scholarly journals Capillary effects on wave breaking

2015 ◽  
Vol 769 ◽  
pp. 541-569 ◽  
Author(s):  
Luc Deike ◽  
Stephane Popinet ◽  
W. Kendall Melville
Keyword(s):  
Surface Tension ◽  
Wave Breaking ◽  
Stokes Equations ◽  
Breaking Waves ◽  
Bond Number ◽  
Capillary Waves ◽  
Two Phase ◽  
Wave Regime ◽  
Capillary Effects ◽  
Wave Energy Dissipation

We investigate the influence of capillary effects on wave breaking through direct numerical simulations of the Navier–Stokes equations for a two-phase air–water flow. A parametric study in terms of the Bond number, $\mathit{Bo}$, and the initial wave steepness, ${\it\epsilon}$, is performed at a relatively high Reynolds number. The onset of wave breaking as a function of these two parameters is determined and a phase diagram in terms of $({\it\epsilon},\mathit{Bo})$ is presented that distinguishes between non-breaking gravity waves, parasitic capillaries on a gravity wave, spilling breakers and plunging breakers. At high Bond number, a critical steepness ${\it\epsilon}_{c}$ defines the onset of wave breaking. At low Bond number, the influence of surface tension is quantified through two boundaries separating, first gravity–capillary waves and breakers, and second spilling and plunging breakers; both boundaries scaling as ${\it\epsilon}\sim (1+\mathit{Bo})^{-1/3}$. Finally the wave energy dissipation is estimated for each wave regime and the influence of steepness and surface tension effects on the total wave dissipation is discussed. The breaking parameter $b$ is estimated and is found to be in good agreement with experimental results for breaking waves. Moreover, the enhanced dissipation by parasitic capillaries is consistent with the dissipation due to breaking waves.

scholarly journals A two-phase flow model for three-dimensional breaking waves over complex topography

2015 ◽  
Vol 471 (2180) ◽  
pp. 20150101 ◽  
Author(s):  
Zhihua Xie
Keyword(s):  
Wave Breaking ◽  
Flow Model ◽  
Two Phase Flow ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Air Entrainment ◽  
Breaking Waves ◽  
Phase Flow ◽  
Complex Topography ◽  
Two Phase

A two-phase flow model has been developed to study three-dimensional breaking waves over complex topography, including the wave pre-breaking, overturning and post-breaking processes. The large-eddy simulation approach has been adopted in this study, where the model is based on the filtered Navier–Stokes equations with the Smagorinsky sub-grid model being used for the unresolved scales of turbulence. The governing equations have been discretized using the finite volume method, with the PISO algorithm being employed for the pressure–velocity coupling. The air–water interface has been captured using a volume of fluid method and the partial cell treatment has been implemented to deal with complex topography in the Cartesian grid. The model is first validated against available analytical solutions and experimental data for solitary wave propagation over constant water depth and three-dimensional breaking waves over a plane slope, respectively. Furthermore, the model is used to study three-dimensional overturning waves over three different bed topographies, with three-dimensional wave profiles and surface velocities being presented and discussed. The overturning jet, air entrainment and splash-up during wave breaking have been captured by the two-phase flow model, which demonstrates the capability of the model to simulate free surface flow and wave breaking problems over complex topography.

scholarly journals Characteristics of Breaking Wave Forces on Piles over a Permeable Seabed

2021 ◽  
Vol 9 (5) ◽  
pp. 520
Author(s):  
Zhenyu Liu ◽  
Zhen Guo ◽  
Yuzhe Dou ◽  
Fanyu Zeng
Keyword(s):  
Wave Breaking ◽  
Stokes Equations ◽  
Slope Angle ◽  
Wave Force ◽  
Breaking Waves ◽  
Offshore Wind ◽  
Secondary Wave ◽  
Wave Forces ◽  
Breaking Wave ◽  
Breaking Wave Forces

Most offshore wind turbines are installed in shallow water and exposed to breaking waves. Previous numerical studies focusing on breaking wave forces generally ignored the seabed permeability. In this paper, a numerical model based on Volume-Averaged Reynolds Averaged Navier–Stokes equations (VARANS) is employed to reveal the process of a solitary wave interacting with a rigid pile over a permeable slope. Through applying the Forchheimer saturated drag equation, effects of seabed permeability on fluid motions are simulated. The reliability of the present model is verified by comparisons between experimentally obtained data and the numerical results. Further, 190 cases are simulated and the effects of different parameters on breaking wave forces on the pile are studied systematically. Results indicate that over a permeable seabed, the maximum breaking wave forces can occur not only when waves break just before the pile, but also when a “secondary wave wall” slams against the pile, after wave breaking. With the initial wave height increasing, breaking wave forces will increase, but the growth can decrease as the slope angle and permeability increase. For inclined piles around the wave breaking point, the maximum breaking wave force usually occurs with an inclination angle of α = −22.5° or 0°.

