scholarly journals BREAKING WAVE CRITERIA; A STUDY EMPLOYING A NUMERICAL WAVE THEORY

1968 ◽  
Vol 1 (11) ◽  
pp. 8 ◽  
Author(s):  
Robert G. Dean
Keyword(s):  
Stream Function ◽  
Nonlinear Wave ◽  
Wave Spectrum ◽  
Small Diameter ◽  
Wave Theory ◽  
Breaking Waves ◽  
Fundamental Period ◽  
Breaking Wave ◽  
Engineering Design Problems ◽  
Wide Range

Although it is well recognized that wave systems in nature are irregular, comprising a spectrum of fundamental periods, there is still a need for improving our understanding of near-breaking nonlinear wave systems which contain a single fundamental period. For example, most of the shallow water design situations and other cases including forces on small diameter structures in which drag forces predominate are more directly treated in terms of a "design wave" rather than a wave spectrum. This situation is contrasted to many important engineering design problems in which the dynamics of the system are paramount; for example, in the case of a moored drilling vessel. Finally, one may reasonably expect that accurate solutions to the problem of nonlinear wave systems with a single fundamental period will lend insight regarding productive approaches to the more realistic problem of a spectrum of nonlinear waves. This paper investigates the applicability of the stream function wave theory1 for the representation of breaking and near-breaking waves. This particular problem has received little attention, although considerable progress has occurred on two related problems: 1. The development of wave theories covering a wide range of relative water depths and wave heights, and 2. The development of wave theories which apply at breaking conditions. In general, although these theories may be applicable for the limiting wave conditions, their basis of derivation is such that they cannot be extended to non-breaking waves. The purpose of the present investigation, then, is to establish whether or not the stream function wave theory can be applied to span the range extending up to breaking conditions.

scholarly journals Semiempirical Dissipation Source Functions for Ocean Waves. Part I: Definition, Calibration, and Validation

2010 ◽  
Vol 40 (9) ◽  
pp. 1917-1941 ◽  
Author(s):  
Fabrice Ardhuin ◽  
Erick Rogers ◽  
Alexander V. Babanin ◽  
Jean-François Filipot ◽  
Rudy Magne ◽  
...  
Keyword(s):  
Wind Speed ◽  
Wave Height ◽  
Wave Breaking ◽  
Wave Spectrum ◽  
Remote Sensing Data ◽  
Ocean Waves ◽  
Breaking Waves ◽  
Global Ocean ◽  
Short Waves ◽  
Wide Range

Abstract New parameterizations for the spectral dissipation of wind-generated waves are proposed. The rates of dissipation have no predetermined spectral shapes and are functions of the wave spectrum and wind speed and direction, in a way consistent with observations of wave breaking and swell dissipation properties. Namely, the swell dissipation is nonlinear and proportional to the swell steepness, and dissipation due to wave breaking is nonzero only when a nondimensional spectrum exceeds the threshold at which waves are observed to start breaking. An additional source of short-wave dissipation is introduced to represent the dissipation of short waves due to longer breaking waves. A reduction of the wind-wave generation of short waves is meant to account for the momentum flux absorbed by longer waves. These parameterizations are combined and calibrated with the discrete interaction approximation for the nonlinear interactions. Parameters are adjusted to reproduce observed shapes of directional wave spectra, and the variability of spectral moments with wind speed and wave height. The wave energy balance is verified in a wide range of conditions and scales, from the global ocean to coastal settings. Wave height, peak and mean periods, and spectral data are validated using in situ and remote sensing data. Some systematic defects are still present, but, overall, the parameterizations probably yield the most accurate estimates of wave parameters to date. Perspectives for further improvement are also given.

scholarly journals The influence of nonlinear interaction on the evolution of waves in a shallow basin

2019 ◽  
Vol 55 (4) ◽  
pp. 82-86
Author(s):  
A. A. Rodin ◽  
N. A. Rodina ◽  
A. A. Kurkin ◽  
E. N. Pelinovsky
Keyword(s):  
Phase Shift ◽  
Shallow Water ◽  
Nonlinear Wave ◽  
Nonlinear Interaction ◽  
Breaking Waves ◽  
Breaking Wave ◽  
Theoretical Predictions ◽  
Shallow Basin ◽  
The Moment

The influence of counter interaction of nonlinear wave in the shallow water has been studied. It is shown that such an interaction leads to a change in the phase of propagation of the main wave, which is forced to propagate along the flow induced by the counter-propagating wave. Estimates of the height of the non-breaking wave at the moment of interaction are in agreement with theoretical predictions. The phase shift in the interaction of non-breaking waves is small enough, but becomes noticeable in the case of the breaking waves motion.

