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 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.

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 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 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 Calculation of the Accelerated Breaking-Roller Propagation Speed and Wave Energy Transfer to the Roller

2011 ◽  
Author(s):  
Takashi Okamoto ◽  
Conceic¸a˜o Juana Fortes
Keyword(s):  
Energy Transfer ◽  
Wave Breaking ◽  
Wave Motion ◽  
Propagation Speed ◽  
Breaking Waves ◽  
Energy Calculation ◽  
Energy Transfer Rate ◽  
Wave Tank ◽  
Slow Decay ◽  
Wave Celerity

Wave breaking has different physics from the potential flow wave motion. The roller model introduced by Svendsen [1] illustrates the separation of the wave motion and the roller. The roller propagation speed, therefore, is a very important factor for the energy calculation of the bore. The wave celerity data collected at the wave tank displays that the maximum roller propagation speed occurs when the wave has already decayed due to the breaking. This fact clearly displays that the bore energy cannot be calculated only from the wave height as it is done for non-breaking waves. It is certain that most the energy is dissipated through the roller formation in the outer surfzone, but a certain amount of energy is transferred to the roller at the same time and it accelerates the bore speed. Slow decay of the roller propagation speed indicates that the excess energy left in the roller dissipates in the inner surfzone at much slower rate than in the outer surfzone. Therefore, these two zones have to be clearly separated, but the amount of energy transferred into the roller is unknown. In this paper, we focus on the examination of the peak roller propagation speed that appears at the border of the outer and the inner surfzone by using the experimental data collected at the wave tank. In that way, the initial condition of roller propagation speed can be determined for the inner surfzone. The energy conservation between the wave motion and the roller kinetic energy derives an equation to calculate the roller propagation speed. The energy transfer rate is estimated by adjusting the value given by the full energy conversion with the observed roller propagation speed. It is found that about half of the energy is transferred into the roller. The model successfully illustrates the peak bore propagation speed which existing formulae cannot explain.

scholarly journals INDIVIDUAL WAVE EFFECTS ON COASTAL STRUCTURE DAMAGE DURING WINDSTORMS

2018 ◽  
pp. 14
Author(s):  
Gregory Westcott ◽  
Annette R. Grilli ◽  
Stephan Grilli ◽  
James T. Kirby ◽  
Fengyan Shi
Keyword(s):  
Structural Damage ◽  
Wave Interaction ◽  
Wave Theory ◽  
Conservation Equation ◽  
Wave Crest ◽  
Linear Wave ◽  
Structure Damage ◽  
Interaction Terms ◽  
Structural Loading ◽  
Set Up

In hazard assessment studies that evaluate the damage caused to coastal structures by windstorm-generated surge and waves, the standard approach has been to estimate structural loading by applying phase-averaged wave propagation models (e.g., SWAN, STWAVE) and storm surge models (e.g., ADCIRC), coupled or not with each other. Bare-earth “Digital Elevation Models” (DEMs) have typically been used as a basis for model grid development, with sometimes empirical adjustments being made to beach profiles or dune crest levels to account for storm-induced erosion. In recent work, the latter approach has been improved by including real time morphodynamic changes in simulations, using models such as XBeach (e.g., Schambach 2017; Schambach et al., 2017), which are still based on the wave action conservation equation, including semi-empirical parameterizations of wave breaking and many formulations based on linear wave theory (e.g., phase/group velocity, radiation stresses,…), as well as low-order wave-wave interaction terms. Finally, structural damage has typically been estimated based on empirical damage curves, developed based on field surveys, that use flow depth and controlling wave crest height as inputs (e.g., Grilli et al., 2017). Neglected in this modeling approach, however, are dynamic set-up and runup effects, as well as strongly nonlinear wave interactions that occur near and in the surf and swash zones.

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 Characteristics of Breaking Wave Forces on Piles over a Permeable Seabed

2021 ◽  
Vol 9 (5) ◽  
pp. 520
Author(s):  
Zhenyu Liu ◽  
Zhen Guo ◽  
Yuzhe Dou ◽  
Fanyu Zeng
Keyword(s):  
Wave Breaking ◽  
Stokes Equations ◽  
Slope Angle ◽  
Wave Force ◽  
Breaking Waves ◽  
Offshore Wind ◽  
Secondary Wave ◽  
Wave Forces ◽  
Breaking Wave ◽  
Breaking Wave Forces

Most offshore wind turbines are installed in shallow water and exposed to breaking waves. Previous numerical studies focusing on breaking wave forces generally ignored the seabed permeability. In this paper, a numerical model based on Volume-Averaged Reynolds Averaged Navier–Stokes equations (VARANS) is employed to reveal the process of a solitary wave interacting with a rigid pile over a permeable slope. Through applying the Forchheimer saturated drag equation, effects of seabed permeability on fluid motions are simulated. The reliability of the present model is verified by comparisons between experimentally obtained data and the numerical results. Further, 190 cases are simulated and the effects of different parameters on breaking wave forces on the pile are studied systematically. Results indicate that over a permeable seabed, the maximum breaking wave forces can occur not only when waves break just before the pile, but also when a “secondary wave wall” slams against the pile, after wave breaking. With the initial wave height increasing, breaking wave forces will increase, but the growth can decrease as the slope angle and permeability increase. For inclined piles around the wave breaking point, the maximum breaking wave force usually occurs with an inclination angle of α = −22.5° or 0°.

scholarly journals Assessment of Numerical Methods for Plunging Breaking Wave Predictions

2021 ◽  
Vol 9 (3) ◽  
pp. 264
Author(s):  
Shanti Bhushan ◽  
Oumnia El Fajri ◽  
Graham Hubbard ◽  
Bradley Chambers ◽  
Christopher Kees
Keyword(s):  
Solitary Wave ◽  
Wave Breaking ◽  
Large Scale ◽  
Turbulence Models ◽  
Navier Stokes ◽  
Wave Crest ◽  
Breaking Wave ◽  
Rans Turbulence Models ◽  
Run Up ◽  
Better Than

This study evaluates the capability of Navier–Stokes solvers in predicting forward and backward plunging breaking, including assessment of the effect of grid resolution, turbulence model, and VoF, CLSVoF interface models on predictions. For this purpose, 2D simulations are performed for four test cases: dam break, solitary wave run up on a slope, flow over a submerged bump, and solitary wave over a submerged rectangular obstacle. Plunging wave breaking involves high wave crest, plunger formation, and splash up, followed by second plunger, and chaotic water motions. Coarser grids reasonably predict the wave breaking features, but finer grids are required for accurate prediction of the splash up events. However, instabilities are triggered at the air–water interface (primarily for the air flow) on very fine grids, which induces surface peel-off or kinks and roll-up of the plunger tips. Reynolds averaged Navier–Stokes (RANS) turbulence models result in high eddy-viscosity in the air–water region which decays the fluid momentum and adversely affects the predictions. Both VoF and CLSVoF methods predict the large-scale plunging breaking characteristics well; however, they vary in the prediction of the finer details. The CLSVoF solver predicts the splash-up event and secondary plunger better than the VoF solver; however, the latter predicts the plunger shape better than the former for the solitary wave run-up on a slope case.

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