Predicting the breaking strength of gravity water waves in deep and intermediate depth

2018 ◽  
Vol 848 ◽  
Author(s):  
Morteza Derakhti ◽  
Michael L. Banner ◽  
James T. Kirby
Keyword(s):  
Wave Energy ◽  
Water Waves ◽  
Breaking Strength ◽  
Modulational Instability ◽  
Rate Of Change ◽  
Strength Parameter ◽  
Wave Crest ◽  
Breaking Wave ◽  
Local Energy ◽  
Energy Dissipated

We revisit the classical but as yet unresolved problem of predicting the strength of breaking 2-D and 3-D gravity water waves, as quantified by the amount of wave energy dissipated per breaking event. Following Duncan (J. Fluid Mech., vol. 126, 1983, pp. 507–520), the wave energy dissipation rate per unit length of breaking crest may be related to the fifth moment of the wave speed and the non-dimensional breaking strength parameter $b$. We use a finite-volume Navier–Stokes solver with large-eddy simulation resolution and volume-of-fluid surface reconstruction (Derakhti & Kirby, J. Fluid Mech., vol. 761, 2014a, pp. 464–506; J. Fluid Mech., vol. 790, 2016, pp. 553–581) to simulate nonlinear wave evolution, with a strong focus on breaking onset and postbreaking behaviour for representative cases of wave packets with breaking due to dispersive focusing and modulational instability. The present study uses these results to investigate the relationship between the breaking strength parameter $b$ and the breaking onset parameter $B$ proposed recently by Barthelemy et al. (J. Fluid Mech., vol. 841, 2018, pp. 463–488). The latter, formed from the local energy flux normalized by the local energy density and the local crest speed, simplifies, on the wave surface, to the ratio of fluid speed to crest speed. Following a wave crest, when $B$ exceeds a generic threshold value at the wave crest (Barthelemy et al. 2018), breaking is imminent. We find a robust relationship between the breaking strength parameter $b$ and the rate of change of breaking onset parameter $\text{d}B/\text{d}t$ at the wave crest, as it transitions through the generic breaking onset threshold ($B\sim 0.85$), scaled by the local period of the breaking wave. This result significantly refines previous efforts to express $b$ in terms of a wave packet steepness parameter, which is difficult to define robustly and which does not provide a generically accurate forecast of the energy dissipated by breaking.

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.

Remote sensing of energy dissipation by individual oceanic whitecaps using above-water digital imagery

2021 ◽  
Author(s):  
Adrian Callaghan
Keyword(s):  
Remote Sensing ◽  
Energy Dissipation ◽  
Breaking Strength ◽  
Ocean Surface ◽  
Field Studies ◽  
Breaking Waves ◽  
Energy Dissipation Rate ◽  
Strength Parameter ◽  
Wave Crest ◽  
Breaking Wave

