Direct numerical simulation of wind turbulence over breaking waves

2018 ◽  
Vol 850 ◽  
pp. 120-155 ◽  
Author(s):  
Zixuan Yang ◽  
Bing-Qing Deng ◽  
Lian Shen
Keyword(s):  
Numerical Simulation ◽  
Kinetic Energy ◽  
Wave Breaking ◽  
Momentum Flux ◽  
Breaking Waves ◽  
Wave Age ◽  
Wave Surface ◽  
Turbulence Statistics ◽  
Large Wave ◽  
Wind Turbulence

We study wind turbulence over breaking waves based on direct numerical simulation (DNS) of two-fluid flows. In the DNS, the air and water are simulated as a coherent system, with the interface captured using the coupled level-set and volume-of-fluid method. Because the wave breaking is an unsteady process, we use ensemble averaging over 100 runs to define turbulence statistics. We focus on analysing the turbulence statistics of the airflow over breaking waves. The effects of wave age and wave steepness are investigated. It is found that before wave breaking, the turbulence statistics are largely influenced by the wave age. The vertical gradient of mean streamwise velocity is positive at small and intermediate wave ages, but it becomes negative near the wave surface at large wave age as the pressure force changes from drag to thrust. Furthermore, wave-coherent motions make increasingly important contributions to the momentum flux and kinetic energy of velocity fluctuations (KE-F) as the wave age increases. During the wave breaking process, spilling breakers do not influence the wind field significantly; in contrast, plunging breakers alter the structures of wind turbulence near the wave surface drastically. It is observed from the DNS results that during wave plunging, a high pressure region occurs ahead of the wave front, which further accelerates the wind in the downstream direction. Meanwhile, a large spanwise vortex is generated, which greatly disturbs the airflow around it, resulting in large magnitudes of Reynolds stress and turbulence kinetic energy (TKE) below the wave crest. Above the crest, the magnitude of KE-F is enhanced during wave plunging at small and large wave ages, but at intermediate wave age, the transient enhancement of KE-F is absent. The effect of wave breaking on the magnitude of KE-F is further investigated through the analysis of the KE-F production. It is discovered that at small wave age, the transient enhancement of KE-F is caused by the appearance of a local maximum in the profile of total momentum flux; but at large wave age, it results from the change in the sign of the KE-F production from negative to positive, due to the sign change in the wave-coherent momentum flux. At intermediate wave age, neither of these two processes is present, and the transient growth of KE-F does not take place.

Direct numerical simulation of scalar transport in turbulent flows over progressive surface waves

2017 ◽  
Vol 819 ◽  
pp. 58-103 ◽  
Author(s):  
Di Yang ◽  
Lian Shen
Keyword(s):  
Numerical Simulation ◽  
Direct Numerical Simulation ◽  
Turbulent Flows ◽  
Viscous Sublayer ◽  
Wall Turbulence ◽  
Scalar Transport ◽  
Wave Age ◽  
Wave Surface ◽  
Scalar Flux ◽  
Flat Wall

The transport of passive scalars in turbulent flows over progressive water waves is studied using direct numerical simulation. A combined pseudo-spectral and finite-difference scheme on a wave-surface-fitted grid is used to simulate the flow and scalar fields above the wave surface. Three representative wave ages (i.e. wave-to-wind speed ratios) are considered, corresponding to slow, intermediate and fast wind-waves, respectively. For each wave condition, four Schmidt numbers are considered for the scalar transport. The presence of progressive surface waves is found to induce significant wave-phase-correlated variation to the scalar field, with the phase dependence varying with the wave age. The time- and plane-averaged profiles of the scalar over waves of various ages exhibit similar vertical structures as those found in turbulence over a flat wall, but with the von Kármán constant and effective wave surface roughness for the mean scalar profile exhibiting considerable variation with the wave age. The profiles of the root-mean-square scalar fluctuations and the horizontal scalar flux exhibit good scaling in the viscous sublayer that agrees with the scaling laws previously reported for flat-wall turbulence, but with noticeable wave-induced variation in the viscous wall region. The profiles of the vertical scalar flux in the viscous sublayer exhibit apparent discrepancies from the reported scaling law for flat-wall turbulence, due to a negative vertical flux region above the windward face of the wave crest. Direct observation and quadrant-based conditional averages indicate that the wave-dependent distributions of the scalar fluctuations and fluxes are highly correlated with the coherent vortical structures in the turbulence, which exhibit clear wave-dependent characteristics in terms of both shape and preferential location.

