAVES IN LONG WAVE RUNUP?

1988 ◽  
Vol 1 (21) ◽  
pp. 14 ◽  
Author(s):  
Costas Emmanuel Synolakis
Keyword(s):  
Solitary Waves ◽  
Laboratory Data ◽  
Long Waves ◽  
Wave Runup ◽  
Long Wave ◽  
Limiting Condition

This is a study of the maximum runup of single long waves on plane beaches. Laboratory data are presented that suggest that solitary waves attain the higher runup distances than other single long waves with identical generation characteristics, such as energy or momentum. These results suggest that solitary waves may provide a limiting condition for long wave runup on plane beaches.

scholarly journals A UNIFIED RUNUP FORMULA FOR BREAKING SOLITARY WAVES ON A UNIFORM BEACH

2018 ◽  
pp. 3
Author(s):  
Yun-Ta Wu ◽  
Philip Li-Fan Liu ◽  
Philip Li-Fan Liu ◽  
Kao-Shu Hwang ◽  
Kao-Shu Hwang ◽  
...  
Keyword(s):  
Solitary Wave ◽  
Solitary Waves ◽  
Large Scale ◽  
Storm Surges ◽  
Research Area ◽  
Easy Access ◽  
Wave Runup ◽  
Wave Flume ◽  
Long Wave ◽  
Analytical Approaches

For coastal management, it is of great importance to understand long-wave induced runup processes and predict maximum runup heights. Long-wave in nature could take different forms, such as swells, storm surges and tsunamis. One of the fundamental waveforms is solitary wave, which has a permanent form in a constant depth. Thus, the issue of solitary wave propagation, shoaling, breaking and runup has been an active research area in coastal engineering community, using experimental, numerical and analytical approaches. Among existing runup experiments, only limited numbers of experiments were conducted in large-scale wave flume facilities because of the lack of easy access. To enhance the range of surf parameters for breaking solitary waves, new laboratory experiments were carried out in a large-scale wave flume with a 1/100 slope. Several wave conditions in the experiments were on the borderline of plunging and spilling breakers. The main objective of this paper is twofold. The first aim is to present a new dataset for solitary wave runup. The second objective aims to develop a unified empirical formula, based on the available runup data in the literature and the present new data, for the runup of breaking solitary waves on a uniform slope.

Long wave runup on piecewise linear topographies

1998 ◽  
Vol 374 ◽  
pp. 1-28 ◽  
Author(s):  
UTKU KÂNOĞLU ◽  
COSTAS EMMANUEL SYNOLAKIS
Keyword(s):  
Solitary Waves ◽  
Numerical Models ◽  
Piecewise Linear ◽  
Physical Parameters ◽  
Wave Runup ◽  
Asymptotic Results ◽  
Tidal Waves ◽  
Topographic Slope ◽  
Long Wave ◽  
Time Histories

We study long-wave evolution and runup on piecewise linear one- and two-dimensional bathymetries analytically and experimentally with the objective of understanding certain coastal effects of tidal waves. We develop a general solution method for determining the amplification factor of different ocean topographies consisting of linearly varying and constant-depth segments to study how spectral distributions evolve over bathymetry, and apply our results to study the evolution of solitary waves. We find asymptotic results which suggest that solitary waves often interact with piecewise linear topographies in a counter-intuitive manner. We compare our analytical predictions with numerical results, with results from a new set of laboratory experiments from a physical model of Revere Beach, and also with the data on wave runup around an idealized conical island. We find good agreement between our theory and the laboratory results for the time histories of free-surface elevations and for the maximum runup heights. Our results suggest that, at least for simple piecewise linear topographies, analytical methods can be used to calculate effectively some important physical parameters in long-wave runup. Also, by underscoring the effects of the topographic slope at the shoreline, this analysis qualitatively suggests why sometimes predictions of field-applicable numerical models differ substantially from observations of tsunami runup.

