Unified Wind Wave Growth and Spectrum Functions for All Water Depths: Field Observations and Model Results

2022 ◽  
Keyword(s):  
Wind Wave ◽  
Peak Frequency ◽  
Wind Forcing ◽  
Spectral Peak ◽  
Dimensionless Frequency ◽  
Wave Age ◽  
Surface Wave Dispersion ◽  
Similarity Functions ◽  
Spectrum Model ◽  
Water Depths

Abstract Wind wave development is governed by the fetch- or duration-limited growth principle that is expressed as a pair of similarity functions relating the dimensionless elevation variance (wave energy) and spectral peak frequency to fetch or duration. Combining the pair of similarity funtions the fetch or duration variable can be removed to form a dimensionless function of elevation variance and spectral peak frequency, which is interepreated as the wave enegry evolution with wave age. The relationship is initially developed for quasi-neural stability and quasi-steady wind forcing conditions. Further analyses show that the same fetch, duration, and wave age similarity functions are applicable to unsteady wind forcing conditions, including rapidly accelerating and decelerating mountain gap wind episodes and tropical cyclone (TC) wind fields. Here it is shown that with the dimensionless frequency converted to dimensionless wavenumber using the surface wave dispersion relationship, the same similarity function is applicable in all water depths. Field data collected in shallow to deep waters and mild to TC wind conditions, and synthetic data generated by spectrum model computations are assembled to illustrate the applicability. For the simulation work, the finite-depth wind wave spectrum model and its shoaling function are formulated for variable spectral slopes. Given wind speed, wave age, and water depth, the measrued and spectrum-computed significant wave heights and the associated growth parameters are in good agreement in forcing conditions from mild to TC winds and in all depths from deep ocean to shallow lake.

The growth of duration-limited wind waves

1978 ◽  
Vol 85 (4) ◽  
pp. 705-730 ◽  
Author(s):  
Hisashi Mitsuyasu ◽  
Kunio Rikiishi
Keyword(s):  
Growth Rate ◽  
Exponential Growth ◽  
Empirical Formula ◽  
Wind Wave ◽  
Wind Waves ◽  
Wave Spectrum ◽  
Peak Frequency ◽  
Spectral Peak ◽  
Spectral Energy ◽  
Wave Spectra

Laboratory measurements have been made of the one-dimensional spectra of the duration-limited wind waves which are generated when a wind abruptly begins to blow over a water surface, maintaining a constant speed during the succeeding period of time. The duration dependences of the wave energy E and the spectral peak frequency fm determined from the measured spectra are slightly different from those inferred from the fetch dependences of these quantities. The normalized spectra of the duration-limited wind waves are also slightly different from those of fetch-limited wind waves: the concentration of the normalized spectral energy near the spectral peak frequency is smaller, in many cases, for the duration-limited wind waves than for fetch-limited wind waves. The exponential growth rates β of the duration-limited wind-wave spectra are generally larger than those of fetch-limited wind-wave spectra. Furthermore, both for the duration-limited wind waves and for fetch-limited wind waves the exponential growth rate has a behaviour which is different from the empirical formula of Snyder & Cox (1966). A new empirical formula for the growth rate of the wave spectrum is proposed, from which the empirical formula of Snyder & Cox (1966) can be derived as a special case. Agreement between the new empirical formula and the experimental results is satisfactory for fetch-limited wave spectra, but is confined to the qualitative features for the duration-limited wave spectra.

scholarly journals Loop-Type Wave-Generation Method for Generating Wind Waves under Long-Fetch Conditions

2017 ◽  
Vol 34 (10) ◽  
pp. 2129-2139 ◽  
Author(s):  
Naohisa Takagaki ◽  
Satoru Komori ◽  
Mizuki Ishida ◽  
Koji Iwano ◽  
Ryoichi Kurose ◽  
...  
Keyword(s):  
Wind Wave ◽  
Wind Waves ◽  
Peak Frequency ◽  
Wave Generation ◽  
New Wave ◽  
Wave Tank ◽  
Irregular Wave ◽  
Wind Speeds ◽  
Type Wave ◽  
Wave Generator

AbstractIt is important to develop a wave-generation method for extending the fetch in laboratory experiments, because previous laboratory studies were limited to the fetch shorter than several dozen meters. A new wave-generation method is proposed for generating wind waves under long-fetch conditions in a wind-wave tank, using a programmable irregular-wave generator. This new method is named a loop-type wave-generation method (LTWGM), because the waves with wave characteristics close to the wind waves measured at the end of the tank are reproduced at the entrance of the tank by the programmable irregular-wave generator and the mechanical wave generation is repeated at the entrance in order to increase the fetch. Water-level fluctuation is measured at both normal and extremely high wind speeds using resistance-type wave gauges. The results show that, at both wind speeds, LTWGM can produce wind waves with long fetches exceeding the length of the wind-wave tank. It is observed that the spectrum of wind waves with a long fetch reproduced by a wave generator is consistent with that of pure wind-driven waves without a wave generator. The fetch laws between the significant wave height and the peak frequency are also confirmed for the wind waves under long-fetch conditions. This implies that the ideal wind waves under long-fetch conditions can be reproduced using LTWGM with the programmable irregular-wave generator.

scholarly journals On Evolution of Young Wind Waves in Time and Space

Atmosphere ◽  
2019 ◽  
Vol 10 (9) ◽  
pp. 562 ◽  
Author(s):  
Shemer
Keyword(s):  
Wave Field ◽  
Field Experiments ◽  
Wind Wave ◽  
Wind Waves ◽  
Wave Generation ◽  
Wind Forcing ◽  
Spatial And Temporal Variation ◽  
Extensive Discussion ◽  
Deterministic Theory ◽  
Theoretical Approaches