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.

Investigation on the Use of a Multiphase Eulerian CFD Solver to Simulate Breaking Waves

2015 ◽  
Author(s):  
Pietro D. Tomaselli ◽  
Erik Damgaard Christensen
Keyword(s):  
Free Surface ◽  
Bubble Column ◽  
Preliminary Investigation ◽  
Air Entrainment ◽  
Breaking Waves ◽  
Breaking Wave ◽  
Main Challenge ◽  
Wide Range ◽  
Entrapped Air ◽  
Dispersed Flows

The main challenge in CFD multiphase simulations of breaking waves is the wide range of interfacial length scales occurring in the flow: from the free surface measurable in meters down to the entrapped air bubbles with size of a fraction of a millimeter. This paper presents a preliminary investigation on a CFD model capable of handling this problem. The model is based on a solver, available in the open-source CFD toolkit OpenFOAM, which combines the Eulerian multi-fluid approach for dispersed flows with a numerical interface sharpening method. The solver, enhanced with additional formulations for mass and momentum transfer among phases, was satisfactorily tested against an experimental bubble column flow. The model was then used to simulate the propagation of a laboratory solitary breaking wave. The motion of the free surface was successfully reproduced up to the breaking point. Further implementations are needed to simulate the air entrainment phenomenon.

Numerical Modeling Using CFD and Potential Wave Theory for Three-Hour Nonlinear Irregular Wave Simulations

2017 ◽  
Author(s):  
Aldric Baquet ◽  
Jang Kim ◽  
Zhenjia (Jerry) Huang
Keyword(s):  
Numerical Modeling ◽  
Potential Theory ◽  
Wave Spectrum ◽  
Nonlinear Effects ◽  
Wave Theory ◽  
Breaking Waves ◽  
Wave Crest ◽  
Fully Nonlinear ◽  
Irregular Wave ◽  
Stokes Waves

In this paper, we focus on the modeling of a fully-nonlinear, steep, irregular wave field of three-hour duration without structures in it. The fully-nonlinear effects are considered in the wave simulations using computational fluid dynamics (CFD), as well as potential theory. The overall approach for the numerical modeling is described in the paper. The Euler Overlay Method (EOM) is used to incorporate incoming waves, nonlinear effects, and CFD simulations in the numerical modeling. For computational efficiency, we also use potential theory to model the fully-nonlinear waves. Numerical damping was applied locally around the breaking region to enable simulations for large breaking waves. To compensate for energy loss in the numerical simulations, energy compensation factors of wave spectral frequency components are applied to the input wave spectrum. Results of convergence study, validation against high-order Stokes waves and fully-nonlinear irregular wave with prescribed target spectrum, as well as comparison between numerical wave crest distributions and those from multiple realizations of wave calibration tests are presented.

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.

Comparing Different Approaches for Calculating Wave Impacts on a Monopile Turbine Foundation

2017 ◽  
Author(s):  
Simon Burmester ◽  
Erik-Jan de Ridder ◽  
Christof Wehmeyer ◽  
Erik Asp ◽  
Philipp Gujer
Keyword(s):  
Stream Function ◽  
Model Test ◽  
Time History ◽  
Breaking Waves ◽  
Offshore Wind ◽  
Breaking Wave ◽  
Good Representation ◽  
Test Results ◽  
Support Structure ◽  
Offshore Wind Turbines

