scholarly journals DEPENDENCIES OF BREAKING TYPE, BREAKING CRITERIA AND ENERGY DISSIPATION ON AMPLITUDE-PHASE FREQUENCY STRUCTURE OF WAVES

2018 ◽  
pp. 72
Author(s):  
Sergey Kuznetsov ◽  
Yana Saprykina ◽  
Valentina Volkova
Keyword(s):  
Wave Energy ◽  
Wave Breaking ◽  
Dissipation Rate ◽  
Vertical Axis ◽  
Breaking Waves ◽  
Horizontal Axis ◽  
Wave Transformation ◽  
Linear Wave ◽  
Frequency Range ◽  
Nonlinear Harmonics

Type of wave breaking - plunging or spilling - depends on symmetry of waves. The spilling waves are asymmetric against horizontal axis and are practically symmetric against vertical axis so the phase shift between first and second nonlinear harmonics (or biphase) is close to zero. The plunging breaking waves have larger asymmetry against vertical axis, (biphase is close to -pi/2), and near symmetric on horizontal axis (close to saw-toothed form). Non-linear wave transformation influences on depth-induced wave breaking. Breaking index depends on relation of wave energy in frequency range of second nonlinear harmonics to wave energy in frequency range of main harmonic and on biphase. The dissipation rate of spilling breaking waves energy quadratically depends on frequency, while in plunging breaking, this dependency is practically linear for all frequencies.

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.

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.

On characteristics of the water-particle velocity in a plunging breaker

1983 ◽  
Vol 126 ◽  
pp. 251-268 ◽  
Author(s):  
Takeo Nakagawa
Keyword(s):  
Wave Energy ◽  
Wave Breaking ◽  
Separate Flow ◽  
Transverse Flow ◽  
Two Dimensional ◽  
Frequency Range ◽  
Flow Component ◽  
Flow Components ◽  
Flow Drag ◽  
Plunging Breaker

Three velocity components of water particles in a plunging breaker over a horizontal step on the bed of a two-dimensional laboratory wave tank have been determined simultaneously by means of an elaborate flowmeter that measures the flow drag on three ‘tension threads’, with each recording a separate flow component.It is found that all three of the r.m.s. values in the plunging breaker become maximum at x/L ≈ 0·7, where x is the distance from the breaking point to the shore and L is the wavelength. It is found that both the velocity and r.m.s. values of the transverse flow component generated by the shoaling and wave breaking become comparable to those of the other two flow components.On the basis of spectral analyses it is found that major wave frequencies in both the longitudinal and vertical flow components of the original two-dimensional wave survive even after experiencing relatively strong shoaling and wave breaking, and part of the original wave energy is transferred to the transverse flow component and is located at these major frequencies. It is found that the majority of the higher-harmonic-frequency components (or turbulent fluctuations) are generated in the shoaling process and that the wave breaking provides a relatively minor contribution to the generation. Finally, it is found that, through the shoaling and wave breaking, the original wave energy is transported to a frequency range lower than the primary wave frequency (negative cascade), as well as to the higher frequency range (positive cascade) in each flow component.

scholarly journals PARAMETERIZATION OF EVOLUTION OF BIPHASE DURING NONLINEAR TRANSFORMATION OF WAVES IN COASTAL ZONE

2017 ◽  
pp. 3
Author(s):  
Yana Saprykina ◽  
Sergey Kuznetsov ◽  
Margarita Shtremel
Keyword(s):  
Experimental Data ◽  
Phase Shift ◽  
Coastal Zone ◽  
Energy Exchange ◽  
Wave Motion ◽  
Empirical Relation ◽  
Breaking Waves ◽  
Wave Transformation ◽  
Nonlinear Harmonics ◽  
Sloping Bottom

Based on experimental data, the problem of parametrization of spatial variation of the phase shift (biphase) between the first and second nonlinear harmonics of wave motion during wave transformation over sloping bottom in the coastal zone is discussed. It is revealed that the biphase values vary in the range [–π/2, π/2]. Biphase variations rigorously follow fluctuations in amplitudes of the first and second harmonics and the periodicity of energy exchange between them. The empirical relation applied in modern practice to calculate the biphase, which depends on the Ursell number, is incorrect for calculating the biphase for wave evolution in the coastal zone, because it does not take into account periodic energy exchange between the nonlinear harmonics. The new approximations of the biphase values for typical scenarios of wave transformations are suggested. It was demonstrated that the biphase of breaking waves defines breaking index and breaking type.

