scholarly journals On a unified breaking onset threshold for gravity waves in deep and intermediate depth water

2018 ◽  
Vol 841 ◽  
pp. 463-488 ◽  
Author(s):  
X. Barthelemy ◽  
M. L. Banner ◽  
W. L. Peirson ◽  
F. Fedele ◽  
M. Allis ◽  
...  
Keyword(s):  
Water Waves ◽  
Wave Packets ◽  
Fluid Velocity ◽  
Bottom Topography ◽  
Breaking Waves ◽  
Wave Crest ◽  
Intermediate Depth ◽  
Local Ratio ◽  
2D And 3D ◽  
Depth Water

We revisit the classical but as yet unresolved problem of predicting the breaking onset of 2D and 3D irrotational gravity water waves. Based on a fully nonlinear 3D boundary element model, our numerical simulations investigate geometric, kinematic and energetic differences between maximally tall non-breaking waves and marginally breaking waves in focusing wave groups. Our study focuses initially on unidirectional domains with flat bottom topography and conditions ranging from deep to intermediate depth (depth to wavelength ratio from 1 to 0.2). Maximally tall non-breaking (maximally recurrent) waves are clearly separated from marginally breaking waves by their normalised energy fluxes localised near the crest tip region. The initial breaking instability occurs within a very compact region centred on the wave crest. On the surface, this reduces to the local ratio of the energy flux velocity (here the fluid velocity) to the crest point velocity for the tallest wave in the evolving group. This provides a robust threshold parameter for breaking onset for 2D wave packets propagating in uniform water depths from deep to intermediate. Further targeted study of representative cases of the most severe laterally focused 3D wave packets in deep and intermediate depth water shows that the threshold remains robust. These numerical findings for 2D and 3D cases are closely supported by our companion observational results. Warning of imminent breaking onset is detectable up to a fifth of a carrier wave period prior to a breaking event.

Observation of the Occurrence of Air Flow Separation Over Water Waves

2010 ◽  
Author(s):  
Zhigang Tian ◽  
Marc Perlin ◽  
Wooyoung Choi
Keyword(s):  
Wind Speed ◽  
Flow Separation ◽  
Water Waves ◽  
High Speed ◽  
Air Flow ◽  
Breaking Waves ◽  
Wave Crest ◽  
Breaking Wave ◽  
Wind Condition ◽  
Separation Criterion

A preliminary study on the occurrence of air flow separation over mechanically generated water waves under following wind conditions is presented. Separated air flows over both non-breaking and breaking waves are observed in the flow visualization. A first attempt to identify an air flow separation criterion based on both wind speed and wave steepness is made. It was believed that, in the case of water waves propagating in the following wind condition, air flow separation will occur only in the presence of breaking waves. However, some laboratory experiments and field measurements suggested the occurrence of air flow separation over nonbreaking waves. Therefore, we conducted lab experiments to observe the air flow over mechanically generated waves. In the experiments, the air is seeded with water droplets generated with a high-pressure spray gun and is illuminated with a thin laser light sheet. A high-speed imaging system is used to record and observe the air flow over the mechanically generated wave waves. Our observations show that the separation of air flow occurs above both breaking and non-breaking wave crests, implying that wave breaking is sufficient, but not necessary for air flow separation. In addition, as compared to the separation over breaking waves, a higher wind speed is necessary for the separation over non-breaking ones, indicating that a robust air flow separation criterion likely depends on both the wave crest geometry and the wind speed above the crest. Our preliminary results support, to a certain degree, such a criterion. To the best of our knowledge, this criterion has not been reported previously in laboratory studies.

Wave-driven currents and vortex dynamics on barred beaches

2001 ◽  
Vol 449 ◽  
pp. 313-339 ◽  
Author(s):  
OLIVER BÜHLER ◽  
TIVON E. JACOBSON
Keyword(s):  
Shallow Water ◽  
Shallow Water Equations ◽  
Water Waves ◽  
Wave Breaking ◽  
Bottom Topography ◽  
Breaking Waves ◽  
Vortex Structures ◽  
Water Model ◽  
Mean Flow ◽  
The Mean

