PHYSICAL INTERPRETATION OF WAVE BREAKING CRITERIA

Author(s):  
Sergey Kuznetsov ◽  
Sergey Kuznetsov ◽  
Yana Saprykina ◽  
Yana Saprykina ◽  
Boris Divinskiy ◽  
...  

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.

Author(s):  
Sergey Kuznetsov ◽  
Sergey Kuznetsov ◽  
Yana Saprykina ◽  
Yana Saprykina ◽  
Boris Divinskiy ◽  
...  

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.


Author(s):  
Sergey Kuznetsov ◽  
Yana Saprykina ◽  
Valentina Volkova

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.


Author(s):  
Fuxian Gong ◽  
Manhar R. Dhanak

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.


Author(s):  
Yana Saprykina ◽  
Sergey Kuznetsov ◽  
Margarita Shtremel

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.


2016 ◽  
Vol 858 ◽  
pp. 354-358
Author(s):  
Tao You ◽  
Li Ping Zhao ◽  
Zheng Xiao ◽  
Lun Chao Huang ◽  
Xiao Rui Han

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.


2020 ◽  
Vol 28 (1) ◽  
pp. 75-82
Author(s):  
Ya. V. Saprykina ◽  
S. Yu. Kuznetsov ◽  
O. A. Kuznetsova ◽  
I. V. Shugan ◽  
Yang-Yih Chen

Author(s):  
Steven A. Schmied ◽  
Jonathan R. Binns ◽  
Martin R. Renilson ◽  
Giles A. Thomas ◽  
Gregor J. Macfarlane ◽  
...  

In this paper, a novel idea to produce continuous breaking waves is discussed, whereby a pressure source is rotated within an annular wave pool. The concept was that the pressure source generates non-breaking waves that propagate inward to the inner ring of the annulus, where a sloping bathymetry (beach) triggers wave breaking. In order to refine the technique, research was conducted to better understand the mechanics of waves generated by a pressure source moving in a circular track in a constrained waterway, the transformation of these waves as they travel across the channel and the effect of the sloping beach on the wave quality for surfing. The quality of the waves was defined in terms of wave height, speed and shape, with the desired aim to create plunging waves, known as “barrels”, that are highly desired by surfers. Surfers also require a long steep crestline or “wall”, to allow a full range of manoeuvres to be performed. Finally, the pool needed to be able to create waves suitable for surfers from beginner to expert level, defined in terms of both the wave height and angle between the wave break point angle and the beach, known a peel angle. The primary novel outcome of the research conducted was to be able to design a pressure source that most efficiently imparted wave making energy into the water, and thus generated the largest possible waves whilst travelling at the required speed for surfing. The major finding was that the design parameters are generally in competition, and to determine a balance of limiting values, the design parameters cannot be considered in isolation. Therefore, a set of empirical relationships between the design parameters were developed to allow the pool to be designed for a combination of desired wave height at the breakpoint, wave shape and given pool radius. The limiting values for the parameters were determined experimentally, with the wave life-cycle from generation through transformation to wave breaking and dissipation used to focus the investigation. Scale model experiments were conducted in both linear and circular tracks. In addition to taking quantitative measurement of wave height and current formation, a method of qualitatively scoring the waves was developed to allow various pressure source shapes, operating conditions and bathymetries to be compared in terms of their suitability for surfing. The best quality waves were produced by a wedge-shaped wavedozer pressure source, such as the device detailed in Driscoll and Renilson [1]. Blockage, defined as the pressure source cross sectional area to channel cross-sectional area, was found to have a significant limitation on the generation of high quality waves suitable for surfing in a constrained waterway. Lateral wave decay, length and depth Froude Numbers also strongly influenced the waves during their life-cycle. Fundamentally, it was determined that only a very small range of design parameter values produce the desired high and shapely waves in the extremely constrained waterway under consideration.


2011 ◽  
Vol 1 (32) ◽  
pp. 13 ◽  
Author(s):  
Marion Tissier ◽  
Philippe Bonneton ◽  
Fabien Marche ◽  
Florent Chazel ◽  
David Lannes

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.


Author(s):  
Steven A. Schmied ◽  
Jonathan R. Binns ◽  
Martin R. Renilson ◽  
Giles A. Thomas ◽  
Gregor J. Macfarlane ◽  
...  

In this paper, a novel idea to produce continuous breaking waves is discussed, whereby a pressure source is rotated within an annular wave pool. The concept is that the inner ring of the annulus has a sloping bathymetry to induce wave breaking from the wake of the pressure source. In order to refine the technique, work is being conducted to better understand the mechanics of surfable waves generated by moving pressure sources in restricted water. This paper reports on the first stage of an experimental investigation of a novel method for generating continuously surfable waves utilising a moving pressure source. The aim was to measure and assess the waves generated by two parabolic pressure sources and a wavedozer [1] for their suitability for future development of continuous breaking surfable waves. The tests were conducted at the Australian Maritime College (AMC), University of Tasmania (UTas) 100 metre long towing tank. The experimental results as variations in wave height (H) divided by water depth (h) as functions of depth Froude number (Frh) and h, together with predictions from both methods, are presented in this paper. Finally, measures of the wave making energy efficiency of each pressure source, and the surfable quality of the waves generated by it, were developed and are presented.


2020 ◽  
Vol 10 (12) ◽  
pp. 4087
Author(s):  
Yana Saprykina

On the basis of field experiment data, the main features of influence of non-linear wave transformation scenarios on cross-shore sediment transport in coastal zones were investigated. The bottom deformations due to the non-linear wave transformation follow the specific scenario. The increase in the second non-linear harmonic amplitude leads to the erosion of the underwater slope at the distances corresponding to this process, with the subsequent accumulation of sandy material closer to the shore at distances where the amplitude decreases during the backward energy transfer to the first harmonic. This can be explained by the change in the phase shift between harmonics during non-linear wave transformation. The second harmonic maximum provides the point near which the bottom deformations occur in different directions. Scenarios of non-linear wave transformation in which backward energy transfer from the second non-linear harmonic to the first is close to the shoreline will contribute to the transport and accumulation of the sediment on the coast. These scenarios are more characteristic of “small waves”. The scenario without a periodical exchange of wave energy between non-linear harmonics (with an increase in the second harmonic only) that is characteristic of large storm waves and plunging breaking waves will lead to the erosion of the underwater bottom profile.


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