In this paper two different approaches to calculate the wave impacts on a monopile are introduced and compared to model test results. Within the scope of the WiFi JIP (Joint Industry Project Wave Impacts on Fixed turbines) model tests at MARIN (Maritime Research Institute Netherlands) and at Deltares were conducted to investigate the effects of steep (and breaking) waves on the support structure of bottom fixed offshore wind turbines. Three different ways to generate breaking waves were used. At MARIN focused waves were generated to obtain breaking wave events. Two different methods to calculate slamming loads on monopiles are compared to the wave impacts measured. The results are analyzed in time history and load maxima plots. In addition the obtained curling factors of the focused waves are compared to irregular sea states recorded on a flat seabed and a sandwave. A good representation of the loads calculated by Wienke’s approach was observed for all waves investigated. However, to estimate the kinematics of focused breaking wave events more accurate methods than stream function are needed.

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.

An Engineering-Model for Extreme Wave-Induced Loads on Monopile Foundations

2017 ◽  
Author(s):  
Hans Fabricius Hansen ◽  
Henrik Kofoed-Hansen
Keyword(s):  
Water Level ◽  
Stream Function ◽  
Wave Theory ◽  
Breaking Waves ◽  
Gradual Transition ◽  
Wave Load ◽  
Sea State ◽  
Load Model ◽  
Wave Basin ◽  
Wave Induced

An extension of the classical Wheeler’s method is here presented and validated. Just as the Wheeler’s method, it relies solely on the measurement of surface elevation in a point to make predictions of the wave induced loads. These measurements may be made in the field, but more often they will be generated in a laboratory wave basin. The classical Wheeler stretching plus Morison load model is augmented by a slamming load model for steep near-breaking and breaking waves, based on work published earlier by Nestegård et.al. (2004). The new model thereby spans the entire range from non-breaking waves to severely breaking overturning waves with a gradual transition. The model has been validated against surface elevations and wave loads measured in a laboratory wave tank and is found to reproduce wave load distributions over a range of sea state conditions well. Examples are given for typical design sea state conditions for offshore wind turbines at exposed locations in Northern Europe. The loads are compared to loads obtained using the stream function wave theory in combination with the Morison’s equation. The stream function wave theory loads are found to generally be lower than the loads predicted using the simple wave load model presented here. This is the case even for mildly non-linear non-breaking waves but becomes much more pronounced for steep near-breaking and breaking waves. Another striking feature of the comparison to regular wave theory is the different distribution of loads. The stream function loads below still water level are often higher than the loads from the simple model, but much lower than the simple load model loads above still water level.

PHYSICAL INTERPRETATION OF WAVE BREAKING CRITERIA

2017 ◽  
Author(s):  
Sergey Kuznetsov ◽  
Sergey Kuznetsov ◽  
Yana Saprykina ◽  
Yana Saprykina ◽  
Boris Divinskiy ◽  
...  
Keyword(s):  
Nonlinear Wave ◽  
Wave Breaking ◽  
Second Harmonic ◽  
Vertical Axis ◽  
Breaking Waves ◽  
Wave Transformation ◽  
Spectral Structure ◽  
Similarity Parameter ◽  
Nonlinear Harmonics ◽  
The Waves

On the base of experimental data it was revealed that type of wave breaking depends on wave asymmetry against the vertical axis at wave breaking point. The asymmetry of waves is defined by spectral structure of waves: by the ratio between amplitudes of first and second nonlinear harmonics and by phase shift between them. The relative position of nonlinear harmonics is defined by a stage of nonlinear wave transformation and the direction of energy transfer between the first and second harmonics. The value of amplitude of the second nonlinear harmonic in comparing with first harmonic is significantly more in waves, breaking by spilling type, than in waves breaking by plunging type. The waves, breaking by plunging type, have the crest of second harmonic shifted forward to one of the first harmonic, so the waves have "saw-tooth" shape asymmetrical to vertical axis. In the waves, breaking by spilling type, the crests of harmonic coincides and these waves are symmetric against the vertical axis. It was found that limit height of breaking waves in empirical criteria depends on type of wave breaking, spectral peak period and a relation between wave energy of main and second nonlinear wave harmonics. It also depends on surf similarity parameter defining conditions of nonlinear wave transformations above inclined bottom.

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