The mechanisms governing the evolution of the wind-wave field in time and in space are not yet fully understood. Various theoretical approaches have been offered to model wind-wave generation. To examine their validity, detailed and accurate experiments under controlled conditions have to be carried out. Since it is next to impossible to get the required control of the governing parameters and to accumulate detailed data in field experiments, laboratory studies are needed. Extensive previously unavailable results on the spatial and temporal variation of wind waves accumulated in our laboratory under a variety of wind-forcing conditions and using diverse measuring techniques are reviewed. The spatial characteristics of the wind-wave field were determined using stereo video imaging. The turbulent airflow above wind waves was investigated using an X-hot film. The wave field under steady wind forcing as well as evolving from rest under impulsive loading was studied. An extensive discussion of the various aspects of wind waves is presented from a single consistent viewpoint. The advantages of the stochastic approach suggested by Phillips over the deterministic theory of wind-wave generation introduced by Miles are demonstrated. Essential differences between the spatial and the temporal analyses of wind waves’ evolution are discussed, leading to examination of the applicability of possible approaches to wind-wave modeling.

scholarly journals Wind Sea and Swell Separation of 1D Wave Spectrum by a Spectrum Integration Method*

2012 ◽  
Vol 29 (1) ◽  
pp. 116-128 ◽  
Author(s):  
Paul A. Hwang ◽  
Francisco J. Ocampo-Torres ◽  
Héctor García-Nava
Keyword(s):  
Integration Method ◽  
Wave Spectrum ◽  
Peak Frequency ◽  
External Information ◽  
Wave Steepness ◽  
Wave Age ◽  
Wide Range ◽  
Wave Development ◽  
Wave Conditions ◽  
Wind Sea

Abstract In an earlier paper by Wang and Hwang, a wave steepness method was introduced to separate the wind sea and swell of the 1D wave spectrum without relying on external information, such as the wind speed. Later, the method was found to produce the unreasonable result of placing the swell–sea separation frequency higher than the wind sea peak frequency. Here, the following two factors causing the erratic performance are identified: (a) the wave steepness method defines the swell–sea separation frequency to be equal to the wind sea peak frequency with a wave age equal to one, and, (b) for more mature wave conditions, the peak frequency of the wave steepness function may not continue monotonic downshifting in high winds if the high-frequency portion of the wave spectrum has a spectral slope milder than −5. Conceptually, the swell–sea separation frequency should be placed between the swell and wind sea peak frequencies rather than at the wind sea peak frequency. Furthermore the wind sea wave age can vary over a considerable range, thus factor a above can lead to incorrect results. Also, because the slope of the wind sea equilibrium spectrum is typically close to −4, factor b becomes a serious restriction in more mature wave conditions. A spectrum integration method generalized from the wave steepness method is presented here for wind sea and swell separation of the 1D wave spectrum without requiring external information. The new spectrum integration method works very well over a wide range of wind wave development stages in the ocean.

scholarly journals Drag of the Water Surface at Very Short Fetches: Observations and Modeling

2008 ◽  
Vol 38 (9) ◽  
pp. 2038-2055 ◽  
Author(s):  
Guillemette Caulliez ◽  
Vladimir Makin ◽  
Vladimir Kudryavtsev
Keyword(s):  
Wind Stress ◽  
Wave Breaking ◽  
Wind Wave ◽  
Wind Forcing ◽  
Wave Steepness ◽  
Surface Drag ◽  
Wave Fields ◽  
Wind Speeds ◽  
Dominant Wave ◽  
Wide Range

Abstract The specific properties of the turbulent wind stress and the related wind wave field are investigated in a dedicated laboratory experiment for a wide range of wind speeds and fetches, and the results are analyzed using the wind-over-waves coupling model. Compared to long-fetch ocean wave fields, wind wave fields observed at very short fetches are characterized by higher significant dominant wave steepness but a much smaller macroscale wave breaking rate. The surface drag dependence on fetch and wind then closely follows the dominant wave steepness dependence. It is found that the dimensionless roughness length z*0 varies not only with wind forcing (or inverse wave age) but also with fetch. At a fixed fetch, when gravity waves develop, z*0 decreases with wind forcing according to a −1/2 power law. Taking into account the peculiarities of laboratory wave fields, the WOWC model predicts the measured wind stress values rather well. The relative contributions to surface drag of the equilibrium-range wave-induced stress and the airflow separation stress due to wave breaking remain small, even at high wind speeds. At moderate to strong winds, the form drag resulting from dominant waves represents the major wind stress component.

scholarly journals Multiple Model Adaptive Nonlinear Observer of Dynamic Positioning Ship

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Yehai Xie ◽  
Xiaogong Lin ◽  
Xinqian Bian ◽  
Dawei Zhao
Keyword(s):  
Wave Spectrum ◽  
Peak Frequency ◽  
Adaptive Observer ◽  
Nonlinear Observer ◽  
Dynamic Positioning ◽  
Multiple Model ◽  
Sea State ◽  
Swarm Optimization ◽  
Filtering Problem ◽  
Spectrum Model

Considering the filtering problem of dynamic positioning (DP) ship for the slowly varying sea state, a multiple model adaptive observer (MMAO) for dynamic positioning ship is presented. The MMAO consists of a bank of nonlinear subobserver and a dynamic weighting signal generator, in which each sub-observer is designed based on different peak frequency of wave spectrum model. To improve the performance of the observer, subobserver using the measurement of position, velocity, and acceleration is used to update the estimated velocity of ship. The observer parameters are optimized using particle swarm optimization (PSO). Finally, the method is verified effective by the computer simulation.

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).

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