A note on the bimodal directional spreading of fetch‐limited wind waves
TL;DR: In this article, the authors measured the directional spectra of fetch-limited wind waves and found that the spreading functions for these spectra are unimodal and narrowest in the region of the spectral peak frequency.
Abstract: Measurements of the directional spectra of fetch-limited wind waves are presented. The directional spreading functions for these spectra are unimodal and narrowest in the region of the spectral peak frequency. Consistent with previous measurements, the spreading broadens for frequencies just above and below the spectral peak frequency. At frequencies of approximately twice the peak frequency, however, the unimodal spreading becomes bimodal, and more wave energy propagates at an angle to the wind than in the wind direction. The bimodal sidelobes continue to separate with increasing frequency and become larger in magnitude. Results obtained with a numerical model with a full solution to the nonlinear terms indicate that the bimodal structure is maintained by directional transfer of energy through nonlinear wave-wave interactions.
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01 Feb 2010TL;DR: The SWAN wave model as discussed by the authors is a wave model based on linear wave theory (SWAN) for oceanic and coastal waters, and it has been shown to be effective in detecting ocean waves.
Abstract: 1. Introduction 2. Observation techniques 3. Description of ocean waves 4. Statistics 5. Linear wave theory (oceanic waters) 6. Waves in oceanic waters 7. Linear wave theory (coastal waters) 8. Waves in coastal waters 9. The SWAN wave model Appendices References Index.
874 citations
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01 Jan 2004TL;DR: The Interaction of Ocean Waves and Wind describes the two-way interaction between wind and ocean waves and shows how ocean waves affect weather forecasting on timescales of 5 to 90 days as discussed by the authors.
Abstract: This book was published in 2004. The Interaction of Ocean Waves and Wind describes in detail the two-way interaction between wind and ocean waves and shows how ocean waves affect weather forecasting on timescales of 5 to 90 days. Winds generate ocean waves, but at the same time airflow is modified due to the loss of energy and momentum to the waves; thus, momentum loss from the atmosphere to the ocean depends on the state of the waves. This volume discusses ocean wave evolution according to the energy balance equation. An extensive overview of nonlinear transfer is given, and as a by-product the role of four-wave interactions in the generation of extreme events, such as freak waves, is discussed. Effects on ocean circulation are described. Coupled ocean-wave, atmosphere modelling gives improved weather and wave forecasts. This volume will interest ocean wave modellers, physicists and applied mathematicians, and engineers interested in shipping and coastal protection.
494 citations
TL;DR: In this paper, the results of a fetch limited wind wave growth experiment in water of finite depth are presented, which involved measurements of wind wave spectra, wind speed and direction at eight stations along the fetch.
290 citations
Cites background from "A note on the bimodal directional s..."
...As mentioned in Section 3, the primary instrumentation used for the measurement of the water surface elevation were surface piercing Zwarts poles ( Young et al., 1995 ) (also known as transmission line wave gauges)....
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TL;DR: In this article, the wave directional spectrum of fetch-limited sea states is estimated from measurements made with a heave-pitch-roll buoy at the Maui location off the west coast of New Zealand.
Abstract: Estimates of the wave directional spectrum of fetch-limited sea states are made from measurements made with a heave–pitch–roll buoy at the Maui location off the west coast of New Zealand. The fetch-limited sea states have significant wave heights between 0.5 and 4.5 m and are observed during persistent southeast wind events, which have a well-defined fetch of 200 km. The integrated properties of the estimated angular spreading distributions are in general agreement with those observed in previous studies. However, the angular distributions estimated for the Maui location are bimodal at frequencies greater than the spectral peak frequency. This result for deep water ocean waves is in contrast to the generally accepted unimodal angular distribution for wind seas, but it supports recently reported measurements of the angular distribution of fetch-limited waves in Lake George, Australia. Parametric relationships that describe the characteristics of the bimodal distributions are derived, and the impor...
175 citations
TL;DR: The wind-sea part of the wave spectrum conforms to established growth curves for significant wave height and peak period, except at inner-shelf stations where a large along-shore windsea component was observed.
