scholarly journals EQUILIBRIUM RANGE SPECTRA IN SHOALING WATER

1970 ◽  
Vol 1 (12) ◽  
pp. 9
Author(s):  
Takeshi Ijima ◽  
Takahido Matsuo ◽  
Kazutami Koga
Keyword(s):  
Water Depth ◽  
Surf Zone ◽  
Breaking Wave ◽  
Wave Spectra ◽  
Frequency Spectra ◽  
Wave Condition ◽  
Wave Heights ◽  
Deep Water Wave ◽  
Equilibrium Range ◽  
Sloping Beach

In shoaling water on sloping beach, waves break by hydraulic instability due to the finiteness of water depth, so that frequency spectra of waves in surf zone must have any limiting form similar to the equilibrium spectrum given by Phillips(l958) In this paper, authors haze derived an equilibrium form of spectra for surf waves from the limiting wave condition at constant water depth by Miche(l944) and from breaking wave experiments on sloped bottom by Iversen(l952) The results arc compared with surf wave spectra obtained from field observations by means of stereo-type wave meter devised by the authors(1968). By means of this spectrum and by deep water wave spectra for various wind conditions, significant wave heights and optimum periods of limiting waves m surf ^one are calculated.

scholarly journals PROBABILITIES OF BREAKING WAVE CHARACTERISTICS

1970 ◽  
Vol 1 (12) ◽  
pp. 25 ◽  
Author(s):  
J. Ian Collins
Keyword(s):  
Shallow Water ◽  
Probability Density ◽  
Deep Water ◽  
Surf Zone ◽  
Probability Distributions ◽  
Rayleigh Distribution ◽  
Breaking Wave ◽  
Wave Characteristics ◽  
Probability Densities ◽  
Wave Heights

Utilizing the hydrodynamic relationships for shoaling and refraction of waves approaching a shoreline over parallel bottom contours a procedure is developed to transform an arbitrary probability density of wave characteristics in deep water into the corresponding breaking characteristics in shallow Water A number of probability distributions for breaking wave characteristics are derived m terms of assumed deep water probability densities of wave heights wave lengths and angles of approach Some probability densities for wave heights at specific locations in the surf zone are computed for a Rayleigh distribution in deep water The probability computations are used to derive the expectation of energy flux and its distribution.

Breaking waves and the equilibrium range of wind-wave spectra

1997 ◽  
Vol 342 ◽  
pp. 377-401 ◽  
Author(s):  
S. E. BELCHER ◽  
J. C. VASSILICOS
Keyword(s):  
High Frequency ◽  
Wind Wave ◽  
Breaking Waves ◽  
Breaking Wave ◽  
Wave Spectra ◽  
Scale Invariant ◽  
Self Similar ◽  
Dynamical Properties ◽  
Dynamical Balance ◽  
Equilibrium Range

When scaled properly, the high-wavenumber and high-frequency parts of wind-wave spectra collapse onto universal curves. This collapse has been attributed to a dynamical balance and so these parts of the spectra have been called the equilibrium range. We develop a model for this equilibrium range based on kinematical and dynamical properties of breaking waves. Data suggest that breaking waves have high curvature at their crests, and they are modelled here as waves with discontinuous slope at their crests. Spectra are then dominated by these singularities in slope. The equilibrium range is assumed to be scale invariant, meaning that there is no privileged lengthscale. This assumption implies that: (i) the sharp-crested breaking waves have self-similar shapes, so that large breaking waves are magnified copies of the smaller breaking waves; and (ii) statistical properties of breaking waves, such as the average total length of breaking-wave fronts of a given scale, vary with the scale of the breaking waves as a power law, parameterized here with exponent D.

The evolution of large non-breaking waves in intermediate and shallow water. I. Numerical calculations of uni-directional seas

2010 ◽  
Vol 467 (2127) ◽  
pp. 778-805 ◽  
Author(s):  
V. Katsardi ◽  
C. Swan
Keyword(s):  
Water Depth ◽  
Wave Train ◽  
Breaking Waves ◽  
Numerical Calculations ◽  
Linear Wave ◽  
Frequency Spectra ◽  
Relative Significance ◽  
Relative Water ◽  
Wave Heights ◽  
Wave Models