We present a theoretical and numerical investigation of longshore currents driven by breaking waves on beaches, especially barred beaches. The novel feature considered here is that the wave envelope is allowed to vary in the alongshore direction, which leads to the generation of strong dipolar vortex structures where the waves are breaking. The nonlinear evolution of these vortex structures is studied in detail using a simple analytical theory to model the effect of a sloping beach. One of our findings is that the vortex evolution provides a robust mechanism through which the preferred location of the longshore current can move shorewards from the location of wave breaking. Such current dislocation is an often-observed (but ill-understood) phenomenon on real barred beaches.To underpin our results, we present a comprehensive theoretical description of the relevant wave–mean interaction theory in the context of a shallow-water model for the beach. Therein we link the radiation-stress theory of Longuet-Higgins & Stewart to recently established results concerning the mean vorticity generation due to breaking waves. This leads to detailed results for the entire life-cycle of the mean-flow vortex evolution, from its initial generation by wave breaking until its eventual dissipative decay due to bottom friction.In order to test and illustrate our theory we also present idealized nonlinear numerical simulations of both waves and vortices using the full shallow-water equations with bottom topography. In these simulations wave breaking occurs through shock formation of the shallow-water waves. We note that because the shallow-water equations also describe the two-dimensional flow of a homentropic perfect gas, our theoretical and numerical results can also be applied to nonlinear acoustics and sound–vortex interactions.

scholarly journals PREDICTING THE BREAKING STRENGTH OF GRAVITY WATER WAVES FROM DEEP TO SHALLOW WATER

2018 ◽  
pp. 9
Author(s):  
James T. Kirby ◽  
Morteza Derakhti ◽  
Michael L. Banner ◽  
Stephan Grilli
Keyword(s):  
Water Waves ◽  
Breaking Strength ◽  
Modulational Instability ◽  
Wave Packets ◽  
Bottom Topography ◽  
Strength Parameter ◽  
Flat Bottom ◽  
Vof Model ◽  
Wave Trains ◽  
Modulated Wave Trains

We revisit the classical but as yet unresolved problem of predicting the breaking strength of 2-D and 3-D gravity water waves.Our goal is to find a robust and local parameterization to predict the breaking strength of 2-D and 3-D gravity water waves. We use a LES/VOF model described by Derakhti & Kirby (2014) to simulate nonlinear wave evolution, breaking onset and post-breaking behavior for representative cases of focused wave packets or modulated wave trains. Using these numerical results, we investigate the relationship between the breaking strength parameter b and the breaking onset parameter B proposed by Barthelemy et al. (2018). While the results are potentially applicable more generally, in this paper we concentrate on breaking events due to focusing or modulational instability in wave packets over flat bottom topography and for conditions ranging from deep to intermediate depth, with depth to wavelength ratios ranging from 0.68 to 0.13.

scholarly journals Time Scale for Scour Beneath Pipelines Due to Long-Crested and Short-Crested Nonlinear Random Waves Plus Current

2021 ◽  
Vol 9 (2) ◽  
pp. 114
Author(s):  
Dag Myrhaug ◽  
Muk Chen Ong
Keyword(s):  
Time Scale ◽  
Current Flow ◽  
Irregular Waves ◽  
Wave Crest ◽  
Random Wave ◽  
Random Waves ◽  
Flow Conditions ◽  
Regular Waves ◽  
Nonlinear Random Waves ◽  
2D And 3D

This article derives the time scale of pipeline scour caused by 2D (long-crested) and 3D (short-crested) nonlinear irregular waves and current for wave-dominant flow. The motivation is to provide a simple engineering tool suitable to use when assessing the time scale of equilibrium pipeline scour for these flow conditions. The method assumes the random wave process to be stationary and narrow banded adopting a distribution of the wave crest height representing 2D and 3D nonlinear irregular waves and a time scale formula for regular waves plus current. The presented results cover a range of random waves plus current flow conditions for which the method is valid. Results for typical field conditions are also presented. A possible application of the outcome of this study is that, e.g., consulting engineers can use it as part of assessing the on-bottom stability of seabed pipelines.

