scholarly journals DIRECTIONAL SPECTRA OF OCEAN SURFACE WAVES

1976 ◽  
Vol 1 (15) ◽  
pp. 18 ◽  
Author(s):  
H. Mitsuyasu ◽  
S. Mizuno
Keyword(s):  
Angular Distribution ◽  
Frequency Spectrum ◽  
Wind Waves ◽  
Wave Spectrum ◽  
Ocean Waves ◽  
Peak Frequency ◽  
Spectral Peak ◽  
Energy Concentration ◽  
Spectral Energy ◽  
Directional Spectrum

From 1971-74 seven cruises were made to measure the directional spectrum of ocean waves by using a cloverleaf buoy. Typical sets of wave data measured both in open seas and in a bay under relatively simple conditions have been analyzed to clarify the fundamental properties of the directional spectrum of ocean waves in deep water. It is shown that the directional wave spectrum can be approximated by the product of the frequency spectrum and a unimodal angular distribution with mean direction approximately equal to that of the wind. The normalized forms of the frequency spectrum show various forms lying between the Pierson-Moskowitz spectrum and the spectrum of laboratory wind wave which has a very sharp energy concentration near the spectral peak frequency. The form of the JONSWAP spectrum is very close to that of laboratory wind waves. The concentration of the spectral energy near the spectral peak frequency seems to decrease with increasing the dimensionless fetch and the spectral form finally approaches to the Pierson-Moskowitz spectrum which can be considered as the spectrum with the least concentration of the normalized spectral energy. However, the definite relation between the shape of the normalized spectrum and the dimensionless fetch has not been obtained. Concerning the angular distribution, it is shown that the shape of angular distribution of the single-peaked wave spectrum in a generating area can be approximated by the function G(6,f) = G'(s) | cos (6-6)/2 | ** proposed originally by Longuet=Higgins et al. (1963). Here G'(s) is a normalizing function, 6 is the mean direction of the spectral component, and s is a parameter which controls the concentration of the angular distribution function.

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 Analysis and Interpretation of Frequency–Wavenumber Spectra of Young Wind Waves

2015 ◽  
Vol 45 (10) ◽  
pp. 2484-2496 ◽  
Author(s):  
Fabien Leckler ◽  
Fabrice Ardhuin ◽  
Charles Peureux ◽  
Alvise Benetazzo ◽  
Filippo Bergamasco ◽  
...  
Keyword(s):  
Wind Wave ◽  
Wind Waves ◽  
Wave Spectrum ◽  
Peak Frequency ◽  
Bimodal Distribution ◽  
Second Order ◽  
The Black Sea ◽  
Full Spectrum ◽  
Directional Spectrum ◽  
Linear Waves

AbstractThe energy level and its directional distribution are key observations for understanding the energy balance in the wind-wave spectrum between wind-wave generation, nonlinear interactions, and dissipation. Here, properties of gravity waves are investigated from a fixed platform in the Black Sea, equipped with a stereo video system that resolves waves with frequency f up to 1.4 Hz and wavelengths from 0.6 to 11 m. One representative record is analyzed, corresponding to young wind waves with a peak frequency fp = 0.33 Hz and a wind speed of 13 m s−1. These measurements allow for a separation of the linear waves from the bound second-order harmonics. These harmonics are negligible for frequencies f up to 3 times fp but account for most of the energy at higher frequencies. The full spectrum is well described by a combination of linear components and the second-order spectrum. In the range 2fp to 4fp, the full frequency spectrum decays like f−5, which means a steeper decay of the linear spectrum. The directional spectrum exhibits a very pronounced bimodal distribution, with two peaks on either side of the wind direction, separated by 150° at 4fp. This large separation is associated with a significant amount of energy traveling in opposite directions and thus sources of underwater acoustic and seismic noise. The magnitude of these sources can be quantified by the overlap integral I(f), which is found to increase sharply from less than 0.01 at f = 2fp to 0.11 at f = 4fp and possibly up to 0.2 at f = 5fp, close to the 0.5π value proposed in previous studies.

