scholarly journals SELF-SIMILAR AND LASER-LIKE REGIMES IN NUMERICAL MODELING OF HASSELMANN KINETIC EQUATION FOR OCEAN WAVES

2019 ◽  
Vol 47 (1) ◽  
pp. 103-106
Author(s):  
A.N. Pushkarev ◽  
V.E. Zakharov
Keyword(s):  
Numerical Modeling ◽  
Kinetic Equation ◽  
Wave Breaking ◽  
Wind Waves ◽  
Ocean Waves ◽  
Black Box ◽  
Wind Forcing ◽  
Power Type ◽  
Self Similar ◽  
Interaction Approximation

The absence of mathematically justified criteria in the models of prediction of wind waves of the ocean, used by the world’s largest centers NOAA (USA) and ECMWF (UK), based on numerical modeling of the Hasselmann kinetic equation, led to erroneous hierarchy and erroneous nonlinear interaction approximation, wind forcing and waves dissipation terms due to wave-breaking. Existing models of wind waves operate in the paradigm of the adjustable «black box», each time requiring reconfiguration. On the basis of numerical simulation, we were able to construct a model, taking into account the wind forcing of the power type in combination with the «implicit» dissipation.

EFFECTS OF AN OIL SLICK ON WIND WAVES1

1979 ◽  
Vol 1979 (1) ◽  
pp. 665-674 ◽  
Author(s):  
Hsien-Ta Liu ◽  
Jung-Tai Lin
Keyword(s):  
Wave Breaking ◽  
Wind Wave ◽  
Wind Waves ◽  
Ocean Waves ◽  
Diesel Oil ◽  
Wave Tank ◽  
Oil Slick ◽  
Wave Profiles ◽  
The Waves ◽  
Integrated Program

ABSTRACT Laboratory experiments were performed to investigate the effects of an oil slick on ocean waves. This is part of an integrated program aimed at understanding the vertical dispersion of oil in the upper ocean. The experiments were conducted in a wind-wave tank which measured 9.1 m long, 1.2 m wide, and 1.8 m deep. Both wind waves and mechanically-generated waves with wind were considered. No. 2 Diesel oil was fed at a rate of 0.35 liters/sec onto the water surface from the upstream end of the wave tank. To measure the wave profiles, an optical sensor-photodiode wave gauge was developed and is described herein. The effects of an oil slick on wind waves were examined in terms of wave profiles and rms wave amplitudes. For wind waves, the presence of the oil slick damps the waves significantly. The amount of damping increases with the wind speed in the range from U∞ = 4 m/sec to 10 m/sec. At U∞ = 10 m/sec, the oil slick breaks into small lenses. The rms amplitudes of the wind-generated waves increase with the fetch without the oil slick, but they do not change appreciably in the presence of the oil slick. For mechanically-generated waves with wind, wave damping by the oil slick becomes insignificant when the waves are sufficiently steep and wave breaking occurs. Prior to wave breaking, however, steepening of the wave crests due to the presence of the oil slick has been observed occasionally as a result of the reduction in the surface tension by the oil film.

scholarly journals The choice of optimal Discrete Interaction Approximation to the kinetic integral for ocean waves

2003 ◽  
Vol 10 (4/5) ◽  
pp. 425-434 ◽  
Author(s):  
V. G. Polnikov
Keyword(s):  
Kinetic Equation ◽  
Water Waves ◽  
Wave Spectrum ◽  
Ocean Waves ◽  
Interaction Processes ◽  
Wave Forecast ◽  
Long Time ◽  
Discrete Interaction ◽  
The One ◽  
Interaction Approximation

Abstract. A lot of discrete configurations for the four-wave nonlinear interaction processes have been calculated and tested by the method proposed earlier in the frame of the concept of Fast Discrete Interaction Approximation to the Hasselmann's kinetic integral (Polnikov and Farina, 2002). It was found that there are several simple configurations, which are more efficient than the one proposed originally in Hasselmann et al. (1985). Finally, the optimal multiple Discrete Interaction Approximation (DIA) to the kinetic integral for deep-water waves was found. Wave spectrum features have been intercompared for a number of different configurations of DIA, applied to a long-time solution of kinetic equation. On the basis of this intercomparison the better efficiency of the configurations proposed was confirmed. Certain recommendations were given for implementation of new approximations to the wave forecast practice.