A Coupled-Mode Technique for the Run-Up of Non-Breaking Dispersive Waves on Plane Beaches

2006 ◽  
Author(s):  
K. A. Belibassakis ◽  
G. A. Athanassoulis
Keyword(s):  
Shallow Water ◽  
Water Waves ◽  
Wave Equations ◽  
Neumann Boundary ◽  
Breaking Waves ◽  
Numerical Results ◽  
Coupled Mode Theory ◽  
Mode Theory ◽  
Coupled Mode ◽  
Run Up

A coupled-mode model is developed and applied to the transformation and run-up of dispersive water waves on plane beaches. The present work is based on the consistent coupled-mode theory for the propagation of water waves in variable bathymetry regions, developed by Athanassoulis & Belibassakis (1999) and extended to 3D by Belibassakis et al (2001), which is suitably modified to apply to a uniform plane beach. The key feature of the coupled-mode theory is a complete modal-type expansion of the wave potential, containing both propagating and evanescent modes, being able to consistently satisfy the Neumann boundary condition on the sloping bottom. Thus, the present approach extends previous works based on the modified mild-slope equation in conjunction with analytical solution of the linearised shallow water equations, see, e.g., Massel & Pelinovsky (2001). Numerical results concerning non-breaking waves on plane beaches are presented and compared with exact analytical solutions; see, e.g., Wehausen & Laitone (1960, Sec. 18). Also, numerical results are presented concerning the run-up of non-breaking solitary waves on plane beaches and compared with the ones obtained by the solution of the shallow-water wave equations, Synolakis (1987), Li & Raichlen (2002), and experimental data, Synolakis (1987).

scholarly journals KINEMATICS OF BREAKING WAVES

1976 ◽  
Vol 1 (15) ◽  
pp. 25 ◽  
Author(s):  
Edward B. Thornton ◽  
James J. Galvin ◽  
Frank L. Bub ◽  
David P. Richardson
Keyword(s):  
Solitary Waves ◽  
Particle Velocity ◽  
Asymptotic Expression ◽  
Breaking Waves ◽  
The Body ◽  
Time Dependent ◽  
Wave Crest ◽  
Periodic Waves ◽  
Water Particle ◽  
Highly Nonlinear

The sight and sound of breaking waves and surf is so familiar and enjoyable that we tend to forget how little we really understand about them. Why is it, that compared to other branches of wave studies our knowledge of breaking waves is so empirical and inexact? The reason must lie partly in the difficulty of finding a precise mathematical description of a fluid flow that is in general nonlinear and time-dependent. The fluid accelerations can no longer be assumed t o be small compared t o gravity, as in Stokes's theory for periodic waves and the theory of cnoidal waves in shallow water, nor is the particle velocity any longer small compared to the phase velocity. The aim of this paper is to bring together s ome recent contributions to the calculation both of steep symmetric waves and of time-dependent surface waves. These have a bearing on the behaviour of whitecaps in deep water and of surf in the breaker zone . Since spilling breakers in gently shoaling water closely resemble solitary waves, we begin with the description of solitary waves of limiting amplitude, then discuss steep waves of arbitrary height. The observed intermittency of whitecaps is discussed in terms of the energy maximum, as a function of wave steepness, In Sections 6 and 7 a simpler description of steady symmetric waves is proposed, using an asymptotic expression for the flow near the wave crest. Finally we describe a new numerical technique (MEL, or mixed Eulerian-Lagrangian) with which it has been found possible to follow the development of periodic waves past the point when overturning takes place. Measurement of waves, and vertical and horizontal water particle velocities were made of spilling, plunging and surging breakers at sandy beaches in the vicinity of Monterey, California. The measured breaking waves, derived characteristically from swell-type waves, can be described as highly nonlinear. Spectra and cross spectra were calculated between waves and velocities. Secondary waves were noted visually and by the strong harmonics in the spectra. The strength of the harmonics is related to the beach steepness, wave height and period. The phase difference between waves and horizontal velocities indicates the unstable crest of the wave leads the velocities on the average by 5-20 degrees. Phase measurements between wave gauges in a line perpendicular to the shore show breaking waves to be frequency nondispersive indicating phase-coupling of the various wave components. The coherence squared values between the sea surface elevation and the horizontal water particle velocity were high in all runs, ranging above 0.8 at the peak of the spectra. The high coherence suggests that most of the motion in the body of breaking waves is wave-induced and not turbulent.

scholarly journals Detection of Breaking Waves in Single Wave Gauge Records of Surface Elevation Fluctuations

