On the Effects of Finite Depth on Wind-Wave Spectra: 1. A Comparison with Deep-Water Equilibrium-Range Slope and Other Spectral Parameters

1982 ◽  
Vol 12 (6) ◽  
pp. 556-568 ◽  
Author(s):  
C. E. Knowles
Keyword(s):  
Deep Water ◽  
Wind Wave ◽  
Finite Depth ◽  
Wave Spectra ◽  
Spectral Parameters ◽  
Water Equilibrium ◽  
Equilibrium Range

Breaking waves and the equilibrium range of wind-wave spectra

1997 ◽  
Vol 342 ◽  
pp. 377-401 ◽  
Author(s):  
S. E. BELCHER ◽  
J. C. VASSILICOS
Keyword(s):  
High Frequency ◽  
Wind Wave ◽  
Breaking Waves ◽  
Breaking Wave ◽  
Wave Spectra ◽  
Scale Invariant ◽  
Self Similar ◽  
Dynamical Properties ◽  
Dynamical Balance ◽  
Equilibrium Range

When scaled properly, the high-wavenumber and high-frequency parts of wind-wave spectra collapse onto universal curves. This collapse has been attributed to a dynamical balance and so these parts of the spectra have been called the equilibrium range. We develop a model for this equilibrium range based on kinematical and dynamical properties of breaking waves. Data suggest that breaking waves have high curvature at their crests, and they are modelled here as waves with discontinuous slope at their crests. Spectra are then dominated by these singularities in slope. The equilibrium range is assumed to be scale invariant, meaning that there is no privileged lengthscale. This assumption implies that: (i) the sharp-crested breaking waves have self-similar shapes, so that large breaking waves are magnified copies of the smaller breaking waves; and (ii) statistical properties of breaking waves, such as the average total length of breaking-wave fronts of a given scale, vary with the scale of the breaking waves as a power law, parameterized here with exponent D.

Spectral Analysis of Ship-Generated Waves in Finite-Depth Water

2002 ◽  
Author(s):  
Carl A. Scragg
Keyword(s):  
Deep Water ◽  
Wave Spectrum ◽  
Finite Depth ◽  
Far Field ◽  
Wave Spectra ◽  
Data Set ◽  
Free Wave ◽  
Common Reference ◽  
Depth Water ◽  
Wave Elevations

Recent efforts to compare the waves generated by different vessels traveling in finite-depth water have struggled with difficulties presented by various data sets of wave elevations (either measurements or predictions) corresponding to different lateral distances from the ship. Some of the attempts to shift the data to a common reference location have relied upon crude and potentially misleading approximations. The use of free-wave spectral-methods not only overcomes such difficulties, but it also provides us the means to accurately extend CFD results into the far field. As in the deep-water case, one can define a free-wave spectrum that is valid for all lateral positions and distances astern of the vessel. The free-wave spectrum contains a complete description of the Kelvin wake, and wave elevations at any far-field position can be readily calculated once the spectrum is known. For the case of infinitely deep water, Eggers, Sharma, and Ward [1967] presented a method by which free-wave spectra can be determined from appropriate measurements of the far-field wave elevations. The current paper discusses the use of free-wave spectra for finite-depth problems and presents a method for the determination of free-wave spectra based upon fitting predicted wave elevations to a corresponding data set. The predicted wave elevations can be calculated from an unknown distribution of finite-depth Havelock singularities. The unknown singularities are determined by minimizing the mean-square-difference between predicted and measured wave fields. The method appears to be quite general and can be used to calculate either finite or infinite-depth free-wave spectra from experimental data or from local CFD predictions.

Spectral Representation of Ship-Generated Waves in Finite-Depth Water

2003 ◽  
Vol 125 (1) ◽  
pp. 65-71 ◽  
Author(s):  
Carl A. Scragg
Keyword(s):  
Deep Water ◽  
Wave Spectrum ◽  
Finite Depth ◽  
Far Field ◽  
Wave Spectra ◽  
Data Set ◽  
Free Wave ◽  
Common Reference ◽  
Depth Water ◽  
Wave Elevations

Recent efforts to compare the waves generated by different vessels traveling in finite-depth water have struggled with difficulties presented by various data sets of wave elevations (either measurements or predictions) corresponding to different lateral distances from the ship. Some of the attempts to shift the data to a common reference location have relied upon crude and potentially misleading approximations. The use of free-wave spectral-methods not only overcomes such difficulties, but is also provides us the means to accurately extend CFD results into the far field. As in the deep-water case, one can define a free-wave spectrum that is valid for all lateral positions and distances astern of the vessel. The free-wave spectrum contains a complete description of the Kelvin wake, and wave elevations at any far-field position can be readily calculated once the spectrum is known. For the case of infinitely deep water, Eggers, Sharma, and Ward [1] presented a method by which free-wave spectra can be determined from appropriate measurements of the far-field wave elevations. The current paper discusses the use of free-wave spectra for finite-depth problems and presents a method for the determination of free-wave spectra based upon fitting predicted wave elevations to a corresponding data set. The predicted wave elevations can be calculated from an unknown distribution of finite-depth Havelock singularities. The unknown singularities are determined by minimizing the mean-square-difference between predicted and measured wave fields. The method appears to be quite general and can be used to calculate either finite or infinite-depth free-wave spectra from experimental data or from local CFD predictions.