scholarly journals A Model of the Air–Sea Momentum Flux and Breaking-Wave Distribution for Strongly Forced Wind Waves

2007 ◽  
Vol 37 (7) ◽  
pp. 1811-1828 ◽  
Author(s):  
Tobias Kukulka ◽  
Tetsu Hara ◽  
Stephen E. Belcher
Keyword(s):  
Momentum Flux ◽  
Breaking Waves ◽  
Wind Forcing ◽  
Small Scale ◽  
Breaking Wave ◽  
Unit Surface Area ◽  
Wave Age ◽  
Coupled Equations ◽  
Wave Distribution ◽  
Equilibrium Range

Abstract Under high-wind conditions, breaking surface waves likely play an important role in the air–sea momentum flux. A coupled wind–wave model is developed based on the assumption that in the equilibrium range of surface wave spectra the wind stress is dominated by the form drag of breaking waves. By conserving both momentum and energy in the air and also imposing the wave energy balance, coupled equations are derived governing the turbulent stress, wind speed, and the breaking-wave distribution (total breaking crest length per unit surface area as a function of wavenumber). It is assumed that smaller-scale breaking waves are sheltered from wind forcing if they are in airflow separation regions of longer breaking waves (spatial sheltering effect). Without this spatial sheltering, exact analytic solutions are obtained; with spatial sheltering asymptotic solutions for small- and large-scale breakers are derived. In both cases, the breaking-wave distribution approaches a constant value for large wavenumbers (small-scale breakers). For low wavenumbers, the breaking-wave distribution strongly depends on wind forcing. If the equilibrium range model is extended to the spectral peak, the model yields the normalized roughness length (Charnock coefficient) of growing seas, which increases with wave age and is roughly consistent with earlier laboratory observations. However, the model does not yield physical solutions beyond a critical wave age, implying that the wind input to the wave field cannot be dominated by breaking waves at all wavenumbers for developed seas (including field conditions).

scholarly journals Observations of Wave Breaking Kinematics in Fetch-Limited Seas

2010 ◽  
Vol 40 (12) ◽  
pp. 2575-2604 ◽  
Author(s):  
Jessica M. Kleiss ◽  
W. Kendall Melville
Keyword(s):  
Surface Area ◽  
Wave Breaking ◽  
Friction Velocity ◽  
Wave Spectrum ◽  
Breaking Waves ◽  
Rayleigh Distribution ◽  
Sea Surface ◽  
Wave Age ◽  
Whitecap Coverage ◽  
C Distribution