Abstract: Wind-sea generation was observed during two experiments off the coast of North Carolina. One event with offshore winds of 9–11 m s−1 directed 20° from shore normal was observed with eight directional stations recording simultaneously and spanning a fetch from 4 to 83 km. An opposing swell of 1-m height and 10-s period was also present. The wind-sea part of the wave spectrum conforms to established growth curves for significant wave height and peak period, except at inner-shelf stations where a large alongshore wind-sea component was observed. At these short fetches, the mean wave direction θm was observed to change abruptly across the wind-sea spectral peak, from alongshore at lower frequencies to downwind at higher frequencies. Waves from another event with offshore winds of 6–14 m s−1 directed 20°–30° from shore normal were observed with two instrument arrays. A significant amount of low-frequency wave energy was observed to propagate alongshore from the region where the wind was strongest. The...
139 citations
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01 Jan 1973
TL;DR: In this article, wave spectra were measured along a profile extending 160 kilometers into the North Sea westward from Sylt for a period of two weeks in 1968 and 1969, with particular emphasis on wave growth under stationary offshore wind conditions and the attenuation of swell in water of finite depth.
Abstract: "Wave spectra were measured along a profile extending 160 kilometers into the North Sea westward from Sylt for a period often weeks in 1968 and 1969. During the main experiment in July 1969, thirteen wave stations were in operation, of which six stations continued measurements into the first two weeks of August. A smaller pilot experiment was carried out in September 1968. Currents, tides, air-sea temperature differences and turbulence in the atmospheric boundary layer were also measured. The goal of the experiment (described in Part 1) was to determine the structure of the source function governing the energy balance of the wave spectrum, with particular emphasis on wave growth under stationary offshore wind conditions (Part 2) and the attenuation of swell in water of finite depth (Part 3). The source functions of wave spectra generated by offshore winds exhibit a characteristic plus-minus signature associated with the shift of the sharp spectral peak towards lower frequencies. The two-lobed distribution of the source function can be explained quantitatively by the nonlinear transfer due to resonant wave-wave interactions (second order Bragg scattering). The evolution of a pronounced peak and its shift towards lower frequencies can also be understood as a selfstabilizing feature of this process. For small fetches, the principal energy balance is between the input by wind in the central region of the spectrum and the nonlinear transfer of energy away from this region to short waves, where it is dissipated, and to longer waves. Most of the wave growth on the forward face of the spectrum can be attributed to the nonlinear transfer to longer waves. For short fetches, approximately (80 ± 20) % of the momentum transferred across the air/sea interface enters the wave field, in agreement with Dobson's direct measurements of the work done on the waves by surface pressures. About 80-90 % of the wave-induced momentum flux passes into currents via the nonlinear transfer to short waves and subsequent dissipation; the rest remains in the wave field and is advected away. At larger fetches the interpretation of the energy balance becomes more ambiguous on account of the unknown dissipation in the low-frequency part of the spectrum. Zero dissipation in this frequency range yields a minimal atmospheric momentum flux into the wave field of the order of (10 to 40) % of the total momentum transfer across the air-sea interface -- but ratios up to 100 % are conceivable if dissipation is important. In general, the ratios (as inferred from the nonlinear energy transfer) lie within these limits over a wide (five-decade) range of fetches encompassing both wave-tank and the present field data, suggesting that the scales of the spectrum continually adjust such that the wave-wave interactions just balance the energy input from the wind. This may explain, among other features, the observed decrease of Phillips' "constant" with fetch. The decay rates determined for incoming swell varied considerably, but energy attenuation factors of two along the length of the profile were typical. This is in order of magnitude agreement with expected damping rates due to bottom friction. However, the strong tidal modulation predicted by theory for the case of a quadratic bottom friction law was not observed. Adverse winds did not affect the decay rate. Computations also rule out wave-wave interactions or dissipation due to turbulence outside the bottom boundary layer as effective mechanisms of swell attenuation. We conclude that either the generally accepted friction law needs to be significantly modified or that some other mechanism, such as scattering by bottom irregularities, is the cause of the attenuation. The dispersion characteristics of the swells indicated rather nearby origins, for which the classical (i event model was generally inapplicable. A strong Doppler modulation by tidal currents was also observed.