The influence of wave breaking on the surface pressure distribution in wind—wave interactions

1990 ◽  
Vol 211 ◽  
pp. 463-495 ◽  
Author(s):  
Michael L. Banner
Keyword(s):  
Pressure Distribution ◽  
Surface Pressure ◽  
Wave Breaking ◽  
Wind Wave ◽  
Wind Waves ◽  
Breaking Waves ◽  
Wind Forcing ◽  
Wave Interactions ◽  
Form Drag ◽  
Surface Pressure Distribution

In reviewing the current status of our understanding of the mechanisms underlying wind-wave generation, it is apparent that existing theories and models are not applicable to situations where the sea surface is disturbed by breaking waves, and that the available experimental data on this question are sparse. In this context, this paper presents the results of a detailed study of the effects of wave breaking on the aerodynamic surface pressure distribution and consequent wave-coherent momentum flux, as well as its influence on the total wind stress.Two complementary experimental configurations were used to focus on the details and consequences of the pressure distribution over breaking waves under wind forcing. The first utilized a stationary breaking wave configuration and confirmed the presence of significant phase shifting, due to air flow separation effects, between the surface pressure and surface elevation (and slope) distributions over a range of wind speeds. The second configuration examined the pressure distribution, recorded at a fixed height above the mean water surface just above the crest level, over short mechanically triggered waves which were induced to break almost continuously under wind forcing. This allowed a very detailed comparison of the form drag for actively breaking waves and for waves of comparable steepness just prior to breaking (‘incipiently’ breaking waves). For these propagating steep-wave experiments, the pressure phase shifts and distributions closely paralleled the stationary configuration findings. Moreover, a large increase (typically 100%) in the total windstress was observed for the breaking waves, with the increase corresponding closely to the comparably enhanced form drag associated with the actively breaking waves.In addition to further elucidating some fundamental features of wind-wave interactions for very steep wind waves, this paper provides a useful data set for future model calculations of wind flow over breaking waves. The results also provide the basis for a parameterization of the wind input source function applicable for a wave field undergoing active breaking, an important result for numerical modelling of short wind waves.

Nonlinear Laser-Like Ocean Waves Radiation Orthogonal to the Wind

2020 ◽  
Author(s):  
Andrei Pushkarev ◽  
Vladimir Zakharov
Keyword(s):  
Wave Energy ◽  
Wind Waves ◽  
Wave Interaction ◽  
Ocean Waves ◽  
Wave Turbulence ◽  
Wave System ◽  
Self Similar ◽  
Similar Solutions ◽  
Ocean Wind ◽  
The Waves

Abstract We study deep water ocean wind-driven waves in strait, with wind directed orthogonally to the shore, through exact Hassel-mann equation. The strait has “dissipative” shores, there is no any reflection from the coast lines. We show that the wave turbulence evolution can be split in time into two different regimes. During the first regime, the waves propagate along the wind, and the wind-driven sea can be described by the self-similar solutions of Hasselmann equation. The second regime starts later in time, after significant enough wave energy accumulation at the down-wind boundary. Since this moment the ensemble of waves propagating against the wind starts its formation. Also, orthogonal to the wind waves, propagating along the strait, start to appear. The wave system eventually reaches asymptotic stationary state in time, consisting of two co-existing states: the first, self-similar wave ensemble, propagating with the wind, and the second – quasi-monochromatic waves, propagating almost orthogonally to the wind direction, and tending to slant against the wind at the angle of 15° closer to the wave turbulence origination shore line. Those “secondary waves” appear only due to intensive nonlinear wave-wave interaction. The total wave energy exceeds its “expected value” approximately by the factor of two, with respect to estimated in the absence of the shores. It is expected that in the reflective shores presence this amplification will grow essentially. We propose to call this “secondary” laser-like Nonlinear Ocean Waves Amplification mechanism by the acronym NOWA.

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.

Kinetic equations for plasmas subjected to a strong time-dependent extenal field. Part 2. The weak-interaction approximation

1974 ◽  
Vol 11 (3) ◽  
pp. 377-387 ◽  
Author(s):  
R. Balescu ◽  
J. H. Misguich
Keyword(s):  
Kinetic Equation ◽  
General Theory ◽  
Weak Interaction ◽  
Weak Coupling ◽  
Kinetic Equations ◽  
Time Dependent ◽  
External Fields ◽  
Interaction Approximation

The general theory developed in part 1 is illustrated for a plasma described by the weak-coupling (Landau) approximation. The kinetic equation, valid for arbitrarily strong external fields, is written out explicitly.

scholarly journals Theoretical interpretation of fetch limited wind-drivensea observations

2005 ◽  
Vol 12 (6) ◽  
pp. 1011-1020 ◽  
Author(s):  
V. E. Zakharov
Keyword(s):  
Gravity Waves ◽  
Wave Breaking ◽  
Field Studies ◽  
The Self ◽  
Theoretical Interpretation ◽  
Simple Analytical Model ◽  
Surface Gravity Waves ◽  
Interaction Terms ◽  
Self Similar ◽  
Similar Solutions

Abstract. We show that the results of major fetch limited field studies of wind-generated surface gravity waves on deep water can be explained in the framework of simple analytical model. The spectra measured in these experiments are described by self-similar solutions of ``conservative" Hasselmann equation that includes only advective and nonlinear interaction terms. Interaction with the wind and dissipation due to the wave breaking indirectly defines parameters of the self-similar solutions.

