scholarly journals SURF SIMILARITY

1974 ◽  
Vol 1 (14) ◽  
pp. 26 ◽  
Author(s):  
J.A. Battjes

This paper deals with the following aspects of periodic water waves breaking on a plane slope breaking criterion, breaker type, phase difference across the surfzone, breaker height-to-depth ratio, run-up and set-up, and reflection. It is shown that these are approximately governed by a single similarity parameter only, embodying both the effects of slope angle and incident wave steepness. Various physical interpretations of this similarity parameter are given, while its role is discussed m general terms from the viewpoint of model prototype similarity.

Author(s):  
Maria Clavero ◽  
Pedro Folgueras ◽  
Pilar Diaz-Carrasco ◽  
Miguel Ortega-Sanchez ◽  
Miguel A. Losada

In the 14th ICCE, Battjes (1974) showed that a single similarity parameter only, embodying both the effects of slope angle and incident wave steepness, was important for many aspects of waves breaking on impermeable slopes, and suggested to call it the "Iribarren number", denoted by "Ir". Ahrens and McCartney (1975) verified the usefulness of Ir to describe run-up and stability on rough permeable slopes. Since then, many researchers applied Ir to characterize and to develop formulae for the design of breakwaters and to verify their stability. On the other hand, depending on their typology, breakwaters reflect, dissipate, transmit, and radiate incident wave energy. Partial standing wave patterns are likely to occur at all types of breakwater, thus playing an important role in defining the wave regime in front of, near (seaward and leeward), and inside the breakwater. The characteristics of the porous medium, relative grain size D/L and relative width, Aeq/L2, are relevant magnitudes in that wave pattern (Vilchez et al. 2016), being D the grain diameter, L the wave length and Aeq the porous area per unit section under the mean water level. Aeq/L2 is a scattering parameter controlling the averaged transformation of the wave inside the porous section of the structure. For a vertical porous breakwater (Type A), Aeq is simply B · h, and for a constant depth, the scattering parameter is reduced to B/L, which is the relative breakwater width.


1976 ◽  
Vol 1 (15) ◽  
pp. 44 ◽  
Author(s):  
Ary Roos ◽  
Jurjen A. Battjes

An experimental study is presented of some characteristic parameters of the flow in the up-rush and down-rush of periodic waves breaking on a plane, smooth slope. The water layer thickness has been measured as a function of time at four locations above still water level. Discharges and particle velocities have been calculated. The results have been made nondimensional on the basis of Hunt's formula for the run-up height. They appear to be either independent of the wave steepness H/L and slope gradient tan Ct or to be a function of a single similarity parameter £ - tana / yH/L only. An hypothesis is stated concerning a relation between the mean rate of overtopping of a dike by waves, and the run-up which would occur under the same circumstances on an uninterrupted slope. On the basis of this hypothesis the overtopping volume per wave can be normalized so as to make it independent of slope angle and wave steepness. A comparison of the result with measurements from other sources indicates a rough agreement.


Fluids ◽  
2020 ◽  
Vol 5 (1) ◽  
pp. 9 ◽  
Author(s):  
Marco Klein ◽  
Matthias Dudek ◽  
Günther F. Clauss ◽  
Sören Ehlers ◽  
Jasper Behrendt ◽  
...  

This paper discusses the potential of deterministic wave prediction as one basic module for decision support of offshore operations. Therefore, methods of different complexity—the linear wave solution, the non-linear Schrödinger equation (NLSE) of two different orders and the high-order spectral method (HOSM)—are presented in terms of applicability and limitations of use. For this purpose, irregular sea states with varying parameters are addressed by numerical simulations as well as model tests in the controlled environment of a seakeeping basin. The irregular sea state investigations focuses on JONSWAP spectra with varying wave steepness and enhancement factor. In addition, the influence of the propagation distance as well as the forecast horizon is discussed. For the evaluation of the accuracy of the prediction, the surface similarity parameter is used, allowing an exact, quantitative validation of the results. Based on the results, the pros and cons of the different deterministic wave prediction methods are discussed. In conclusion, this paper shows that the classical NLSE is not applicable for deterministic wave prediction of arbitrary irregular sea states compared to the linear solution. However, the application of the exact linear dispersion operator within the linear dispersive part of the NLSE increased the accuracy of the prediction for small wave steepness significantly. In addition, it is shown that non-linear deterministic wave prediction based on second-order NLSE as well as HOSM leads to a substantial improvement of the prediction quality for moderate and steep irregular wave trains in terms of individual waves and prediction distance, with the HOSM providing a high accuracy over a wider range of applications.