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>

Covariate Extreme Value Analysis Using Wave Spectral Partitioning

2020 ◽  
Vol 37 (5) ◽  
pp. 873-888 ◽  
Author(s):  
Jesús Portilla-Yandún ◽  
Edwin Jácome
Keyword(s):  
Extreme Values ◽  
Wind Waves ◽  
Spectral Energy Distribution ◽  
Wave Spectrum ◽  
Wave Climate ◽  
Extreme Value ◽  
Extreme Value Analysis ◽  
Spectral Energy ◽  
Value Analysis ◽  
Spectral Partitioning

AbstractAn important requirement in extreme value analysis (EVA) is for the working variable to be identically distributed. However, this is typically not the case in wind waves, because energy components with different origins belong to separate data populations, with different statistical properties. Although this information is available in the wave spectrum, the working variable in EVA is typically the total significant wave height Hs, a parameter that does not contain information of the spectral energy distribution, and therefore does not fulfill this requirement. To gain insight in this aspect, we develop here a covariate EVA application based on spectral partitioning. We observe that in general the total Hs is inappropriate for EVA, leading to potential over- or underestimation of the projected extremes. This is illustrated with three representative cases under significantly different wave climate conditions. It is shown that the covariate analysis provides a meaningful understanding of the individual behavior of the wave components, in regard to the consequences for projecting extreme values.

scholarly journals Predicting Ocean Waves along the U.S. East Coast During Energetic Winter Storms: sensitivity to Whitecapping parameterizations

2018 ◽  
Author(s):  
Mohammad Nabi Allahdadi ◽  
Ruoying He ◽  
Vincent S. Neary
Keyword(s):  
East Coast ◽  
Wave Spectrum ◽  
Ocean Waves ◽  
Spectral Energy ◽  
Frequency Spectra ◽  
Winter Storms ◽  
Wave Parameters ◽  
Wind Input ◽  
Simulation Results ◽  
The U.S

Abstract. The performance of two methods for quantifying whitecapping dissipation incorporated in the SWAN wave model is evaluated for waves generated along and off the U.S. East Coast under energetic winter storms with a predominantly westerly wind. Parameterizing the whitecapping effect can be done using the Komen-type schemes, which are based on mean spectral parameters, or the saturation-based (SB) approach of van der Westhuysen (2007), which is based on local wave parameters and the saturation level concept of the wave spectrum (we use Komen and Westhuysen to denote these two approaches). Observations of wave parameters and frequency spectra at four NDBC buoys are used to evaluate simulation results. Model-data comparisons show that when using the default parameters in SWAN, both Komen and Westhuysen methods underestimate wave height. Simulations of mean wave period using the Komen method agree with observations, but those using the Westhuysen method are substantially lower. Examination of source terms shows that the Westhuysen method underestimates the total energy transferred into the wave action equations, especially in the lower frequency bands that contain higher spectral energy. Several causes for this underestimation are identified. The primary reason is the difference between the wave growth conditions along the East Coast during winter storms and the conditions used for the original whitecapping formula calibration. In addition, some deficiencies in simulation results are caused along the coast by the slanting fetch effect that adds low-frequency components to the 2-D wave spectra. These components cannot be simulated partly or entirely by available wind input formulations. Further, the effect of boundary layer instability that is not considered in the Komen and Westhuysen whitecapping wind input formulas may cause additional underestimation.

The directional spectrum of ocean waves, and processes of wave generation

1962 ◽  
Vol 265 (1322) ◽  
pp. 286-315 ◽  
Keyword(s):  
Pressure Fluctuations ◽  
Wave Spectrum ◽  
Ocean Waves ◽  
Wave Generation ◽  
Air Pressure ◽  
Sea Surface ◽  
Shear Instability ◽  
Main Stage ◽  
Sea Waves ◽  
Directional Spectrum

This paper describes some recent observations of the directional spectrum of sea waves and of air pressure fluctuations at the sea surface, and discusses their implications for theories of wave generation. The angular spread of the wave energy in the generating area is found to be comparable with the ‘resonance angle’ sec -1 ( σU/g ) ( σ = wave frequency, U = wind speed) but lies slightly below it in the middle range of frequencies. The best fit to the directional spectrum F ( σ, ɸ ) is shown to be a cosine-power law: F ( σ, ɸ ) ∝ cos 2s (1/2 ɸ ), where s decreases as σ in ­ creases. At the higher frequencies the total spectrum satisfies the equilibrium law: F ( σ ) ∝ σ -5 . The initial stages of wave generation are attributed to turbulence in the air stream, and the main stage of growth to the shear instability mechanism described by Miles. At the highest frequencies the form of the spectrum suggests that wave breaking plays a predominant part, as proposed by Phillips. The broadening of the angular distribution at the highest frequencies may also be due partly to third-order ‘resonant’ interactions among components of the wave spectrum . The air-pressure fluctuations are nearly in phase with the vertical displacement of the sea surface (over most of the frequency range) and are consistent with the shear-flow model proposed by Miles. The turbulent component of the air pressure is much smaller than was previously supposed.