In deep water it is well known that the evolution of the largest waves in realistic, broad-banded frequency spectra is governed by dispersive focusing. However, as the water depth reduces this process weakens and the relative significance of wave modulation is shown to be increasingly important. This leads to very different extreme wave groups, the properties of which are critically dependent upon the local nonlinearity. To explore these effects, and to provide a physical explanation for their occurrence, two complementary wave models are employed. The combined numerical results show that the nature of large uni-directional waves varies depending on the relative water depth. As the water depth reduces, both the bound and resonant interactions become more significant. However, the third-order resonant terms have the most profound influence. By modifying both the amplitude and phase of the underlying linear wave components, the largest waves arise as a local instability within a truncated quasi-regular wave train; the latter appearing because of an initial narrowing of the underlying frequency spectrum. Furthermore, the numerical calculations show that, with large changes in both the spectral shape and the phasing of the wave components, both the maximum crest elevations and wave heights are less than those predicted by linear theory.

scholarly journals DEFORMATION UP TO BREAKING OF PERIODIC WAVES ON A BEACH

1976 ◽  
Vol 1 (15) ◽  
pp. 26 ◽  
Author(s):  
Ib A. Svendson ◽  
J. Buhr Hansen
Keyword(s):  
Wave Height ◽  
Water Depth ◽  
Wave Length ◽  
Empirical Relation ◽  
Breaking Point ◽  
Periodic Waves ◽  
Depth Ratio ◽  
Surface Profiles ◽  
Deep Water Wave ◽  
Sloping Beach

An experimental description is presented for 'the transformation of periodic waves which approach breaking on a gently sloping beach. The data include the variation of wave height, phase velocity, wave surface profiles, and the maximum value of the wave height to water depth ratio (H/h)max around the breaking point. The results are compared with the theories of sinusoidal and cnoidal wave shoaling, and the latter is shown in most cases to agree remarkably well when the laminar energy loss along the walls and bottom of the wave tank is included. An empirical relation is established between wave length to water depth ratio L/h at the breaking point and the deep water wave steepness H0/L0. Also the maximum wave height to water depth ratio at breaking shows considerably less scattering than found previously, when plotted versus S = hx L/h, hx being bottom slope.

scholarly journals Estimation of Wave-Breaking Index by Learning Nonlinear Relation Using Multilayer Neural Network

2022 ◽  
Vol 10 (1) ◽  
pp. 50
Author(s):  
Miyoung Yun ◽  
Jinah Kim ◽  
Kideok Do
Keyword(s):  
Neural Network ◽  
Wave Height ◽  
Water Depth ◽  
Wave Breaking ◽  
Water Wave ◽  
Breaking Wave ◽  
Empirical Equations ◽  
Bottom Slope ◽  
Proposed Model ◽  
Deep Water Wave

Estimating wave-breaking indexes such as wave height and water depth is essential to understanding the location and scale of the breaking wave. Therefore, numerous wave-flume laboratory experiments have been conducted to develop empirical wave-breaking formulas. However, the nonlinearity between the parameters has not been fully incorporated into the empirical equations. Thus, this study proposes a multilayer neural network utilizing the nonlinear activation function and backpropagation to extract nonlinear relationships. Existing laboratory experiment data for the monochromatic regular wave are used to train the proposed network. Specifically, the bottom slope, deep-water wave height and wave period are plugged in as the input values that simultaneously estimate the breaking-wave height and wave-breaking location. Typical empirical equations employ deep-water wave height and length as input variables to predict the breaking-wave height and water depth. A newly proposed model directly utilizes breaking-wave height and water depth without nondimensionalization. Thus, the applicability can be significantly improved. The estimated wave-breaking index is statistically verified using the bias, root-mean-square errors, and Pearson correlation coefficient. The performance of the proposed model is better than existing breaking-wave-index formulas as well as having robust applicability to laboratory experiment conditions, such as wave condition, bottom slope, and experimental scale.

scholarly journals Cubipod® Armor Design in Depth-Limited Regular Wave-Breaking Conditions

2018 ◽  
Vol 6 (4) ◽  
pp. 150 ◽  
Author(s):  
M. Gómez-Martín ◽  
María Herrera ◽  
Jose Gonzalez-Escriva ◽  
Josep Medina
Keyword(s):  
Water Depth ◽  
Wave Breaking ◽  
Experimental Methodology ◽  
Small Scale ◽  
Breaking Wave ◽  
Regular Wave ◽  
Empirical Formulas ◽  
Physical Tests ◽  
Wave Conditions ◽  
Deep Water Wave

