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M. L. Banner and I. R. Young

Abstract

This study examines the performance of a state-of-the-art spectral wind wave model that uses a full solution to the nonlinear interaction source term. The situation investigated here is fetch-limited wind wave evolution, for which a significant observational database exists. The authors consider both the evolutionary characteristics such as the predicted development of wave energy and peak wave frequency with fetch, as well as the predicted local features of the directional wavenumber spectrum: the spectral shape of the dominant wave direction slice, together with the directional spreading function. In view of the customary practice of constraining the shape of the spectral tail region, this investigation required relaxing the constrained tail assumption. This has led to new insight into the dynamic role of the spectral tail region.

The calculations have focused on the influence of two of the source terms in the spectral evolution (radiative transfer) equation for the energy density spectrum—those due to wind input and to dissipation predominantly through wave breaking. While the form of the wind input source term exerts some influence, the major impact arises from the dissipation source term, for which the authors explore a range of variants of the quasi-linear form proposed by Hasselmann. Due to the nonlinear coupling of spectral components through the wave–wave interaction term, it is only possible to obtain a detailed physical understanding of spectral evolution through such numerical experiments.

The results point to basic shortcomings in the present source terms. These lead to predicted local spectral properties and fetch evolution characteristics that differ significantly from the available observations. It is concluded that further refinement of the dissipation source term is required to improve modeling capabilities for wind sea evolution.

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Jose Henrique G. M. Alves and Michael L. Banner

Abstract

A new formulation of the spectral dissipation source term S ds for wind-wave modeling applications is investigated. This new form of S ds is based on a threshold behavior of deep-water wave-breaking onset associated with nonlinear wave-group modulation. It is expressed in terms of the azimuth-integrated spectral saturation, resulting in a nonlinear dependence of dissipation rates on the local wave spectrum. Validation of the saturation-based S ds is made against wave field parameters derived from observations of fetch-limited wind-wave evolution. Simulations of fetch-limited growth are made with a numerical model featuring an exact nonlinear form of the wave–wave-interactions source term S nl. For reference, the performance of this saturation-based S ds is compared with the performance of the wave-dissipation source-term parameterization prescribed for the Wave Modeling Project (WAM) wind-wave model. Calculations of integral spectral parameters using the saturation-based model for S ds agree closely with fetch-limited observations. It is also shown that the saturation-based S ds can be readily adjusted to accommodate several commonly used parameterizations of the wind input source term S in. Also, this new form of S ds provides greater flexibility in controlling the shape of the wave spectrum in the short gravity-wave region.

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Michael L. Banner, Johannes R. Gemmrich, and David M. Farmer

Abstract

Recent numerical model studies of nonlinear deep water wave group evolution suggest that wave breaking onset is associated primarily with a threshold behavior linked to the nonlinear wave group hydrodynamics. Motivated by these findings, a recently published probability analysis of observed dominant ocean wind wave breaking events reported a threshold behavior using the significant wave steepness as a measure of the mean nonlinearity of these waves. The present study investigates whether a similar threshold dependence in terms of an appropriate spectral measure of wave steepness, the spectral saturation, may be found for the breaking probability of shorter wind waves above the spectral peak. Extensive data records of open ocean whitecap breaking wave occurrences for wind speeds up to 18 m s−1 were analyzed for breaking probability dependence on spectral saturation in spectral bands with center frequencies ranging from 1 to 2.48 times the spectral peak frequency. Results are based on the measured ratio of passage rates past a fixed point of breaking crests to total crests for different wave scales. An extension of the zero-crossing method for counting wave crests was developed. Using this method the authors found that in any spectral subrange within the observed range of frequencies, a strong correlation exists between breaking probability and an appropriate mean spectral steepness parameter and that this correlation is characterized by a robust threshold behavior, just as was reported previously for the spectral peak waves. Further, to offset the influence of increasing directional spreading of the waves above the spectral peak frequency, an empirical directional spreading function was used to normalize the azimuth-integrated spectral saturation. Under this normalization, the spectral saturation threshold for breaking onset appears to have a common level over the frequency range investigated. This study also examined the correlation of breaking probability with spectral peak wave age. The low correlation found for all spectral ranges investigated suggests that nonlinear wave hydrodynamics are more important than wind forcing for the breaking of these wind waves.

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Jose Henrique G. M. Alves, Michael L. Banner, and Ian R. Young

Abstract

The time-honored topic of fully developed wind seas pioneered by Pierson and Moskowitz is revisited to review the asymptotic evolution limits of integral spectral parameters used by the modeling community in the validation of wind-wave models. Discrepancies are investigated between benchmark asymptotic limits obtained by scaling integral spectral parameters using alternative wind speeds. Using state-of-the-art wind and wave modeling technology, uncertainties in the Pierson–Moskowitz limits due to inhomogeneities in the wind fields and contamination of the original data by crossing seas and swells are also investigated. The resulting reanalyzed database is used to investigate the optimal scaling wind parameter and to refine the levels of the full-development asymptotes of nondimensional integral wave spectral parameters used by the wind-wave modeling community. The results are also discussed in relation to recent advances in quantifying wave-breaking probability of wind seas. The results show that the parameterization of integral spectral parameters and the scaling of nondimensional asymptotes as a function of U 10 yields relations consistent with similarity theory. On the other hand, expressing integral spectral parameters and scaling nondimensional asymptotes as a function of u∗ or alternative proposed scaling wind speeds yields relations that do not conform to similarity requirements as convincingly. The reanalyzed spectra are used to investigate parameter values and shapes of analytical functions representing fully developed spectra. These results support an analytical form with a spectral tail proportional to f −4.

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E. J. Walsh, C. W. Wright, M. L. Banner, D. C. Vandemark, B. Chapron, J. Jensen, and S. Lee

Abstract

During the Southern Ocean Waves Experiment (SOWEX), registered ocean wave topography and backscattered power data at Ka band (36 GHz) were collected with the NASA Scanning Radar Altimeter (SRA) off the coast of Tasmania under a wide range of wind and sea conditions, from quiescent to gale-force winds with 9-m significant wave height. Collection altitude varied from 35 m to over 1 km, allowing determination of the sea surface mean square slope (mss), the directional wave spectrum, and the detailed variation of backscattered power with incidence angle, which deviated from a simple Gaussian scattering model. The non-Gaussian characteristics of the backscatter increased systematically with the mss, suggesting that a global model to characterize Ka-band radar backscatter from the sea surface within 25° of nadir might be possible.

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