Void fraction measurements in breaking waves

2007 ◽  
Vol 463 (2088) ◽  
pp. 3151-3170 ◽  
Author(s):  
C.E Blenkinsopp ◽  
J.R Chaplin
Keyword(s):  
Void Fraction ◽  
Wave Breaking ◽  
Breaking Waves ◽  
Phase Detection ◽  
Bubble Plume ◽  
Two Phase ◽  
Void Fractions ◽  
Highly Sensitive ◽  
Energy Dissipated ◽  
Degree Of Similarity

This paper describes detailed measurements and analysis of the time-varying distribution of void fractions in three different breaking waves under laboratory conditions. The measurements were made with highly sensitive optical fibre phase detection probes and document the rapid spatial and temporal evolutions of both the bubble plume generated beneath the free surface and the splashes above. Integral properties of the measured void fraction fields reveal a remarkable degree of similarity between characteristics of the two-phase flow in different breaker types as they evolve with time. Depending on the breaker type, the energy expended in entraining air and generating splash accounts for a minimum of between 6.5 and 14% of the total energy dissipated during wave breaking.

Numerical Simulation of Wave Interaction With a Pair of Fixed Large Tandem Cylinders Subjected to Regular, Non-Breaking Waves

2021 ◽  
Author(s):  
M. Mohseni ◽  
C. Guedes Soares
Keyword(s):  
Numerical Model ◽  
Wave Field ◽  
Circular Cross Section ◽  
Wave Interaction ◽  
Breaking Waves ◽  
Wave Loading ◽  
Two Phase ◽  
Wave Regime ◽  
Wave Amplification ◽  
Vof Model

Abstract The wave interaction with cylinders placed in proximity results in significant modification of the wave field, wave-induced processes, and wave loading. The evaluation of such a complex wave regime and accurate assessment of the wave loading requires an efficient and accurate numerical model. Concerning the wave scattering types identified by Swan et al. (2015) and lateral progressive edge waves, this paper presents the application of a two-phase Computational Fluid Dynamics (CFD) model to carry out a detailed investigation of nonlinear wave field surrounding a pair of columns placed in the tandem arrangement in the direction of wave propagation and corresponding harmonics. The numerical analysis is conducted using the Unsteady Reynolds-Averaged Navier-Stokes/VOF model based on the OpenFOAM framework combined with the olaFlow toolbox for wave generation/absorption. For the simulations, the truncated cylinders are assumed vertical and surface piercing with a circular cross-section subjected to regular, non-breaking fifth-order Stokes waves propagating with moderate steepness in deep water. Primarily, the numerical model is validated with experimental data provided by ITTC (OEC)[1] for a single cylinder. Future, the given simulations are conducted for different centre-to-centre distances between the tandem large cylinders. The results show the evolution of a strong wave diffraction pattern and consequently high wave amplification harmonics around cylinders are apparent.

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.

Numerical Simulation of Two-Phase Slug Flows in Microchannels

2009 ◽  
Author(s):  
A. Mehdizadeh ◽  
S. A. Sherif ◽  
W. E. Lear
Keyword(s):  
Surface Tension ◽  
Slug Flow ◽  
Stokes Equations ◽  
Pressure Fluctuations ◽  
Water Interface ◽  
Liquid Slug ◽  
Complex Flow ◽  
Two Phase ◽  
Air Water Interface ◽  
Slug Flows

In this paper the Navier-stokes equations for a single liquid slug have been solved in order to predict the circulation patterns within the slug. Surface tension effects on the air-water interface have been investigated by solving the Young–Laplace equation. The calculated interface shape has been utilized to define the liquid slug geometry at the front and tail interfaces of the slug. Then the effects of the surface tension on the hydrodynamics of the two-phase slug flow have been compared to those where no surface tension forces exist. The importance of the complex flow field features in the vicinity of the two interfaces has been investigated by defining a non-dimensional form of the wall shear stress. The latter quantity has been formulated based on non-dimensional parameters in order to define a general Moody friction factor for typical two-phase slug flows in microchannels. Moreover, the hydrodynamics of slug flow formation has been examined using computational fluid dynamics (CFD). The volume-of-fluid (VOF) method has been applied to monitor the growth of the instability at the air-water interface. The lengths of the slugs have been correlated to the pressure fluctuations in the mixing region of the air and water streams at an axisymmetric T-junction. The main frequencies of the pressure fluctuations have been investigated using the Fast Fourier Transform (FFT) method.

Wave Load and Structural Analysis for a Jack-Up Platform in Freak Waves

2007 ◽  
Author(s):  
Ould el Moctar ◽  
Thomas E. Schellin ◽  
Milovan Peric
Keyword(s):  
Structural Model ◽  
Stokes Equations ◽  
Nonlinear Effects ◽  
Breaking Waves ◽  
Wave Loads ◽  
Wave Load ◽  
Two Phase ◽  
Freak Waves ◽  
Highly Nonlinear ◽  
Jack Up

The paper analyzed effects of freak waves on a mobile jack-up drilling platform stationed in exposed waters of the North Sea. Under freak wave conditions, highly nonlinear effects, such as wave run-up on platform legs and impact-related wave loads on the hull, had to be considered. Traditional methods based on the Morison formula needed to be critically examined to accurately predict these loads. Our analysis was based on the use of advanced CFD techniques. The code used here solves the Reynolds-averaged Navier-Stokes equations and relies on the interface-capturing technique of the volume-of-fluid type. It computed the two-phase flow of water and air to describe the physics associated with complex free-surface shapes with breaking waves and air trapping, hydrodynamic phenomena that had to be considered to yield reliable predictions. Lastly, the FEM was used to apply the wave-induced loads onto a comprehensive finite element structural model of the platform, yielding deformations and stresses.

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