Armor stability formulas for mound breakwaters are commonly based on 2D small-scale physical tests conducted in non-overtopping and non-breaking conditions. However, most of the breakwaters built around the world are located in breaking or partially-breaking wave conditions, where they must withstand design storms having some percentage of large waves breaking before they reach the structure. In these cases, the design formulas for non-breaking wave conditions are not fully valid. This paper describes the specific 2D physical model tests carried out to analyze the trunk hydraulic stability of single- and double-layer Cubipod® armors in depth-limited regular wave breaking and non-overtopping conditions with horizontal foreshore (m = 0) and armor slope (α) with cotα = 1.5. An experimental methodology was established to ensure that 100 waves attacked the armor layer with the most damaging combination of wave height (H) and wave period (T) for the given water depth (hs). Finally, for a given water depth, empirical formulas were obtained to estimate the Cubipod® size which made the armor stable regardless of the deep-water wave storm.

scholarly journals WAVE HEIGHT DISTRIBUTION AND WAVE GROUPING IN SURF ZONE

1982 ◽  
Vol 1 (18) ◽  
pp. 4 ◽  
Author(s):  
Hajime Mase ◽  
Yuichi Iwagaki
Keyword(s):  
Wave Height ◽  
Surf Zone ◽  
Irregular Waves ◽  
Wave Transformation ◽  
Height Distribution ◽  
Frequency Distributions ◽  
Irregular Wave ◽  
Wave Height Distribution ◽  
Wave Heights ◽  
Deep Water Wave

The main purpose of this paper is to propose a model for prediction of the spatial distributions of representative wave heights and the frequency distributions of wave heights of irregular waves in shallow-water including the surf zone. In order to examine the validity of the model, some experiments of irregular wave transformation have been made. In addition, an attempt has been made to clarify the spatial distribution of wave grouping experimentally. Especially the present paper focuses finding the effects of the bottom slope and the deep-water wave steepness on the wave height distribution and wave grouping.

scholarly journals The Effect of Wave Breaking on Surf-Zone Turbulence and Alongshore Currents: A Modeling Study*

2005 ◽  
Vol 35 (11) ◽  
pp. 2187-2203 ◽  
Author(s):  
Falk Feddersen ◽  
J. H. Trowbridge
Keyword(s):  
Drag Coefficient ◽  
Water Depth ◽  
Wave Breaking ◽  
Surf Zone ◽  
Model Parameters ◽  
Breaking Wave ◽  
Bottom Stress ◽  
The Mean ◽  
Alongshore Current ◽  
Bed Roughness

Abstract The effect of breaking-wave-generated turbulence on the mean circulation, turbulence, and bottom stress in the surf zone is poorly understood. A one-dimensional vertical coupled turbulence (k–ɛ) and mean-flow model is developed that incorporates the effect of wave breaking with a time-dependent surface turbulence flux and uses existing (published) model closures. No model parameters are tuned to optimize model–data agreement. The model qualitatively reproduces the mean dissipation and production during the most energetic breaking-wave conditions in 4.5-m water depth off of a sandy beach and slightly underpredicts the mean alongshore current. By modeling a cross-shore transect case example from the Duck94 field experiment, the observed surf-zone dissipation depth scaling and the observed mean alongshore current (although slightly underpredicted) are generally reproduced. Wave breaking significantly reduces the modeled vertical shear, suggesting that surf-zone bottom stress cannot be estimated by fitting a logarithmic current profile to alongshore current observations. Model-inferred drag coefficients follow parameterizations (Manning–Strickler) that depend on the bed roughness and inversely on the water depth, although the inverse depth dependence is likely a proxy for some other effect such as wave breaking. Variations in the bed roughness and the percentage of breaking-wave energy entering the water column have a comparable effect on the mean alongshore current and drag coefficient. However, covarying the wave height, forcing, and dissipation and bed roughness separately results in an alongshore current (drag coefficient) only weakly (strongly) dependent on the bed roughness because of the competing effects of increased turbulence, wave forcing, and orbital wave velocities.

Surf zone transformation of wave height to water depth ratios

1992 ◽  
Vol 17 (1-2) ◽  
pp. 49-70 ◽  
Author(s):  
R.C. Nelson ◽  
J. Gonsalves
Keyword(s):  
Wave Height ◽  
Water Depth ◽  
Surf Zone
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