3,264 citations
TL;DR: In this article, the energy flux in a finite-depth gravity-wave spectrum resulting from weak non-linear couplings between the spectral components is evaluated by means of a perturbation method.
Abstract: The energy flux in a finite-depth gravity-wave spectrum resulting from weak non-linear couplings between the spectral components is evaluated by means of a perturbation method. The fifth-order analysis yields a fourth-order effect comparable in magnitude to the generating and dissipating processes in wind-generated seas. The energy flux favours equidistribution of energy and vanishes in the limiting case of a white, isotropic spectrum. The influence on the equilibrium structure of fully developed wave spectra and on other phenomena in random seas is discussed briefly.
1,220 citations
26 Sep 1985-Philosophical transactions - Royal Society. Mathematical, physical and engineering sciences
TL;DR: In this paper, the directional spectrum of wind-generated waves on deep water is determined by using a modification of Barber's (1963) method, and the results reveal that the frequency spectrum in the rear face is inversely proportional to the fourth power of the frequency.
Abstract: From observations of wind and of water surface elevation at 14 wave staffs in an array in Lake Ontario and in a large laboratory tank, the directional spectrum of wind-generated waves on deep water is determined by using a modification of Barber's (1963) method. Systematic investigations reveal the following: (a) the frequency spectrum in the rear face is inversely proportional to the fourth power of the frequency $\omega $, with the equilibrium range parameter and the peak enhancement factor clearly dependent on the ratio of wind speed to peak wave speed; (b) the angular spreading $\theta $ of the wave energy is of the form sech$^{2}$ ($\beta \theta $), where $\beta $ is a function of frequency relative to the peak; (c) depending on the gradient of the fetch, the direction of the waves at the spectral peak may differ from the mean wind direction by up to 50 degrees, but this observed difference is predictable by a similarity analysis; (d) under conditions of strong wind forcing, significant effects on the phase velocity caused by amplitude dispersion and the presence of bound harmonics are clearly observed and are in accordance with the Stokes theory, whereas (e) the waves under natural wind conditions show amplitude dispersion, but bound harmonics are too weak to be detected among the background of free waves.
983 citations
TL;DR: In this paper, the authors consider the energy transfer equation for well-developed ocean waves under the influence of wind, and study the conditions for the existence of an equilibrium solution in which wind input, wave-wave interaction and dissipation balance each other.
Abstract: We consider the energy transfer equation for well-developed ocean waves under the influence of wind, and study the conditions for the existence of an equilibrium solution in which wind input, wave-wave interaction and dissipation balance each other. For the wind input we take the parameterization proposed by Snyder and others, which was based on their measurements in the Bight of Abaco and which agrees with Miles's theory. The wave-wave interaction is computed with an algorithm given recently by S. Hasselmann and others. The dissipation is less well-known, but we will make the general assumption that it is quasi-linear in the wave spectrum with a factor coefficient depending only on frequency and integral spectral parameters. In the first part of this paper we investigate whether the assumption that the equilibrium spectrum exits and is given by the Pierson-Moskowitz spectrum with a standard type of angular distribution leads to a reasonable dissipation function. We find that this is not the case...
982 citations
TL;DR: In this article, it was shown that the directional wave spectrum can be approximated by the product of the frequencyspectrum and a unimodal angular distribution with mean direction approximately equal to that of the wind, and that various forms of frequency spectra exist, even in relatively simple wave systems, dependingon their generating conditions.
Abstract: Analysis of the directional spectra of typical sets of surface wave data obtained in the open sea as well asa bay using a cloverleaf buoy system are reported. It is shown that the directional wave spectrum can be approximated by the product of the frequencyspectrum and a unimodal angular distribution with mean direction approximately equal to that of thewind, and that various forms of frequency spectra exist, even in relatively simple wave systems, dependingon their generating conditions. Ocean waves at fairly short dimensionless fetches show spectral forms withvery narrow spectral width, which are similar to those of laboratory wind waves. On the other hand, thespectral forms for ocean waves at very long dimensionless fetches are quite similar to the Pierson-Moskowitzspectra, which are considered, within our present data, to be the wave spectra with the largest spectral width.Finally, there exist many ocean waves at moderate dimensionless fetches, which show spectral forms with interminate spect...
551 citations