Long wave generation by the shoaling and breaking of transient wave groups on a beach

2006 ◽  
Vol 462 (2070) ◽  
pp. 1853-1876 ◽  
Author(s):  
T.E Baldock
Keyword(s):  
Shallow Water ◽  
Water Waves ◽  
Surf Zone ◽  
Laboratory Data ◽  
Short Wave ◽  
Long Waves ◽  
Transient Wave ◽  
Wave Groups ◽  
Spatial Gradients ◽  
Long Wave

This paper presents new laboratory data on the generation of long waves by the shoaling and breaking of transient-focused short-wave groups. Direct offshore radiation of long waves from the breakpoint is shown experimentally for the first time. High spatial resolution enables identification of the relationship between the spatial gradients of the short-wave envelope and the long-wave surface. This relationship is consistent with radiation stress theory even well inside the surf zone and appears as a result of the strong nonlinear forcing associated with the transient group. In shallow water, the change in depth across the group leads to asymmetry in the forcing which generates significant dynamic setup in front of the group during shoaling. Strong amplification of the incident dynamic setup occurs after short-wave breaking. The data show the radiation of a transient long wave dominated by a pulse of positive elevation, preceded and followed by weaker trailing waves with negative elevation. The instantaneous cross-shore structure of the long wave shows the mechanics of the reflection process and the formation of a transient node in the inner surf zone. The wave run-up and relative amplitude of the radiated and incident long waves suggests significant modification of the incident bound wave in the inner surf zone and the dominance of long waves generated by the breaking process. It is proposed that these conditions occur when the primary short waves and bound wave are not shallow water waves at the breakpoint. A simple criterion is given to determine these conditions, which generally occur for the important case of storm waves.

Resonance of Long Wave Runup on South China Sea’s Piecewise Topographies

2017 ◽  
Vol 11 (01) ◽  
pp. 1740003 ◽  
Author(s):  
Xi Zhao ◽  
Hua Liu
Keyword(s):  
South China Sea ◽  
South China ◽  
Shallow Water Equations ◽  
Long Waves ◽  
Propagation Path ◽  
Wave Runup ◽  
Resonant Frequencies ◽  
Tsunami Waves ◽  
Long Wave ◽  
Resonant Phenomena

Solving the linear shallow water equations on a profile of four segments and matching the solutions on the turning points, runup of periodic long waves is obtained analytically. The resonant phenomena appear when periodic long waves propagate on piecewise topographies. According to the propagation path of tsunami waves, several profiles in the South China Sea are picked up. The topographies can be simplified to a four-segments profile which comprises a horizontal deep seabed, a continental foundation, a continental slope and a continental shelf from the trench to the shore. The runup amplification are calculated both analytically and numerically. Resonant phenomena appear and the values of runup are quite large at the resonant frequencies.

scholarly journals On Galilean Invariant and Energy Preserving BBM-Type Equations

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 878
Author(s):  
Alexei Cheviakov ◽  
Denys Dutykh ◽  
Aidar Assylbekuly
Keyword(s):  
Wave Equation ◽  
Conservation Laws ◽  
Numerical Simulations ◽  
Solitary Waves ◽  
Local Symmetry ◽  
Symmetry And Conservation Laws ◽  
Higher Order ◽  
Special Equation ◽  
Long Wave ◽  
Local Symmetries

We investigate a family of higher-order Benjamin–Bona–Mahony-type equations, which appeared in the course of study towards finding a Galilei-invariant, energy-preserving long wave equation. We perform local symmetry and conservation laws classification for this family of Partial Differential Equations (PDEs). The analysis reveals that this family includes a special equation which admits additional, higher-order local symmetries and conservation laws. We compute its solitary waves and simulate their collisions. The numerical simulations show that their collision is elastic, which is an indication of its S−integrability. This particular PDE turns out to be a rescaled version of the celebrated Camassa–Holm equation, which confirms its integrability.