An experimental investigation of incipient spilling breakers

2009 ◽  
Vol 633 ◽  
pp. 271-283 ◽  
Author(s):  
J. D. DIORIO ◽  
X. LIU ◽  
J. H. DUNCAN
Keyword(s):  
Wave Breaking ◽  
High Speed ◽  
Phase Speed ◽  
Breaking Waves ◽  
Front Face ◽  
Geometrical Parameters ◽  
Instability Mechanism ◽  
Scaling Relationships ◽  
Self Similar ◽  
Spilling Breakers

In the present paper, the profiles of incipient spilling breaking waves with wavelengths ranging from 10 to 120cm were studied experimentally in clean water. Short-wavelength breakers were generated by wind, while longer-wavelength breakers were generated by a mechanical wavemaker, using either a dispersive focusing or a sideband instability mechanism. The crest profiles of these waves were measured with a high-speed cinematic laser-induced fluorescence technique. For all the wave conditions reported herein, wave breaking was initiated with a capillary-ripple pattern as described in Duncan et al. (J. Fluid Mech., vol. 379, 1999, pp. 191–222). In the present paper, it is shown that at incipient breaking the crest shape is self-similar with two geometrical parameters that depend only on the slope of a particular point on the front face of the gravity wave. The scaling relationships appear to be universal for the range of wavelengths studied herein and hold for waves generated by mechanical wavemakers and by wind. The slope measure is found to be dependent on the wave phase speed and the rate of growth of the crest height prior to incipient breaking.

Long-term evolution of directional spectra of wind waves modelled by DNS and kinetic equations, and comparison with airborne measurements

2021 ◽  
Author(s):  
Sergei Annenkov ◽  
Victor Shrira ◽  
Leonel Romero ◽  
Ken Melville
Keyword(s):  
Angular Distribution ◽  
Kinetic Equation ◽  
Kinetic Theory ◽  
Wind Waves ◽  
Kinetic Equations ◽  
Spectral Peak ◽  
Angular Width ◽  
Angular Structure ◽  
Airborne Measurements ◽  
Steady Growth

<p>We consider the evolution of directional spectra of waves generated by constant and changing wind, modelling it by direct numerical simulation (DNS), based on the Zakharov equation. Results are compared with numerical simulations performed with the Hasselmann kinetic equation and the generalised kinetic equation, and with airborne measurements of waves generated by offshore wind, collected during the GOTEX experiment off the coast of Mexico. Modelling is performed with wind measured during the experiment, and the initial conditions are taken as the observed spectrum at the moment when wind waves prevail over swell after the initial part of the evolution.</p><p>Directional spreading is characterised by the second moment of the normalised angular distribution function, taken at selected wavenumbers relative to the spectral peak. We show that for scales longer than the spectral peak the angular spread predicted by the DNS is close to that predicted by both kinetic equations, but it underestimates the corresponding measured value, apparently due to the presence of swell. For the spectral peak and shorter waves, the DNS shows good agreement with the data. A notable feature is the steady growth of angular width at the spectral peak with time/fetch, in contrast to nearly constant width in the kinetic equations modelling. Dependence of angular width on wavenumber is shown to be much weaker than predicted by the kinetic equations. A more detailed consideration of the angular structure at the spectral peak at large fetches shows that the kinetic equations predict an angular distribution with a well-defined peak at the central angle, while the DNS reproduces the observed angular structure, with a flat peak over a range of angles.</p><p>In order to study in detail the differences between the predictions of the DNS and the kinetic equations modelling under idealised conditions, we also perform numerical simulations for the case of constant wind forcing. As in the previous case of forcing by real wind, the most striking difference between the kinetic equations and the DNS is the steady growth with time of angular width at the spectral peak, which is demonstrated by the DNS, but is not present in the modelling with the kinetic equations. We show that while the kinetic theory, both in the case of the Hasselmann equation and the generalised kinetic equation, predicts a relatively simple shape of the spectral peak, the DNS shows a more complicated structure, with a flat top and dependence of the peak position on angle. We discuss the approximations employed in the derivation of the kinetic theory and the possible causes of the found differences of directional structure.</p>

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