scholarly journals A MODEL FOR BREAKER DECAY ON BEACHES

1984 ◽  
Vol 1 (19) ◽  
pp. 6 ◽  
Author(s):  
William R. Dally ◽  
Robert G. Dean ◽  
Robert A. Dalrymple
Keyword(s):  
Surf Zone ◽  
Laboratory Data ◽  
Wave Theory ◽  
Energy Balance Equation ◽  
Bottom Friction ◽  
Breaking Wave ◽  
Linear Wave ◽  
Wave Decay ◽  
Equilibrium Beach Profile ◽  
Wide Range

Based on the observation that a shallow water breaking wave propagating over a region of uniform depth will reform and stabilize after some distance, an intuitive expression for the rate of energy dissipation is developed. Using linear wave theory and the energy balance equation, analytical solutions for monochromatic waves breaking on a flat shelf, plane slope, and "equilibrium" beach profile are presented and compared to laboratory data from Horikawa and Kuo (1966) with favorable results. Set-down/up in the mean water level, bottom friction losses, and bottom profiles of arbitrary shape are then introduced and the equations solved numerically. The model is calibrated and verified to laboratory data with very good results for wave decay for a wide range of beach slopes and incident conditions, but not so favorable for set-up. A test run on a prototype scale profile containing two bar and trough systems demonstrates the model's ability to describe the shoaling, breaking, and wave reformation process commonly observed in nature. Bottom friction is found to play a negligible role in wave decay in the surf zone when compared to shoaling and breaking.

scholarly journals Bathymetric Inversion and Uncertainty Estimation from Synthetic Surf-Zone Imagery with Machine Learning

2020 ◽  
Vol 12 (20) ◽  
pp. 3364
Author(s):  
Adam Collins ◽  
Katherine Brodie ◽  
Andrew Spicer Bak ◽  
Tyler Hesser ◽  
Matthew Farthing ◽  
...  
Keyword(s):  
Surf Zone ◽  
Mean Squared Error ◽  
Numerical Models ◽  
Wave Theory ◽  
Complete Information ◽  
Breaking Wave ◽  
Linear Wave ◽  
Wave Refraction ◽  
Additional Information ◽  
Single Frame

Resolving surf-zone bathymetry from high-resolution imagery typically involves measuring wave speeds and performing a physics-based inversion process using linear wave theory, or data assimilation techniques which combine multiple remotely sensed parameters with numerical models. In this work, we explored what types of coastal imagery can be best utilized in a 2-dimensional fully convolutional neural network to directly estimate nearshore bathymetry from optical expressions of wave kinematics. Specifically, we explored utilizing time-averaged images (timex) of the surf-zone, which can be used as a proxy for wave dissipation, as well as including a single-frame image input, which has visible patterns of wave refraction and instantaneous expressions of wave breaking. Our results show both types of imagery can be used to estimate nearshore bathymetry. However, the single-frame imagery provides more complete information across the domain, decreasing the error over the test set by approximately 10% relative to using timex imagery alone. A network incorporating both inputs had the best performance, with an overall root-mean-squared-error of 0.39 m. Activation maps demonstrate the additional information provided by the single-frame imagery in non-breaking wave areas which aid in prediction. Uncertainty in model predictions is explored through three techniques (Monte Carlo (MC) dropout, infer-transformation, and infer-noise) to provide additional actionable information about the spatial reliability of each bathymetric prediction.

scholarly journals WAVE HEIGHT DECAY MODEL WITHIN A SURF ZONE

1986 ◽  
Vol 1 (20) ◽  
pp. 52
Author(s):  
Shigeki Sakai ◽  
Kouetsu Hiyamizu ◽  
Hiroshi Saeki
Keyword(s):  
Energy Dissipation ◽  
Wave Height ◽  
Surf Zone ◽  
Wave Theory ◽  
Momentum Balance ◽  
Breaking Wave ◽  
Good Prediction ◽  
Linear Wave ◽  
Energy And Momentum ◽  
Spilling Breaker