<p>Breaking waves are an important physical feature of the ocean surface and play a fundamental role in many air-sea interaction processes. Sufficiently energetic breaking waves can entrain enough air that they appear as whitecaps on the ocean surface and these are the focus of this work. Phillips (1985) presents a statistical description of the length of breaking wave crest per unit area within a breaking speed interval Λ(c), often referred to as the “lambda distribution”. Many field studies have measured Λ(c) using digital image remote sensing of the ocean surface, corroborating the theoretical work of Phillips. In conjunction with the so-called breaking strength parameter, b, defined by Duncan (1981), the fifth moment of Λ(c) has been used to quantify the energy dissipation rate of the surface breaking wave field. Within the Duncan framework, many numerical and experimental laboratory studies have shown that b is not constant but depends on the spectral and physical slope of the breaking waves, and it can vary by several orders of magnitude.</p><p>Significant effort has been made to estimate the average value of the breaking strength parameter for populations of breaking waves observed in the field, <b>. This can be achieved with measurements of Λ(c), an estimate of the wind to wave energy flux and assumptions of a stationary wave field. While several recent field studies have estimated <b> to be O(1 X 10<sup>-3</sup>), independent estimates of <b> derived from averaging values of b estimated for individual whitecaps in a given sea state have not yet been reported.</p><p>Here digital images of the sea surface are analysed and the volume-time-integral (VTI) method presented in Callaghan et al (2016) is used to estimate b on a whitecap-by-whitecap basis. The VTI method uses the time-evolving surface foam area of a whitecap together with a laboratory-determined average turbulence intensity inside a breaking wave crest, to estimate the total energy dissipated by an individual whitecap. This total energy loss can then be used to calculate the average energy dissipation rate of an individual whitecap, from which b can be estimated.</p><p>The dataset presented here consists of approximately 500 whitecaps and the range of b values estimated is distributed between 1 X 10<sup>-4</sup> to 1 X 10<sup>-2</sup>, with average values lying close to 1-2 X 10<sup>-3</sup>. This range of b values agrees well with laboratory results amassed over decades of experimental research. Furthermore, the average values of 1-2 X 10<sup>-3 </sup>agree very well with two recent <b> values reported in Zappa et al. (2016) and Korinenko et al. (2020). These results suggest that the VTI method can be a useful tool to remotely estimate the energy dissipation, and its rate, of individual whitecaps in the field using above-water digital image remote sensing.</p>

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.

scholarly journals SURF ZONE WAVE HEATING BY ENERGY DISSIPATION OF BREAKING WAVES

2018 ◽  
pp. 2 ◽  
Author(s):  
Zhangping Wei ◽  
Robert A. Dalrymple
Keyword(s):  
Internal Energy ◽  
Wave Energy ◽  
Water Waves ◽  
Wave Breaking ◽  
Surf Zone ◽  
Current System ◽  
Breaking Waves ◽  
Breaking Wave ◽  
Conservation Of Energy ◽  
Wave Heating

This study investigates surf zone wave heating due to the dissipation of breaking wave energy by using the Smoothed Particle Hydrodynamics method. We evaluate the surf zone wave heating by examining the increase of internal energy of the system, which is computed based on the conservation of energy. The equivalent temperature profile is calculated based on a simple conversion relationship between energy and temperature. We first examine the surf zone wave heating based on long-crested wave breaking over a planar beach, and we consider spilling breaker and weakly plunging breaker. Numerical results show that breaking of water waves in the surf zone increases the internal energy of water body. Furthermore, the dissipation of incident wave energy is fully converted into the internal energy in a thermally isolated system, confirming the energy conservation of the present numerical approach. It is further found that the long-crested wave breaking generates undertow, which transports the generated wave heating from the surf zone to deep waters. We further carry out numerical experiments to examine surf zone wave heating due to short-crested wave breaking over a beach. The internal energy generation mainly follows the isolated wave breakers, and there is a 3D pattern of wave heating due to the complicated wave breaking process and current system. In general, the magnitude of the generated internal energy or temperature by dissipation of breaking wave energy in the surf zone is relatively small. The present study shows that the generated water temperature is in the order of 10^-3 Kelvin for wave breaking over a typical coastal beach.

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.

scholarly journals Nonlinear wave energy modelling in the surf zone

1996 ◽  
Vol 3 (2) ◽  
pp. 127-134 ◽  
Author(s):  
Th. V. Karambas
Keyword(s):  
Wave Energy ◽  
Surf Zone ◽  
Energy Balance Equation ◽  
Propagation Model ◽  
Breaking Wave ◽  
Dissipation Term ◽  
Energy Modelling ◽  
Turbulence Effects ◽  
Energy And Momentum ◽  
Energy Equations

Abstract. Breaking wave energy in the surf zone is modelled through the incorporation of the time dependent energy balance equation in a non linear dispersive wave propagation model. The energy equations solved simultaneously with the momentum and continuity equation. Turbulence effects and the non uniform horizontal velocity distribution due to breaking is introduced in both the energy and momentum equations. The dissipation term is a function of the velocity defect derived from a turbulent analysis. The resulting system predicts both wave characteristics (surface elevation and velocity) and the energy distribution inside surf zone. The model is validated against experimental data and analytical expressions.