2019 ◽  
Vol 36 (9) ◽  
pp. 1863-1879 ◽  
Author(s):  
Dan Liberzon ◽  
Alexandru Vreme ◽  
Sagi Knobler ◽  
Itamar Bentwich
Keyword(s):  
Water Waves ◽  
Cost Effective ◽  
Breaking Waves ◽  
Recognition Algorithm ◽  
New Method ◽  
Surface Elevation ◽  
Detection Accuracy ◽  
Single Wave ◽  
Accurate Detection ◽  
Forced Waves

We report the development of a new method for accurate detection of breaking water waves that addresses the need for an accurate and cost-effective method that is independent of human decisions. The new detection method, which enables the detection of breakers using only surface elevation fluctuation measurements from a single wave gauge, supports the development of a new method for research relating to water waves and wind–wave interactions. According to the proposed method, detection is based on the use of the phase-time method to identify breaking-associated patterns in the instantaneous frequency variations of surface elevation fluctuations. A wavelet-based pattern recognition algorithm is devised to detect such patterns and provide accurate detection of breakers in the examined records. Validation and performance tests, conducted using both laboratory and open-sea data, including mechanically generated and wind-forced waves, are reported as well. These tests allow us to derive a set of parameters that assure high detection accuracy rates. The method is shown to be capable to achieve a positive detection rate exceeding 90%.

scholarly journals A Mild-Slope System for Bragg Scattering of Water Waves by Sinusoidal Bathymetry in the Presence of Vertically Sheared Currents

2019 ◽  
Vol 7 (1) ◽  
pp. 9 ◽  
Author(s):  
Kostas Belibassakis ◽  
Julien Touboul ◽  
Elodie Laffitte ◽  
Vincent Rey
Keyword(s):  
Resonant Frequency ◽  
Water Waves ◽  
Bottom Topography ◽  
Wave System ◽  
Bragg Scattering ◽  
Wave Flume ◽  
Seabed Topography ◽  
Incident Waves ◽  
Slope System ◽  
A Current

Extended mild-slope models (MMSs) are examined for predicting the characteristics of normally incident waves propagating over sinusoidal bottom topography in the presence of opposing shearing currents. It is shown that MMSs are able to provide quite good predictions in the case of Bragg scattering of waves over rippled bathymetry without a current, but fail to provide good predictions concerning the resonant frequency in the additional presence of a current. In order to resolve the above mismatch, a two-equation mild-slope system (CMS2) is derived from a variational principle based on the representation of the wave potential expressed as a superposition of the forward and backward components. The latter system is compared against experimentally measured data collected in a wave flume and is shown to provide more accurate predictions concerning both the resonant frequency and the amplitude of the reflection coefficient. Future work will be devoted to the examination of the derived model for a more general wave system over realistic seabed topography.

scholarly journals Quantum Mechanical and Optical Analogies in Surface Gravity Water Waves

Fluids ◽  
2019 ◽  
Vol 4 (2) ◽  
pp. 96 ◽  
Author(s):  
Georgi Gary Rozenman ◽  
Shenhe Fu ◽  
Ady Arie ◽  
Lev Shemer
Keyword(s):  
Quantum Mechanics ◽  
Gravity Waves ◽  
Water Waves ◽  
Water Wave ◽  
Wave Packets ◽  
Theoretical Models ◽  
Surface Gravity ◽  
Finite Width ◽  
Self Healing ◽  
Surface Gravity Waves

We present the theoretical models and review the most recent results of a class of experiments in the field of surface gravity waves. These experiments serve as demonstration of an analogy to a broad variety of phenomena in optics and quantum mechanics. In particular, experiments involving Airy water-wave packets were carried out. The Airy wave packets have attracted tremendous attention in optics and quantum mechanics owing to their unique properties, spanning from an ability to propagate along parabolic trajectories without spreading, and to accumulating a phase that scales with the cubic power of time. Non-dispersive Cosine-Gauss wave packets and self-similar Hermite-Gauss wave packets, also well known in the field of optics and quantum mechanics, were recently studied using surface gravity waves as well. These wave packets demonstrated self-healing properties in water wave pulses as well, preserving their width despite being dispersive. Finally, this new approach also allows to observe diffractive focusing from a temporal slit with finite width.

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