A model for wave height decay of a spilling breaker is proposed. The energy dissipation of a breaking wave is approximated by that of a propagating bore. In order to explain the gentle decay of spilling breaker at the initial stage, a development of a foam region, which indicates the amount of foam on the wave profile and determines the rate of energy dissipation, is considered. In addition to this formulation, the energy and momentum balance equations are described by a linear wave theory in shallow water and are simultaneously solved. Comparisons with experimental results show that the model gives a good prediction in both inner and outer regions, and that two coefficients in the present model are related to the deep water wave steepness and the slope of beaches.

scholarly journals Nonlinear wave energy modelling in the surf zone

1996 ◽  
Vol 3 (2) ◽  
pp. 127-134 ◽  
Author(s):  
Th. V. Karambas
Keyword(s):  
Wave Energy ◽  
Surf Zone ◽  
Energy Balance Equation ◽  
Propagation Model ◽  
Breaking Wave ◽  
Dissipation Term ◽  
Energy Modelling ◽  
Turbulence Effects ◽  
Energy And Momentum ◽  
Energy Equations

Abstract. Breaking wave energy in the surf zone is modelled through the incorporation of the time dependent energy balance equation in a non linear dispersive wave propagation model. The energy equations solved simultaneously with the momentum and continuity equation. Turbulence effects and the non uniform horizontal velocity distribution due to breaking is introduced in both the energy and momentum equations. The dissipation term is a function of the velocity defect derived from a turbulent analysis. The resulting system predicts both wave characteristics (surface elevation and velocity) and the energy distribution inside surf zone. The model is validated against experimental data and analytical expressions.

scholarly journals NUMERICAL MODEL OF BREAKING WAVE AROUND A RIVER MOUTH

1986 ◽  
Vol 1 (20) ◽  
pp. 97
Author(s):  
Jong-Sup Lee ◽  
Toru Sawaragi ◽  
Ichiro Deguchi
Keyword(s):  
Numerical Model ◽  
Wave Breaking ◽  
Small Amplitude ◽  
River Mouth ◽  
Wave Theory ◽  
Experimental Result ◽  
Breaking Wave ◽  
Linear Wave ◽  
Amplitude Wave ◽  
Current Interaction

Equations for wave kinematics and wave dynamics based on small amplitude wave theory have been used in the prediction of wave deformations and wave-indused currents. However, the applicability of the linear wave theory is questionable in a river mouth where forced wave breaking and strong wave-current interaction take place. A numerical model based on the non-linear dispersive wave theory has been developed, the results by this model was compared with the values of the experiments and the linear theory. Wave transformations including shoaling, wave-current interaction and wave breaking by the model showed a good agreement with the experimental result. In the prediction of wave-induced currents, the excess momentum flux (Pxx) computed by the model has more reasonable value than the radiation stress ( Sxx) calculated by the small amplitude wave theory.

scholarly journals BORE PROPAGATION SPEED AT THE TERMINATION OF WAVE BREAKING

2011 ◽  
Vol 1 (32) ◽  
pp. 7 ◽  
Author(s):  
Takashi Okamoto ◽  
Conceição Juana Fortes ◽  
David R. Basco
Keyword(s):  
Wave Breaking ◽  
Propagation Speed ◽  
Wave Theory ◽  
Theoretical Models ◽  
Breaking Wave ◽  
Linear Wave ◽  
Mass Transportation ◽  
Higher Harmonics ◽  
Wave Celerity ◽  
Set Up

Wave breaking is the most important event in nearshore hydrodynamics because of the energy exertion and mass transportation during the event drive all the nearshore phenomena, such as wave set-up/down, long shore current, and nearshore circulation. Wave celerity is a key parameter in wave breaking especially for the mass transportation, the energy dissipation during the wave breaking event, and the wave breaking index calculation, for example. There are many models to calculate the wave celerity during the breaking event (bore propagation speed) and it is well known that the bore propagation speed is faster than that is given by linear wave theory. But Okamoto et al. (2008) found the bore propagation speed at the termination location of wave breaking becomes much slower than the theoretical estimation when the termination of wave breaking occurs on inversely sloped bottom. In this paper, the bore propagation speed at the termination location of wave breaking is examined with the experimental data collected in a wave tank with simplified bar-trough beach settings. Comparisons with theoretical models are presented. Fourier analysis is performed to investigate the evolution of higher harmonics and synthesized time series, which is a simple summation of linear wave components, is constructed by using the obtained information to calculate the wave celerity during and after the wave breaking. Calculation result reveals that as the breaking wave approaches to the termination, the bore propagation speed decreases towards the value which can be explained by the existence of slowly and independently propagating higher harmonics.