Abstract Breaking waves play an important role in air–sea interaction, enhancing momentum flux from the atmosphere to the ocean, dissipating wave energy that is then available for turbulent mixing, injecting aerosols and sea spray into the atmosphere, and affecting air–sea gas transfer due to air entrainment. In this paper observations are presented of the occurrence of breaking waves under conditions of strong winds (10–25 m s−1) and fetch-limited seas (0–500 km) in the Gulf of Tehuantepec Experiment (GOTEX) in 2004. An airborne nadir-looking video camera, along with a global positioning system (GPS) and inertial motion unit (IMU), provided digital videos of the breaking sea surface and position in an earth frame. In particular, the authors present observations of Λ(c), which is the distribution of breaking wave crest lengths per unit sea surface area, per unit increment in velocity c or scalar speed c, first introduced by O. M. Phillips. In another paper, the authors discuss the effect of processing methodology on the resulting shape of the Λ(c) distribution. In this paper, the elemental method of measuring breaking crests is used to investigate the Λ(c) distributions under a variety of wind and wave conditions. The integral and the first two moments of the Λ(c) distributions are highly correlated with the active breaking rate and the active whitecap coverage. The computation of whitecap coverage yields a larger observational dataset from which the variability of whitecap coverage with wind speed, friction velocity, wave age, and wave slope is presented and compared to previous observations. The dependence of the active breaking rate on the spectral peak steepness is in agreement with previous studies. Dimensional analysis of Λ(c) indicates that scaling with friction velocity and gravity, as in the classical fetch relations, collapses the breaking distributions more effectively than scaling with dominant wave parameters. Significant wave breaking is observed at speeds near the spectral peak in young seas only, consistent with previous studies. The fourth and fifth moments of Λ(c) are related to the flux of momentum transferred by breaking waves to the underlying water and the rate of wave energy dissipation, respectively. The maximum in the fourth moment occurs at breaking speeds of 5–5.5 m s−1, and the maximum in the fifth moment occurs at 5.8–6.8 m s−1, apparently independent of wave age. However, when nondimensionalized by the phase speed at the peak of the local wave spectrum cp, the maxima in the nondimensionalized fourth and fifth moments show a decreasing trend with wave age, obtaining the maxima at dimensionless speeds c/cp near unity at smaller wave ages and moving to lower dimensionless speeds c/cp ≪ 1 at larger wave ages. The angular dependence of Λ(c) is predominantly unimodal and better aligned with the wind direction than the dominant wave direction. However, the directional distribution of Λ(c) is broadest for small c and often exhibits a bimodal structure for slow breaking speeds under developing seas. An asymmetry in the directional distribution is also observed for moderately developed seas. Observations are compared to the Phillips model for Λ(c) in the equilibrium range of the wave spectrum. Although the ensemble of Λ(c) distributions appears consistent with a c−6 function, the distributions are not described by a constant power-law exponent. However, the Λ(c) observations are described well by the Rayleigh distribution for slow and intermediate speeds, yet fall above the Rayleigh distribution for the fastest breaking speeds. From the Rayleigh description, it is found that the dimensionless width of the Λ(c) distribution increases weakly with dimensionless fetch, s/u*e = 1.69χ0.06, where s is the Rayleigh parameter, u*e is the effective friction velocity, and the dimensionless fetch is a function of the fetch X and gravitational acceleration g. The nondimensionalized total length of breaking per unit sea surface area is found to decrease with dimensionless fetch for intermediate to fully developed seas, , where A is the total length of breaking crests per unit sea surface area.

scholarly journals Observations of the Transfer of Energy and Momentum to the Oceanic Surface Boundary Layer beneath Breaking Waves

2016 ◽  
Vol 46 (6) ◽  
pp. 1823-1837 ◽  
Author(s):  
Malcolm E. Scully ◽  
John H. Trowbridge ◽  
Alexander W. Fisher
Keyword(s):  
Vertical Velocity ◽  
Wave Breaking ◽  
Momentum Flux ◽  
Surface Flux ◽  
Breaking Waves ◽  
Surface Boundary ◽  
Wave Band ◽  
Surface Boundary Layer ◽  
Order Of Magnitude ◽  
Energy And Momentum

AbstractMeasurements just beneath the ocean surface demonstrate that the primary mechanism by which energy from breaking waves is transmitted into the water column is through the work done by the covariance of turbulent pressure and velocity fluctuations. The convergence in the vertical transport of turbulent kinetic energy (TKE) balances the dissipation rate of TKE at first order and is nearly an order of magnitude greater than the sum of the integrated Eulerian and Stokes shear production. The measured TKE transport is consistent with a simple conceptual model that assumes roughly half of the surface flux of TKE by wave breaking is transmitted to depths greater than the significant wave height. During conditions when breaking waves are inferred, the direction of momentum flux is more aligned with the direction of wave propagation than with the wind direction. Both the energy and momentum fluxes occur at frequencies much lower than the wave band, consistent with the time scales associated with wave breaking. The largest instantaneous values of momentum flux are associated with strong downward vertical velocity perturbations, in contrast to the pressure work, which is associated with strong drops in pressure and upward vertical velocity perturbations.

scholarly journals Breaking-Wave Induced Transient Pore Pressure in a Sandy Seabed: Flume Modeling and Observations