Evolution of bubble statistics in intermediate water due to phase shifted breaking wave groups

2021 ◽  
Author(s):  
Konstantinos Chasapis ◽  
Eugeny Buldakov ◽  
Helen Czerski
Keyword(s):  
Phase Shift ◽  
Amplitude Spectrum ◽  
Phase Shifts ◽  
Front Face ◽  
Wave Crest ◽  
Breaking Wave ◽  
Intermediate Water ◽  
Maximum Volume ◽  
Wave Groups ◽  
Single Wave

<p>The bubbles generated by breaking waves in the open ocean are an important feature of the ocean surface. They affect optical and acoustical properties of the top few meters of the ocean, influence surfactant scavenging, aerosol production and air-sea gas transfer. Short-lived larger bubbles which re-surface and burst dominate the transfer of less soluble gases such as carbon dioxide. A single wave crest approaching breaking deforms rapidly and in a storm sea the most common breaker is the spilling type. Detailed observations in space and time connecting the shape of the spilling breaker to subsequent bubble populations are limited, and the effect on the bubble penetration depth and residence time underwater is particularly important. In this study, we carried out a series of experiments to track the formation and evolution of large bubbles for different local crest geometries.</p><p>A breaking wave in a wave flume was generated with dispersive focusing of a wave group. The group has a pre-defined amplitude spectrum. Running experiments with different phase shifts of the same amplitude spectrum showed that when a peak-focussed wave (zero phase shift) breaks, then wave groups with other added phase shifts break as well. To investigate possible differences in the deformation of those breakers a laser imaging technique was used. An algorithm identified the 2D shape of the breaker in successive images. It also separated the crests from bulges based on geometric criteria. We showed that, despite wave groups having same spectra, the extracted bulges differed locally in shape, volume and velocity for each phase shift at the location of breaking. Therefore, breakers ranging from the more traditional spilling type, which has a bulge that collapses on the front face of the wave, to the micro-plunging type, which has a pronounced overturning tip, were observed depending on the phase shift. </p><p>The evolution of bubbles for each phase shifted bulge was captured by a high speed camera and measured by a feature extraction algorithm. We generally found that spilling bulges created fewer bubbles in total than micro-plungers. They also created fewer larger bubbles, i.e. with radius r>1 mm, at all measured flume areas. In contrast, micro-plungers that trap air within a small cavity as they break had less steep size distributions for r>1 mm. The maximum volume of air per radius showed a gradual shift from r>1 mm to r=1 mm moving away from the breaking location for all breakers. It is interesting, finally, that the maximum volume per radius did not shift to smaller radii as time passes. This is an indication that the largest bubbles, i.e. r>4 mm, rise to the surface and burst instead of splitting into smaller ones, irrespectively of the local breaker properties. </p>

A new Boussinesq method for fully nonlinear waves from shallow to deep water

2002 ◽  
Vol 462 ◽  
pp. 1-30 ◽  
Author(s):  
P. A. MADSEN ◽  
H. B. BINGHAM ◽  
HUA LIU
Keyword(s):  
Laplace Equation ◽  
Infinite Series ◽  
Deep Water ◽  
Water Waves ◽  
Modulational Instability ◽  
Surface Boundary ◽  
Nonlinear Water Waves ◽  
Finite Series ◽  
Starting Point ◽  
Highly Nonlinear

A new method valid for highly dispersive and highly nonlinear water waves is presented. It combines a time-stepping of the exact surface boundary conditions with an approximate series expansion solution to the Laplace equation in the interior domain. The starting point is an exact solution to the Laplace equation given in terms of infinite series expansions from an arbitrary z-level. We replace the infinite series operators by finite series (Boussinesq-type) approximations involving up to fifth-derivative operators. The finite series are manipulated to incorporate Padé approximants providing the highest possible accuracy for a given number of terms. As a result, linear and nonlinear wave characteristics become very accurate up to wavenumbers as high as kh = 40, while the vertical variation of the velocity field becomes applicable for kh up to 12. These results represent a major improvement over existing Boussinesq-type formulations in the literature. A numerical model is developed in a single horizontal dimension and it is used to study phenomena such as solitary waves and their impact on vertical walls, modulational instability in deep water involving recurrence or frequency downshift, and shoaling of regular waves up to breaking in shallow water.

