TRANSFORMATION, BREAKING AND RUN-UP OF A LONG WAVE OF FINITE HEIGHT

On studying the transformation, breaking and run-up of a relatively steep wave of a short period, the theory for waves of permanent type has given us many fruitful results. However, the theory gradually loses its applicability as a wave becomes flat, since a considerable deformation of the wave profile is inevitable in its propagation. In § 1, a discussion concerning the transformation of a long wave in a channel of variable section is presented based on the non-linear shallow water theory. Approximate solutions obtained by G. B. Whitham's method (1958) are shown. Further, some brief considerations are given to the effects of bottom friction on wave transformation. In § 2, breaking of a long wave is discussed. Breakings on a uniformly sloping beach and on a beach of parabolic profile are considered and the effects of beach profile on breaking are clarified. Finally in § 3, experimental results on wave run-up over l/30 slope are described in comparing with the Kaplan's results.

Download Full-text

UNDULAR BORE DEVELOPMENT OVER A LABORATORY FRINGING REEF

Coastal Engineering Proceedings ◽

10.9753/icce.v36.currents.53 ◽

2018 ◽

pp. 53 ◽

Cited By ~ 1

Author(s):

Marion Tissier ◽

Jochem Dekkers ◽

Ad Reniers ◽

Stuart Pearson ◽

Ap Van Dongeren

Keyword(s):

Coral Reefs ◽

Wave Field ◽

Reef Flat ◽

Wave Transformation ◽

Undular Bore ◽

Fringing Reef ◽

Long Wave ◽

Reef Type ◽

Run Up ◽

Infragravity Wave

Several studies have reported the development of undular bores over fringing coral reefs (e.g, Gallagher, 1976; Nwogu and Demirbilek, 2010) but the importance of this phenomenon for reef hydrodynamics has never been studied. Yet, the transformation of a long wave (e.g., swell or infragravity wave) into an undular bore leads to significant modifications of the wave field. The formation of undulations is for example associated to a significant increase of the leading bore height. Moreover, if the undulations have enough time to develop (i.e. if the reef flat is wide enough), the initial long wave will ultimately split into a series of solitons (e.g., Grue et al., 2008). All this is likely to affect wave run-up. As reeffronted coastlines are particularly vulnerable to flooding, a good understanding of long wave transformation over the reef flat, including their possible transformation into undular bores, is crucial. In this study, we investigate undular bore development over reef-type profiles based on a series of laboratory experiments. More specifically, we aim to characterize the conditions under which undular bores develop, and analyse how their development affect the hydrodynamics at the toe of the reef-lined beach and the resulting wave run-up.

Download Full-text

INTERACTION OF IDEALIZED URBAN INFRASTRUCTURE AND LONG WAVES DURING RUN-UP AND ON-LAND FLOW PROCESS IN COASTAL REGIONS

Coastal Engineering Proceedings ◽

10.9753/icce.v33.currents.18 ◽

2012 ◽

Vol 1 (33) ◽

pp. 18 ◽

Cited By ~ 1

Author(s):

Nils Goseberg ◽

Torsten Schlurmann

Keyword(s):

Shock Wave ◽

Urban Infrastructure ◽

Coastal Regions ◽

Flow Process ◽

Long Wave ◽

Roughness Elements ◽

Shock Wave Generation ◽

Run Up ◽

Sloping Beach ◽

Good Agreement

This paper reports experimental results of long wave run-up climbing up a 1:40 sloping beach. The resulting maximum run-up is compared with analytical results and a good agreement is found for single sinusoidal waves with uniform wave period and varying amplitude. Subsequently, the interaction with macro-roughness elements on the beach is investigated for different long-shore obstruction ratios. The reduction in wave run-up is expressed by means of a nomogram relating the wave run-up without macro-roughness elements present to those cases where on-land flow is modified by macro-roughness. The presented results mainly focus on a non-staggered and non-rotated macro-roughness configuration. In addition to the run-up reduction, surface elevation profiles on the shore are presented, that address the shock wave generation when the wave tongue approaches the first row of macro-roughness elements.

Download Full-text

Numerical study of periodic long wave run-up on a rigid vegetation sloping beach

Coastal Engineering ◽

10.1016/j.coastaleng.2016.12.004 ◽

2017 ◽

Vol 121 ◽

pp. 158-166 ◽

Cited By ~ 15

Author(s):

Jun Tang ◽

Yongming Shen ◽

Derek M. Causon ◽

Ling Qian ◽

Clive G. Mingham

Keyword(s):

Numerical Study ◽

Rigid Vegetation ◽

Long Wave ◽

Run Up ◽

Sloping Beach

Download Full-text

FULLY NONLINEAR BOUSSINESQ-TYPE MODELLING OF INFRAGRAVITY WAVE TRANSFORMATION OVER A LOW-SLOPING BEACH

Coastal Engineering Proceedings ◽

10.9753/icce.v33.currents.28 ◽

2012 ◽

Vol 1 (33) ◽

pp. 28 ◽

Cited By ~ 1

Author(s):

Marion Tissier ◽

Philippe Bonneton ◽

Gerben Ruessink ◽

Fabien Marche ◽

Florent Chazel ◽

...