On periodic water-waves and their convergence to solitary waves in the long-wave limit

1981 ◽  
Vol 303 (1481) ◽  
pp. 633-669 ◽  
Keyword(s):  
Integral Equation ◽  
Solitary Waves ◽  
Water Waves ◽  
Periodic Problem ◽  
Existence Theory ◽  
Periodic Waves ◽  
Equation Formulation ◽  
Long Wave ◽  
Integral Equation Formulation ◽  
Wave Limit

A detailed discussion of Nekrasov’s approach to the steady water-wave problems leads to a new integral equation formulation of the periodic problem. This development allows the adaptation of the methods of Amick & Toland (1981) to show the convergence of periodic waves to solitary waves in the long-wave limit. In addition, it is shown how the classical integral equation formulation due to Nekrasov leads, via the Maximum Principle, to new results about qualitative features of periodic waves for which there has long been a global existence theory (Krasovskii 1961, Keady & Norbury 1978).

5. Long Waves and Conjunctures of Democratization

2018 ◽  
pp. 67-81
Author(s):  
Dirk Berg-Schlosser
Keyword(s):  
Eighteenth Century ◽  
Long Waves ◽  
Political Equality ◽  
Short Term ◽  
Late Eighteenth Century ◽  
Long Wave ◽  
Late Eighteenth ◽  
The Future ◽  
History Of

This chapter focuses on the history of democratization since the late eighteenth century. It introduces the concepts of ‘waves’ (trends) and ‘conjunctures’ (briefer turmoils) and delineates the major developments in this respect. In this way, the major long-term and short-term factors leading to the emergence and breakdowns of democracies are also highlighted. The first long wave occurred during the period 1776–1914, followed by the first positive conjuncture in 1918–19, the second long wave (with some intermittent turbulences) in 1945–88, and the latest conjuncture in 1989–90. The chapter identifies the main ingredients to democratization throughout history, namely: republicanism, representation, and political equality. It concludes by considering some of the current perspectives and dangers for the future of democracy.

scholarly journals Estimation of Irregular Wave Runup on Intermediate and Reflective Beaches Using a Phase-Resolving Numerical Model

2020 ◽  
Vol 8 (12) ◽  
pp. 993
Author(s):  
Jonas Pinault ◽  
Denis Morichon ◽  
Volker Roeber
Keyword(s):  
Time Series ◽  
Best Practices ◽  
Numerical Models ◽  
Laboratory Data ◽  
Irregular Waves ◽  
Wave Transformation ◽  
Model Parameters ◽  
Wave Runup ◽  
Data Set ◽  
Promising Alternative

Accurate wave runup estimations are of great interest for coastal risk assessment and engineering design. Phase-resolving depth-integrated numerical models offer a promising alternative to commonly used empirical formulae at relatively low computational cost. Several operational models are currently freely available and have been extensively used in recent years for the computation of nearshore wave transformations and runup. However, recommendations for best practices on how to correctly utilize these models in computations of runup processes are still sparse. In this work, the Boussinesq-type model BOSZ is applied to calculate runup from irregular waves on intermediate and reflective beaches. The results are compared to an extensive laboratory data set of LiDAR measurements from wave transformation and shoreline elevation oscillations. The physical processes within the surf and swash zones such as the transfer from gravity to infragravity energy and dissipation are accurately accounted for. In addition, time series of the shoreline oscillations are well captured by the model. Comparisons of statistical values such as R2% show relative errors of less than 6%. The sensitivity of the results to various model parameters is investigated to allow for recommendations of best practices for modeling runup with phase-resolving depth-integrated models. While the breaking index is not found to be a key parameter for the examined cases, the grid size and the threshold depth, at which the runup is computed, are found to have significant influence on the results. The use of a time series, which includes both amplitude and phase information, is required for an accurate modeling of swash processes, as shown by computations with different sets of random waves, displaying a high variability and decreasing the agreement between the experiment and the model results substantially. The infragravity swash SIG is found to be sensitive to the initial phase distribution, likely because it is related to the short wave envelope.

Experimental statistics of long wave runup on a plane beach

2013 ◽  
Vol 65 ◽  
pp. 195-200 ◽  
Author(s):  
Petr Denissenko ◽  
Ira Didenkulova ◽  
Artem Rodin ◽  
Madis Listak ◽  
Efim Pelinovsky
Keyword(s):  
Wave Runup ◽  
Long Wave
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