Characteristics of Transforming Waves Breaking Over a Fringing Reef

2019 ◽  
Author(s):  
Fuxian Gong ◽  
Manhar R. Dhanak
Keyword(s):  
Energy Flux ◽  
Wave Breaking ◽  
Reef Flat ◽  
Stokes Equations ◽  
Second Harmonic ◽  
Breaking Waves ◽  
Wave Transformation ◽  
Fundamental Wave ◽  
Fringing Reef ◽  
Wave Shoaling

Abstract Direct numerical simulation (DNS), based on solution of the Navier Stokes equations, is used to study the characteristics of the transformation of monochromatic waves over a simplified fringing reef, including wave shoaling, and wave breaking that occurs under certain circumstances. The reef geometry involves a sloped plane beach extended with a simple submerged horizontal reef flat. The characteristics are studied for several case studies involving a selection of submergence depths on the reef flat and for a range of incident wave conditions, corresponding to nonbreaking, a spilling breaker and a plunging breaker, are considered. The results are compared with those of laboratory experiments (Kouvaras and Dhanak, 2018). Consistent with other studies, generation of harmonics of the fundamental wave frequency is found to accompany the wave transformation over the reef and the process of transfer of energy through wave breaking. The energy flux decreases dramatically in the onshore direction when the waves break. The more severe the wave breaking process, the greater the decrease in energy flux, particularly in the wave shoaling process. Most of the wave energy is carried by the first harmonic throughout its passage over the fringing reef. In nonbreaking waves, the energy gradually transfers from the first harmonic to the second harmonic due to bottom effects in terms of flat wave troughs and secondary waves. The further the distance away from the fore edge of the reef, the larger the percentage of the transmission, resulting in a single dominant harmonic frequency at the end of the wave surfing zone. For breaking waves, the energy carried by the first harmonic gradually decreases in the onshore direction. Energy transmission between harmonics is not as efficient as nonbreaking waves, while wave dissipation is significant in the wave breaking process.

scholarly journals Observations of Breaking Waves and Energy Dissipation in Modulated Wave Groups

2018 ◽  
Vol 48 (12) ◽  
pp. 2937-2948 ◽  
Author(s):  
David W. Wang ◽  
Hemantha W. Wijesekera
Keyword(s):  
Energy Dissipation ◽  
Wave Height ◽  
Wave Breaking ◽  
Dissipation Rate ◽  
Breaking Waves ◽  
Wave Groups ◽  
Dissipation Rates ◽  
Local Wave ◽  
Tke Dissipation Rate ◽  
The Impact

AbstractIt has been recognized that modulated wave groups trigger wave breaking and generate energy dissipation events on the ocean surface. Quantitative examination of wave-breaking events and associated turbulent kinetic energy (TKE) dissipation rates within a modulated wave group in the open ocean is not a trivial task. To address this challenging topic, a set of laboratory experiments was carried out in an outdoor facility, the Oil and Hazardous Material Simulated Environment Test Tank (203 m long, 20 m wide, 3.5 m deep). TKE dissipation rates at multiple depths were estimated directly while moving the sensor platform at a speed of about 0.53 m s−1 toward incoming wave groups generated by the wave maker. The largest TKE dissipation rates and significant whitecaps were found at or near the center of wave groups where steepening waves approached the geometric limit of waves. The TKE dissipation rate was O(10−2) W kg−1 during wave breaking, which is two to three orders of magnitude larger than before and after wave breaking. The enhanced TKE dissipation rate was limited to a layer of half the wave height in depth. Observations indicate that the impact of wave breaking was not significant at depths deeper than one wave height from the surface. The TKE dissipation rate of breaking waves within wave groups can be parameterized by local wave phase speed with a proportionality breaking strength coefficient dependent on local steepness. The characterization of energy dissipation in wave groups from local wave properties will enable a better determination of near-surface TKE dissipation of breaking waves.

scholarly journals Spectrally Resolved Energy Dissipation Rate and Momentum Flux of Breaking Waves

2008 ◽  
Vol 38 (6) ◽  
pp. 1296-1312 ◽  
Author(s):  
Johannes R. Gemmrich ◽  
Michael L. Banner ◽  
Chris Garrett
Keyword(s):  
Energy Dissipation ◽  
Wave Field ◽  
Wave Energy ◽  
Dissipation Rate ◽  
Momentum Flux ◽  
Phase Speed ◽  
Breaking Waves ◽  
Energy Dissipation Rate ◽  
Small Scale ◽  
Breaking Wave

Abstract Video observations of the ocean surface taken from aboard the Research Platform FLIP reveal the distribution of the along-crest length and propagation velocity of breaking wave crests that generate visible whitecaps. The key quantity assessed is Λ(c)dc, the average length of breaking crests per unit area propagating with speeds in the range (c, c + dc). Independent of the wave field development, Λ(c) is found to peak at intermediate wave scales and to drop off sharply at larger and smaller scales. In developing seas breakers occur at a wide range of scales corresponding to phase speeds from about 0.1 cp to cp, where cp is the phase speed of the waves at the spectral peak. However, in developed seas, breaking is hardly observed at scales corresponding to phase speeds greater than 0.5 cp. The phase speed of the most frequent breakers shifts from 0.4 cp to 0.2 cp as the wave field develops. The occurrence of breakers at a particular scale as well as the rate of surface turnover are well correlated with the wave saturation. The fourth and fifth moments of Λ(c) are used to estimate breaking-wave-supported momentum fluxes, energy dissipation rate, and the fraction of momentum flux supported by air-entraining breaking waves. No indication of a Kolmogorov-type wave energy cascade was found; that is, there is no evidence that the wave energy dissipation is dominated by small-scale waves. The proportionality factor b linking breaking crest distributions to the energy dissipation rate is found to be (7 ± 3) × 10−5, much smaller than previous estimates.