scholarly journals EFFECT OF WAVE-CURRENT INTERACTION ON THE WAVE PARAMETER

1982 ◽  
Vol 1 (18) ◽  
pp. 28
Author(s):  
Yu-Cheng Li ◽  
John B. Herbich
Keyword(s):  
Wave Height ◽  
Wave Length ◽  
Wave Theory ◽  
Length Change ◽  
Numerical Calculations ◽  
Wave Parameter ◽  
Linear Wave ◽  
Linear Wave Theory ◽  
Wide Range ◽  
Non Linear

The interaction of a gravity wave with a steady uniform current is described in this paper. Numerical calculations of the wave length change by different non-linear wave theories show that errors in the results computed by the linear wave theory are less than 10 percent within the range of 0.15 < d/Ls s 0.40, 0.01 < Hs/Ls < 0.07 and -0.15 < U/Cs i 0.30. Numerical calculations of wave height change employing different wave theories show that errors in the results obtained by the linear wave theory in comparison with the non-linear theories are greater when the opposing relative current and wave steepness become larger. However, within range of the following currents such errors will not be significant. These results were verified by model tests. Nomograms for the modification of wave length and wave height by the linear wave theory and Stokes1 third order theory are presented for a wide range of d/Ls, Hs/Ls and U/C. These nomograms provide the design engineer with a practical guide for estimating wave lengths and heights affected by currents.

scholarly journals MODIFICATION OF WAVE SPECTRA ON THE CONTINENTAL SHELF AND IN THE SURF ZONE

2011 ◽  
Vol 1 (8) ◽  
pp. 2 ◽  
Author(s):  
Charles L. Bretschneider
Keyword(s):  
Continental Shelf ◽  
Shallow Water ◽  
Surf Zone ◽  
Wind Waves ◽  
Wave Spectrum ◽  
Breaking Waves ◽  
Bottom Friction ◽  
Breaking Wave ◽  
Predominant Period ◽  
Significant Period

This paper discusses the problem pertaining to the modification of the wave spectrum over the continental shelf. Modification factors include bottom friction, percolation, refraction, breaking waves, ocean currents, and regeneration of wind waves in shallow water, among other factors. A formulation of the problem is presented but no general solution is made, primarily because of lack of basic data. Several special solutions are presented based on reasonable assumptions. The case for a steep continental shelf with parallel bottom contours and wave crests parallel to the coast and for which bottom friction is neglected has been investigated. For this case it is found that the predominant period shifts toward longer periods. The implication is, for example, that the significant periods observed along the U. S. Pacific coast are longer than those which would be observed several miles westward over deep water. The case for a gentle continental shelf with parallel bottom contour and wave crests parallel to the coast and for which bottom friction is important has also been investigated. For this case it is found that the predominant period shifts toward shorter periods as the water depth decreases. The implication is, for example, that the significant periods observed in the shallow water over the continental shelf are shorter than those which would be observed beyond the continental slope. In very shallow water, because shoaling becomes important, a secondary peak appears at higher periods. The joint distribution of wave heights and wave periods is required in order to determine the most probable maximum breaking wave, which can be of lesser height than the most probable maximum non-breaking wave. In very shallow water the most probable maximum breaking wave which first occurs would be governed by the breaking depth criteria, whereas in deepwater wave steepness can also be a governing factor. It can be expected that in very shallow water the period of the most probable maximum breaking wave should be longer than the significant period; and for deeper water the period of the most probable maximum breaking wave can be less than the significant period.