Stochastic Analysis of a Nonlinear Energy Harvester Model

2014 ◽  
Author(s):  
P. D. Spanos ◽  
A. Richichi ◽  
F. Arena
Keyword(s):  
Dynamic Analysis ◽  
Wave Energy ◽  
Water Waves ◽  
Nonlinear Dynamic Analysis ◽  
Nonlinear Effects ◽  
Wave Energy Converter ◽  
Statistical Linearization ◽  
Energy Converter ◽  
Domain Integration ◽  
Stiffness And Damping

Floating oscillating-bodies are a kind of wave energy converter developed for harvesting the great amount of energy related to water waves (see Falcão [1] for a review). Although the assumptions of small-wave and linear behavior of oscillating system are reasonable for most of the time during which a floating point harvester is in operation, nonlinear effects may be significant in extreme sea states situations. In this paper a nonlinear dynamic analysis of a point harvester wave energy converter is conducted. The model involves a tightly moored single-body floating device; it captures motion in the horizontal and vertical directions. The stiffness and damping forces, being functions of the displacement and velocity components, make the system nonlinear and coupled. For the input forces, the erratic nature of the waves is modeled by a stochastic process. Specifically, wind-generated waves are modeled by means of the JONSWAP spectrum. The method of statistical linearization [2] is used to determine iteratively the effective linear stiffness and damping matrices and response statistics of the system and to proceed to conducting a dynamic analysis of the harvester model. The reliability of the linearization based approach is demonstrated by comparison with time domain integration, Monte Carlo simulation, data. This approach offers the appealing feature of conducting efficiently a variety of parameter studies which can expedite preliminary evaluations, inter alia, of competing design scenarios for the energy converter in a stochastic environmental setting.

Effect of Oscillating Water Column Chamber Inclination on the Performance of a Savonius Rotor

2020 ◽  
Vol 142 (4) ◽  
Author(s):  
Deepak D. Prasad ◽  
M. Rafiuddin Ahmed ◽  
Young-Ho Lee
Keyword(s):  
Water Column ◽  
Wave Energy ◽  
Hollow Structure ◽  
Flow Characteristics ◽  
Wave Crest ◽  
Oscillating Water Column ◽  
Sea State ◽  
Wave Condition ◽  
Improved Performance ◽  
Incident Waves

Abstract The power potential in the waves that hit all the coasts worldwide has been estimated to be of the order of 1 TW. Each wave crest transmits 10–50 kW/m of energy, which is 15–20 times higher than wind or solar energies. The availability of wave energy is 90% compared to 30% for wind and solar energies. The oscillating water column (OWC), which is the most investigated wave energy converter consists of a partially submerged hollow structure positioned either vertically or inclined. The bidirectional airflow above the water column drives a turbine. The conventional OWCs experience flow separation at the sharp corners of the chamber. To address this issue, researchers have proposed inclining the chamber at an angle with respect to the incident waves to improve the flow characteristics. In the present work, the effect of OWC inclination on rotor performance is studied using the computational fluid dynamics (CFD) code ansys-cfx. The results highlight that the 55 deg inclined OWC showed improved performance compared to the conventional OWC and modified OWC (optimized in a previous work). The maximum power for the inclined OWC was 13% higher than that for the rotor in the modified OWC and 28% than that in the conventional OWC at mean wave condition. The 55 deg inclined OWC recorded peak rotor power of 23.2 kW with an efficiency of 27.6% at the mean sea state. The peak power and efficiency at maximum sea state were 26.5 kW and 21.5%, respectively.

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