Research and Analysis on the Wave Transformation and Irregular Wave Breaking Criterion on the Shore

2016 ◽  
Vol 858 ◽  
pp. 354-358
Author(s):  
Tao You ◽  
Li Ping Zhao ◽  
Zheng Xiao ◽  
Lun Chao Huang ◽  
Xiao Rui Han
Keyword(s):  
Theoretical Model ◽  
Wave Height ◽  
Wave Breaking ◽  
Surf Zone ◽  
Breaking Waves ◽  
Wave Transformation ◽  
Breaking Wave ◽  
Height Distribution ◽  
Flume Experiments ◽  
Irregular Wave

Within the surf zone which is the region extending from the seaward boundary of wave breaking to the limit of wave uprush, breaking waves are the dominant hydrodynamics acting as the key role for sediment transport and beach profile change. Breaking waves exhibit various patterns, principally depending on the incident wave steepness and the beach slope. Based on the equations of conservation of mass, momentum and energy, a theoretical model for wave transformation in and outside the surf zone was obtained, which is used to calculate the wave shoaling, wave set-up and set down and wave height distributions in and outside the surf zone. The analysis and comparison were made about the breaking point location and the wave height variation caused by the wave breaking and the bottom friction, and about the wave breaking criterion under regular and irregular breaking waves. Flume experiments relating to the regular and irregular breaking wave height distribution across the surf zone were conducted to verify the theoretical model. The agreement is good between the theoretical and experimental results.

Finite Element Analysis for Water Turbine of Horizontal Axis Rotor Wave Energy Converter

2014 ◽  
Vol 530-531 ◽  
pp. 906-910
Author(s):  
Dong Dong Hu ◽  
Yan Jun Liu ◽  
Li Kang Hong ◽  
Xiao Chen Guo
Keyword(s):  
Finite Element ◽  
Stress Response ◽  
Wave Energy ◽  
Stress Responses ◽  
Wave Energy Converter ◽  
Horizontal Axis ◽  
Linear Wave ◽  
Energy Converter ◽  
Element Analysis ◽  
Water Turbine

Horizontal axis rotor wave energy converter is a new form for utilization of ocean wave energy, and the axis of its water turbine is parallel with the sea level and perpendicular to the direction of wave. This paper employed the linear wave theory and Froude-Krylov presumptive method to calculate the wave force, which was exerted on the wave energy converter in extremely arduous wave conditions. The finite element research on the deformation and the stress response of the water turbine was carried out to assess its security. The results show that the deformation and the stress responses both reach their maximum values at the 3rd mode shape about 90Hz, and the deformation response is 0.4208mm and the stress response is 0.8052MPa at this frequency, which are both within the required security range.

scholarly journals SERRE GREEN-NAGHDI MODELLING OF WAVE TRANSFORMATION BREAKING AND RUN-UP USING A HIGH-ORDER FINITE-VOLUME FINITE-DIFFERENCE SCHEME

2011 ◽  
Vol 1 (32) ◽  
pp. 13 ◽  
Author(s):  
Marion Tissier ◽  
Philippe Bonneton ◽  
Fabien Marche ◽  
Florent Chazel ◽  
David Lannes
Keyword(s):  
Energy Dissipation ◽  
Finite Difference ◽  
Finite Volume ◽  
Wave Breaking ◽  
Ad Hoc ◽  
Laboratory Data ◽  
Breaking Waves ◽  
Wave Transformation ◽  
Finite Volume Schemes ◽  
Boussinesq Model

In this paper, a fully nonlinear Boussinesq model is presented and applied to the description of breaking waves and shoreline motions. It is based on Serre Green-Naghdi equations, solved using a time-splitting approach separating hyperbolic and dispersive parts of the equations. The hyperbolic part of the equations is solved using Finite-Volume schemes, whereas dispersive terms are solved using a Finite-Difference method. The idea is to switch locally in space and time to NSWE by skipping the dispersive step when the wave is ready to break, so as the energy dissipation due to wave breaking is predicted by the shock theory. This approach allows wave breaking to be handled naturally, without any ad-hoc parameterization for the energy dissipation. Extensive validations of the method are presented using laboratory data.

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