2016 ◽  
Vol 797 ◽  
pp. 644-664 ◽  
Author(s):  
Gal Akrish ◽  
Oded Rabinovitch ◽  
Yehuda Agnon

Nonlinear evolution of long-crested wave groups can lead to extreme interactions with coastal and marine structures. In the present study the role of nonlinear evolution in the formation of extreme run-up events on a vertical wall is investigated. To this end, the fundamental problem of interaction between non-breaking water waves and a vertical wall over constant water depth is considered. In order to simulate nonlinear wave–wall interactions, the high-order spectral method is applied to a computational domain which aims to represent a two-dimensional wave flume. Wave generation is simulated at the flume entrance by means of the additional potential concept. Through this concept, the implementation of a numerical wavemaker is applicable. In addition to computational efficiency, the adopted numerical approach enables one to consider the evolution of nonlinear waves while preserving full dispersivity. Utilizing these properties, the influence of the nonlinear wave evolution on the wave run-up can be examined for a wide range of water depths. In shallow water, it is known that nonlinear evolution of incident waves may result in extreme run-up events due to the formation of an undular bore. The present study reveals the influence of the nonlinear evolution on the wave run-up in deep-water conditions. The results suggest that extreme run-up events in deep water may occur as a result of the disintegration of incident wave groups into envelope solitons.


2011 ◽  
Vol 1 (8) ◽  
pp. 4
Author(s):  
Thorndike Saville

The distribution of wave steepness (H/T ) for fully developed sea is obtained from Bretschneider's joint distribution of wave height and wave period. This steepness distribution is used with standard wave runup curves to develop a frequency curve of wave run-up. Use of this run-up distribution curve will permit more accurate estimation of the variability in wave run-up for design cases, and particularly the percent of time in which run-ups will exceed that predicted for the significant wave. The distribution may also be used with normal overtopping procedures to determine more accurate estimates of overtopping quantities. Wave run-up may be defined as the vertical height above mean water level to which water from a breaking wave will rise on a structure face. Accurate design data on the height of wave run-up is needed for determination of design crest elevations of protective structures subject to wave action such as seawalls, beach fills, surge barriers, and dams. Such structures are normally designed to prevent wave overtopping with consequent flooding on the landward side and, if of an earth type, possible failure by rearface erosion. Because of the importance of wave run-up elevations in determining structure heights and freeboards, a great deal of work has been done in the past six years in an attempt to relate wave run-up to incident wave characteristics, and slope or structure characteristics. Compilations based largely on laboratory experimental work have been made and have fe-?* suited in curves similar to those shown in Figure 1 which is reprinted from the U. S. Beach Erosion Board Technical Report No. 4. Such curves most frequently have related the dimensionless ratio of relative run-up (R/H ) to incident wave steepness in deep water (H /T ), as a function of structure type or slope. (H is the equivalent deep water wave height.) The curves shown in Figure 1 are of this type, and pertain to structures having a depth of water greater than three wave heights at the toe of the structure; this depth limitation in effect means that the wave breaks directly on the structure. The curves shown in Figure 1 are a portion of a set of five separate figures, covering different structure depths (d/H ). All are published in Beach Erosion Board Technical Report Number 4. These curves were derived primarily from small scale laboratory tests. Further laboratory tests with much larger waves (heights two to five feet) have shown that a scale effect exists for some conditions.