Keyword(s):

Surf Zone ◽

Field Studies ◽

Wave Transformation ◽

Type Model ◽

Infragravity Waves ◽

Fully Nonlinear ◽

Complex Interactions ◽

Long Wave ◽

Sloping Beach ◽

Infragravity Wave

Recent field studies over low sloping beaches have shown that infragravity waves could dissipate a significant part of their energy in the inner surf zone. This phenomenon and the associated short- and long-wave transformations are not well-understood. In this paper, we assess the ability of the fully nonlinear Boussinesq-type model introduced in Bonneton et al. (2011) to reproduce short and long wave transformation in a case involving a strong infragravity wave dissipation close to the shoreline. This validation study, based on van Dongeren et al. (2008)’s laboratory experiments, suggests that the model is able to predict infragravity wave breaking as well as the complex interactions between short and long waves in the surf zone.

Download Full-text

Long Wave Run-Up Resonance in a Multi-Reflection System

Applied Sciences ◽

10.3390/app10186172 ◽

2020 ◽

Vol 10 (18) ◽

pp. 6172

Author(s):

Shanshan Xu ◽

Frédéric Dias

Keyword(s):

Boundary Condition ◽

Shallow Water ◽

Shallow Water Equations ◽

Incoming Wave ◽

Wave Trapping ◽

Relaxation Zone ◽

Long Wave ◽

Nonlinear Shallow Water Equations ◽

Run Up ◽

Sloping Beach

Wave reflection and wave trapping can lead to long wave run-up resonance. After reviewing the theory of run-up resonance in the framework of the linear shallow water equations, we perform numerical simulations of periodic waves incident on a linearly sloping beach in the framework of the nonlinear shallow water equations. Three different types of boundary conditions are tested: fully reflective boundary, relaxation zone, and influx transparent boundary. The effect of the boundary condition on wave run-up is investigated. For the fully reflective boundary condition, it is found that resonant regimes do exist for certain values of the frequency of the incoming wave, which is consistent with theoretical results. The influx transparent boundary condition does not lead to run-up resonance. Finally, by decomposing the left- and right-going waves into a multi-reflection system, we find that the relaxation zone can lead to run-up resonance depending on the length of the relaxation zone.

Download Full-text

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

Natural Hazards and Earth System Sciences Discussions ◽

10.5194/nhessd-1-561-2013 ◽

2013 ◽

Vol 1 (2) ◽

pp. 561-582

Author(s):

A. Ezersky ◽

D. Tiguercha ◽

E. Pelinovsky

Keyword(s):

Particle Velocity ◽

Tsunami Wave ◽

Earthquake Magnitude ◽

Tsunami Source ◽

Bottom Relief ◽

Shallow Water Theory ◽

Resonance Effects ◽

Long Wave ◽

Run Up ◽

Linear Shallow Water Theory

Abstract. Run-up of long wave 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 non-linear corrections are obtained for the run-up stage. It is demonstrated that bottom profile influences the run-up characteristics and can lead to the resonance effects: increasing 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 increasing of run-up heights for weakest earthquakes and tsunami wave does not break on chosen bottom relief if the earthquake magnitude does not exceed 7.8.

Download Full-text

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

Natural Hazards and Earth System Science ◽

10.5194/nhess-13-2745-2013 ◽

2013 ◽

Vol 13 (11) ◽

pp. 2745-2752 ◽

Cited By ~ 14

Author(s):

A. Ezersky ◽

D. Tiguercha ◽

E. Pelinovsky

Keyword(s):

Particle Velocity ◽

Tsunami Wave ◽

Earthquake Magnitude ◽

Tsunami Source ◽

Bottom Relief ◽

Shallow Water Theory ◽

Resonance Effects ◽

Long Wave ◽

Run Up ◽

Linear Shallow Water Theory

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.

Download Full-text

Numerical Investigation of Wave Period Influence on Long Wave Run-Up on Slope With Rigid Vegetation

Volume 7: Ocean Engineering ◽

10.1115/omae2016-54298 ◽

2016 ◽

Author(s):

Jun Tang ◽

Yongming Shen

Keyword(s):

Shallow Water Equations ◽

Water Wave ◽

Wave Period ◽

Coastal Vegetation ◽

Coastal Structures ◽

Rigid Vegetation ◽

Comparison With Experiment ◽

Long Wave ◽

Nonlinear Shallow Water Equations ◽

Run Up

Coastal vegetation can not only provide shade to coastal structures but also reduce wave run-up. Study of long water wave climb on vegetation beach is fundamental to understanding that how wave run-up may be reduced by planted vegetation along coastline. The present study investigates wave period influence on long wave run-up on a partially-vegetated plane slope via numerical simulation. The numerical model is based on an implementation of Morison’s formulation for rigid structures induced inertia and drag stresses in the nonlinear shallow water equations. The numerical scheme is validated by comparison with experiment results. The model is then applied to investigate long wave with diverse periods propagating and run-up on a partially-vegetated 1:20 plane slope, and the sensitivity of run-up to wave period is investigated based on the numerical results.

Download Full-text