2021 ◽  
Vol 9 (2) ◽  
pp. 160
Author(s):  
Changfei Li ◽  
Fuping Gao ◽  
Lijing Yang
Keyword(s):  
Pore Pressure ◽  
Wave Height ◽  
Wave Breaking ◽  
Breaking Waves ◽  
Breaking Wave ◽  
Regular Waves ◽  
Large Wave ◽  
Pore Pressures ◽  
Linear Waves ◽  
Wave Induced

Previous studies on wave-induced pore pressure in a porous seabed mainly focused on non-breaking regular waves, e.g., Airy linear waves or Stokes non-linear waves. In this study, breaking-wave induced pore pressure response in a sandy seabed was physically simulated with a large wave flume. The breaking-wave was generated by superimposing a series of longer waves onto the foregoing shorter waves at a specified location. Water surface elevations and the corresponding pore pressure in the process of wave breaking were measured simultaneously at three typical locations, i.e., at the rear, just at, and in front of the wave breaking location. Based on test results, characterization parameters are proposed for the wave surface elevations and the corresponding pore-pressures. Flume observations indicate that the wave height was greatly diminished during wave breaking, which further affected the pore-pressure responses. Moreover, the measured values of the characteristic time parameters for the breaking-wave induced pore-pressure are larger than those for the free surface elevation of breaking-waves. Under the action of incipient-breaking or broken waves, the measured values of the amplitude of transient pore-pressures are generally smaller than the predicted results with the analytical solution by Yamamoto et al. (1978) for non-breaking regular waves with equivalent values of characteristic wave height and wave period.

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.

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°.

scholarly journals Suppression of Wind Ripples and Microwave Backscattering Due to Turbulence Generated by Breaking Surface Waves

2020 ◽  
Vol 12 (21) ◽  
pp. 3618
Author(s):  
Stanislav Ermakov ◽  
Vladimir Dobrokhotov ◽  
Irina Sergievskaya ◽  
Ivan Kapustin
Keyword(s):  
Remote Sensing ◽  
Surface Waves ◽  
Wave Breaking ◽  
Wave Train ◽  
Wind Waves ◽  
Breaking Waves ◽  
Doppler Spectrum ◽  
Strong Wave ◽  
Wave Maker ◽  
Radar Backscattering

The role of wave breaking in microwave backscattering from the sea surface is a problem of great importance for the development of theories and methods on ocean remote sensing, in particular for oil spill remote sensing. Recently it has been shown that microwave radar return is determined by both Bragg and non-Bragg (non-polarized) scattering mechanisms and some evidence has been given that the latter is associated with wave breaking, in particular, with strong breaking such as spilling or plunging. However, our understanding of mechanisms of the action of strong wave breaking on small-scale wind waves (ripples) and thus on the radar return is still insufficient. In this paper an effect of suppression of radar backscattering after strong wave breaking has been revealed experimentally and has been attributed to the wind ripple suppression due to turbulence generated by strong wave breaking. The experiments were carried out in a wind wave tank where a frequency modulated wave train of intense meter-decimeter-scale surface waves was generated by a mechanical wave maker. The wave train was compressed according to the gravity wave dispersion relation (“dispersive focusing”) into a short-wave packet at a given distance from the wave maker. Strong wave breaking with wave crest overturning (spilling) occurred for one or two highest waves in the packet. Short decimeter-centimeter-scale wind waves were generated at gentle winds, simultaneously with the long breaking waves. A Ka-band scatterometer was used to study microwave backscattering from the surface waves in the tank. The scatterometer looking at the area of wave breaking was mounted over the tank at a height of about 1 m above the mean water level, the incidence angle of the microwave radiation was about 50 degrees. It has been obtained that the radar return in the presence of short wind waves is characterized by the radar Doppler spectrum with a peak roughly centered in the vicinity of Bragg wave frequencies. The radar return was strongly enhanced in a wide frequency range of the radar Doppler spectrum when a packet of long breaking waves arrived at the area irradiated by the radar. After the passage of breaking waves, the radar return strongly dropped and then slowly recovered to the initial level. Measurements of velocities in the upper water layer have confirmed that the attenuation of radar backscattering after wave breaking is due to suppression of short wind waves by turbulence generated in the breaking zone. A physical analysis of the effect has been presented.

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