Cyclic Soil Loads on an Offshore Wind Turbine During Storm

2018 ◽  
Author(s):  
Shaofeng Wang ◽  
Torben J. Larsen
Keyword(s):  
Wind Turbine ◽  
Wave Theory ◽  
Offshore Wind ◽  
Irregular Waves ◽  
Offshore Wind Turbine ◽  
Breaking Wave ◽  
Cyclic Loads ◽  
Linear Wave ◽  
Pile Settlement ◽  
Cyclic Degradation

Offshore wind turbines are subjected to combined static and cyclic loads due to its self weight, wind, current and waves. For the design of support structures, a point of concern is whether the highly varying loads may cause cyclic degradation of the soil leading to a permanent undesired pile settlement and tilting for the wind turbine. In particular during a severe storm, the large cyclic loads are being more critical as the wind and waves are typically from a single direction. The DTU 10MW wind turbine supported by a jacket at 33 m water depth is considered in this study, where the piles are axially loaded in order to bear the moment under wind and wave actions. This paper investigates the cyclic loads using traditional linear irregular waves and fully nonlinear irregular waves realized from the wave solver Ocean-Wave3D previously validated until near-breaking wave conditions. This study shows that the nonlinear irregular waves introduce more extreme cyclic loads, which result in significantly larger pile settlement than using linear wave realizations. For the case in this study, linear wave theory underestimates pile settlement at least 30% compared to nonlinear wave realizations.

scholarly journals COMPUTATIONS OF LONGSHORE CURRENTS

1964 ◽  
Vol 1 (9) ◽  
pp. 12
Author(s):  
Tsao-Yi Chiu ◽  
Per Bruun
Keyword(s):  
Wave Height ◽  
Wave Breaking ◽  
Surf Zone ◽  
Wave Spectrum ◽  
Wave Theory ◽  
Breaking Wave ◽  
Height Distribution ◽  
Longshore Current ◽  
Longshore Currents ◽  
Actual Height

This article introduces the longshore current computations based on theories published under the title "Longshore Currents and Longshore Troughs" (Bruun, 1963). Two approaches are used to formulate the longshore current velocities for a beach profile with one bar under the following assumptions: (1) that longshore current is evenly distributed (or a mean can be taken) along the depthj (2) that the solitary wave theory is applicable for waves in the surf zone; (3) that the statistical wave-height distribution for a deep water wave spectrum with a single narrow band of frequencies can be used near the shore, and (4) that the depth over the bar crest, Dcr, equal 0.8Hv/i /o\. Breaking wave height H^Q/^X is designated to be the actual height equal to Hw-j (significant wave height). Diagrams have been constructed for both approaches for beach profiles with one bar, from which longshore current velocities caused by various wave-breaking conditions can be read directly. As for longshore currents along the beach with a multibar system, fifteen diagrams covering a great variety of wave-breaking conditions are provided for obtaining longshore current velocities in different troughs.

scholarly journals Dynamics of Wave Setup over a Steeply Sloping Fringing Reef

2015 ◽  
Vol 45 (12) ◽  
pp. 3005-3023 ◽  
Author(s):  
Mark L. Buckley ◽  
Ryan J. Lowe ◽  
Jeff E. Hansen ◽  
Ap R. Van Dongeren
Keyword(s):  
Wave Theory ◽  
Water Levels ◽  
Wave Radiation ◽  
Linear Wave ◽  
Radiation Stress ◽  
Wave Setup ◽  
Fringing Reef ◽  
Linear Wave Theory ◽  
Stress Gradients ◽  
Wide Range

AbstractHigh-resolution observations from a 55-m-long wave flume were used to investigate the dynamics of wave setup over a steeply sloping reef profile with a bathymetry representative of many fringing coral reefs. The 16 runs incorporating a wide range of offshore wave conditions and still water levels were conducted using a 1:36 scaled fringing reef, with a 1:5 slope reef leading to a wide and shallow reef flat. Wave setdown and setup observations measured at 17 locations across the fringing reef were compared with a theoretical balance between the local cross-shore pressure and wave radiation stress gradients. This study found that when radiation stress gradients were calculated from observations of the radiation stress derived from linear wave theory, both wave setdown and setup were underpredicted for the majority of wave and water level conditions tested. These underpredictions were most pronounced for cases with larger wave heights and lower still water levels (i.e., cases with the greatest setdown and setup). Inaccuracies in the predicted setdown and setup were improved by including a wave-roller model, which provides a correction to the kinetic energy predicted by linear wave theory for breaking waves and produces a spatial delay in the wave forcing that was consistent with the observations.

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