scholarly journals A Two-Scale Approximation for Efficient Representation of Nonlinear Energy Transfers in a Wind Wave Spectrum. Part II: Application to Observed Wave Spectra

2009 ◽  
Vol 39 (10) ◽  
pp. 2451-2476 ◽  
Author(s):  
William Perrie ◽  
Donald T. Resio
Keyword(s):  
Wind Waves ◽  
Spectral Energy Distribution ◽  
Wave Spectrum ◽  
Field Research ◽  
New Method ◽  
Spectral Energy ◽  
Net Energy ◽  
Wave Spectra ◽  
Spectral Evolution ◽  
Long Distance

Abstract In Part I of this series, a new method for estimating nonlinear transfer rates in wind waves, based on a two-scale approximation (TSA) to the full Boltzmann integral (FBI) for quadruplet wave–wave interactions, was presented, and this new method was tested for idealized spectral data. Here, the focus is on comparisons of the TSA and the discrete interaction approximation (DIA) with the FBI for observed wave spectra from field measurements. Observed wave spectra are taken from a wave gauge array in Currituck Sound and a directional waverider off the coast near the Field Research Facility at Duck, North Carolina. Results show that the TSA compares much more favorably to the FBI than does the DIA, even for cases in which the parametric component of the formulation does not capture the spectral energy distribution very well. These results remain valid for the TSA estimates when the FBI results are significantly affected by the directional distribution of energy. It is also shown that although nonlinear transfers are substantially weaker in swell portions of the spectrum these interactions contribute significantly to the spectral evolution and net energy balance in long-distance swell propagation.

scholarly journals Numerical simulation of wave spectrum during a typhoon

2021 ◽  
Vol 290 ◽  
pp. 02019
Author(s):  
Congying Kong ◽  
Hao Liu
Keyword(s):  
Growth Process ◽  
Wind Waves ◽  
Wave Spectrum ◽  
Wave Model ◽  
Third Generation ◽  
Wavewatch Iii ◽  
Directional Spectrum ◽  
The Third ◽  
Sea Area ◽  
The Relationship

The third-generation wave model WAVEWATCH-III was used to numerically simulate the wave under the influence of a typhoon in the coastal area of China. The wave spectrum at the buoy point was output, and the characteristics of the wave spectrum were analyzed. The change of the wave spectrum during the typhoon process reflected the growth process of typhoon formation, development and extinction. The relationship between the wave spectrum and the wind direction was intuitively shown by the directional spectrum, indicating the coexistence of wind waves and swells in the sea area during the typhoon process.

scholarly journals FIELD STUDIES OF RUN-UP ON DISSIPATIVE BEACHES

1984 ◽  
Vol 1 (19) ◽  
pp. 28 ◽  
Author(s):  
Christopher T. Carlson
Keyword(s):  
Time Series ◽  
Incident Wave ◽  
Wind Waves ◽  
Peak Frequency ◽  
Distribution Functions ◽  
Cumulative Distribution ◽  
Statistical Hypothesis ◽  
Spectral Energy ◽  
Run Up ◽  
Incident Waves

Field measurements of narrow-band incident wind waves and the resulting run-up were made photographically at two different natural sand beaches along San Francisco Bay. The run-up spectra derived from the field-measured time series show some energy at the incident-wave peak frequency, with the predominant run-up spectral energy concentrated in frequency bands below the incident-wave peak frequency. Observations of the swash time series recorded at both beaches indicate that the low-frequency run-up is generated on the beach face by the interaction between the run-up and backwash during the swash cycle. Coherence analyses indicate that the offshore incident waves and run-up on the beach are not linearly correlated but that the run-up is correlated in the alongshore direction. The slopes of the log-log run-up spectra computed over the frequency band of the incident waves are all approximately -3. Statistical hypothesis tests were used to compare the empirical run-up cumulative distribution functions with both normal and Rayleigh distribution functions.

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