2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Marin Marin ◽  
M. M. Bhatti

AbstractThe present study deals with the head-on collision process between capillary–gravity solitary waves in a finite channel. The present mathematical modeling is based on Nwogu’s Boussinesq model. This model is suitable for both shallow and deep water waves. We have considered the surface tension effects. To examine the asymptotic behavior, we employed the Poincaré–Lighthill–Kuo method. The resulting series solutions are given up to third-order approximation. The physical features are discussed for wave speed, head-on collision profile, maximum run-up, distortion profile, the velocity at the bottom, and phase shift profile, etc. A comparison is also given as a particular case in our study. According to the results, it is noticed that the free parameter and the surface tension tend to decline the solitary-wave profile significantly. However, the maximum run-up amplitude was affected in great measure due to the surface tension and the free parameter.


2021 ◽  
Vol 9 (7) ◽  
pp. 784
Author(s):  
Arnida Lailatul Latifah ◽  
Durra Handri ◽  
Ayu Shabrina ◽  
Henokh Hariyanto ◽  
E. van Groesen

This paper shows simulations of high waves over different bathymetries to collect statistical information, particularly kurtosis and crest exceedance, that quantifies the occurrence of exceptionally extreme waves. This knowledge is especially pertinent for the design and operation of marine structures, safe ship trafficking, and mooring strategies for ships near the coast. Taking advantage of the flexibility to perform numerical simulations with HAWASSI software, with the aim of investigating the physical and statistical properties for these cases, this paper investigates the change in wave statistics related to changes in depth, breaking and differences between long- and short-crested waves. Three different types of bathymetry are considered: run-up to the coast with slope 1/20, waves over a shoal, and deep open-water waves. Simulations show good agreement in the examined cases compared with the available experimental data and simulations. Then predictive simulations for cases with a higher significant wave height illustrate the changes that may occur during storm events.


2018 ◽  
Author(s):  
Ming-ming Liu ◽  
Ming Zhao ◽  
Lin Lu

Water waves play an important role in local scour around subsea pipelines laid on the sandy seabed, especially in shallow water regions. In this paper, a two-dimensional numerical model is employed to predict local scour around submarine pipelines under water waves in shoaling condition. The motion of water under waves is simulated by solving the Reynolds Averaged Navier-Stokes (RANS) equations. The evolution of the seabed surface near the pipeline is predicted by solving the conservation of the sediment mass, which transport in the water in the forms of bed load and suspended load. The main aim of this study is to investigate the effect of the seabed slope on the scour profiles and scour depth. To achieve this aim, numerical simulations of scour around a pipeline on a flat seabed and on a slope seabed with a slope angle of 15° are conducted for various wave conditions.


Author(s):  
K. A. Belibassakis ◽  
G. A. Athanassoulis

A coupled-mode model is developed and applied to the transformation and run-up of dispersive water waves on plane beaches. The present work is based on the consistent coupled-mode theory for the propagation of water waves in variable bathymetry regions, developed by Athanassoulis & Belibassakis (1999) and extended to 3D by Belibassakis et al (2001), which is suitably modified to apply to a uniform plane beach. The key feature of the coupled-mode theory is a complete modal-type expansion of the wave potential, containing both propagating and evanescent modes, being able to consistently satisfy the Neumann boundary condition on the sloping bottom. Thus, the present approach extends previous works based on the modified mild-slope equation in conjunction with analytical solution of the linearised shallow water equations, see, e.g., Massel & Pelinovsky (2001). Numerical results concerning non-breaking waves on plane beaches are presented and compared with exact analytical solutions; see, e.g., Wehausen & Laitone (1960, Sec. 18). Also, numerical results are presented concerning the run-up of non-breaking solitary waves on plane beaches and compared with the ones obtained by the solution of the shallow-water wave equations, Synolakis (1987), Li & Raichlen (2002), and experimental data, Synolakis (1987).


1976 ◽  
Vol 1 (15) ◽  
pp. 45 ◽  
Author(s):  
Udo Berger ◽  
Soren Kohlhase

As under oblique wave approach water waves are reflected by a vertical wall, a wave branching effect (stem) develops normal to the reflecting wall. The waves progressing along the wall will steep up. The wave heights increase up to more than twice the incident wave height. The £jtudy has pointed out that this effect, which is usually called MACH-REFLECTION, is not to be taken as an analogy to gas dynamics, but should be interpreted as a diffraction problem.


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