The equilibrium range of wind wave spectra: an explanation based on white noise

2007 ◽  
Vol 6 (4) ◽  
pp. 345-348 ◽  
Author(s):  
Dejun Dai ◽  
Wei Wang ◽  
Fangli Qiao ◽  
Yeli Yuan
Keyword(s):  
White Noise ◽  
Wind Wave ◽  
Wave Spectra ◽  
Equilibrium Range

scholarly journals Ocean Surface Wave Spectra inside Tropical Cyclones

2017 ◽  
Vol 47 (10) ◽  
pp. 2393-2417 ◽  
Author(s):  
Paul A. Hwang ◽  
Yalin Fan ◽  
Francisco J. Ocampo-Torres ◽  
Héctor García-Nava
Keyword(s):  
Wind Wave ◽  
Radial Distance ◽  
Doppler Frequency ◽  
Radial Dependence ◽  
Clear Correlation ◽  
Wave Spectra ◽  
Spectral Slope ◽  
Spectral Parameters ◽  
Spectral Models ◽  
Wide Range

AbstractDirectional wave spectra acquired in hurricane reconnaissance missions are compared with wind-wave spectral models. The comparison result is quantified with two indices of model–measurement spectral agreement. In the main region of hurricane coverage, the indices vary sinusoidally with the azimuth angle referenced to the hurricane heading while showing a weak dependence on the radial distance from the hurricane center. The measured spectra agree well with three models evaluated in the back and right quarters, and they are underdeveloped in the front and left quarters. The local wind and wave directions also show a weak radial dependence and sinusoidal variation along the azimuth. The wind and wave vectors are almost collinear in the back and right quarters; they diverge azimuthally and become almost perpendicular in the left quarter. The azimuthally cyclical correlation between the indices of spectral agreement and the wind-wave directional difference is well described by the sinusoidal variations. Also discussed is the wide range of the spectral slopes observed in both hurricane and nonhurricane field data. It is unlikely that the observed spectral slope variation is caused by Doppler frequency shift from background currents. No clear correlation is found between spectral slope and various wind and wave parameters. The result suggests that the spectral slope needs to be treated as a stochastic random variable. Complementing the existing wind-wave spectral models that prescribe a fixed spectral slope of either −4 or −5, a general spectral model with its spectral parameters accommodating a variable spectral slope is introduced.

scholarly journals On Natural Modulational Bandwidth of Deep-Water Surface Waves

Fluids ◽  
2019 ◽  
Vol 4 (2) ◽  
pp. 67
Author(s):  
Alexander Babanin ◽  
Miguel Onorato ◽  
Luigi Cavaleri
Keyword(s):  
Deep Water ◽  
Water Surface ◽  
Laboratory Experiments ◽  
Wind Wave ◽  
Wave Spectra ◽  
Field Observations ◽  
Wave Steepness ◽  
Side Band ◽  
Wave Trains

We suggest that there exists a natural bandwidth of wave trains, including trains of wind-generated waves with a continuous spectrum, determined by their steepness. Based on laboratory experiments with monochromatic waves, we show that, if no side-band perturbations are imposed, the ratio between the wave steepness and bandwidth is restricted to certain limits. These limits are consistent with field observations of narrow-banded wind-wave spectra if a characteristic width of the spectral peak and average steepness are used. The role of the wind in such modulation is also discussed.

scholarly journals Nonlinear energy fluxes and the finite depth equilibrium range in wave spectra

2001 ◽  
Vol 106 (C4) ◽  
pp. 6985-7000 ◽  
Author(s):  
Donald T. Resio ◽  
Jorgen H. Pihl ◽  
Barbara A. Tracy ◽  
C. Linwood Vincent
Keyword(s):  
Finite Depth ◽  
Wave Spectra ◽  
Energy Fluxes ◽  
Equilibrium Range ◽  
Nonlinear Energy

scholarly journals Wind-wave amplification mechanisms: possible models for steep wave events in finite depth

2013 ◽  
Vol 1 (4) ◽  
pp. 3099-3127 ◽  
Author(s):  
P. Montalvo ◽  
R. Kraenkel ◽  
M. A. Manna ◽  
C. Kharif
Keyword(s):  
Wind Velocity ◽  
Deep Water ◽  
Growth Rates ◽  
Linear Growth ◽  
Wind Wave ◽  
Finite Depth ◽  
Wave Number ◽  
Linear Growth Rate ◽  
Wave Age ◽  
Wave Amplification

Abstract. We extend the Miles' mechanism of wind-wave generation to finite depth. A β-Miles linear growth rate depending on the depth and wind velocity is derived and allows the study of linear growth rates of surface waves from weak to moderate winds in finite depth h. The evolution of β is plotted, for several values of the dispersion parameter kh with k the wave number. For constant depths we find that no matter what the values of wind velocities are, at small enough wave age the β-Miles linear growth rates are in the known deep water limit. However winds of moderate intensities prevent the waves from growing beyond a critical wave age, which is also constrained by the water depth and is less than the wave age limit of deep water. Depending on wave age and wind velocity, the Jeffreys' and Miles' mechanisms are compared to determine which of them dominates. A wind-forced nonlinear Schrödinger equation is derived and the Akhmediev, Peregrine and Kuznetsov–Ma breather solutions for weak wind inputs in finite depth h are obtained.

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