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Ali Tamizi
and
Ian R. Young

Abstract

The spatial structure of both the wind and wave fields within tropical cyclones is investigated using two large databases. The first of these was compiled from global overpasses of tropical cyclones by satellite altimeters. The second dataset consists of an extensive collection of North American buoy measurements during the passage of tropical cyclones (hurricanes). The combined datasets confirm the vortex structure of the tropical cyclone wind field with the strongest winds to the right (Northern Hemisphere) of the storm. The wave field largely mirrors the wind field but with greater right–left asymmetry that results from the extended fetch to the right of the translating tropical cyclone. The extensive in situ buoy database confirms previous studies indicating that the one-dimensional spectra are generally unimodal. The directional spectra are, however, directionally skewed, consisting of remotely generated waves radiating out from the center of the storm and locally generated wind sea. The one-dimensional wave spectra have many similarities to fetch-limited cases, although for a given peak frequency the spectra contain less energy than for a fetch-limited case. This result is consistent with the fact that much of the wave field is dominated by remotely generated waves.

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Ian R. Young
and
Alexander V. Babanin

Abstract

This paper considers an experimental attempt to estimate the spectral distribution of the dissipation due to breaking of dominant waves. A field wave record with an approximately 50% dominant-breaking rate was analyzed. Segments of the record, comprising sequences of breaking waves, were used to obtain the “breaking spectrum,” and segments of nonbreaking waves were used to obtain the “nonbreaking spectrum.” The clear visible difference between the two spectra was attributed to the dissipation due to breaking. This assumption was supported by independent measurements of total dissipation of kinetic energy in the water column at the measurement location. It is shown that the dominant breaking causes energy dissipation throughout the entire spectrum at scales smaller than the spectral peak waves. The dissipation rate at each frequency is linear in terms of the wave spectral density at that frequency, with a correction for the directional spectral width. A formulation for the spectral dissipation function able to accommodate this effect is suggested. Directional spectra of the breaking and nonbreaking waves are also considered. It is shown that directional dissipation rates at oblique angles are higher than the dissipation in the main wave propagation direction.

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Ian R. Young
,
Emmanuel Fontaine
,
Qingxiang Liu
, and
Alexander V. Babanin

Abstract

The wave climate of the Southern Ocean is investigated using a combined dataset from 33 years of altimeter data, in situ buoy measurements at five locations, and numerical wave model hindcasts. The analysis defines the seasonal variation in wind speed and significant wave height, as well as wind speed and significant wave height for a 1-in-100-year return period. The buoy data include an individual wave with a trough to crest height of 26.4 m and suggest that waves in excess of 30 m would occur in the region. The extremely long fetches, persistent westerly winds, and procession of low pressure systems that traverse the region generate wave spectra that are unique. These spectra are unimodal but with peak frequencies that propagate much faster than the local wind. This situation results in a unique energy balance in which waves at the spectra peak grow as a result of nonlinear transfer without any input from the local wind.

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Michael L. Banner
,
Alexander V. Babanin
, and
Ian R. Young

Abstract

The breaking probability is investigated for the dominant surface waves observed in three geographically diverse natural bodies of water: Lake Washington, the Black Sea, and the Southern Ocean. The breaking probability is taken as the average number of breaking waves passing a fixed point per wave period. The data covered a particularly wide range of dominant wavelengths (3–300 m) and wind speeds (5–20 m s−1). In all cases, the wave breaking events were detected visually. It was found that the traditional approach of relating breaking probability to the wind speed or wave age provided reasonable correlations within individual datasets, but when the diverse datasets are combined, these correlations are significantly degraded.

Motivated by the results of recent computational studies of breaking onset in wave groups, the authors investigated the hypothesis that nonlinear hydrodynamic processes associated with wave groups are more fundamental to the process of breaking than previously advocated aerodynamic properties, such as the wind speed or wave age. Further, these computational studies suggest that the significant wave steepness is an appropriate parameter for characterizing the nonlinear group behavior.

Based on this approach, analysis of the data revealed that the probability of dominant wave breaking is strongly correlated with the significant wave steepness for the broad range of wave conditions investigated. Of particular interest is a threshold of this parameter below which negligible dominant wave breaking occurs. Once this threshold is exceeded, a near-quadratic dependence of the breaking probability on the significant wave steepness was observed, with a correlation coefficient of 0.78. The inclusion of parameters representing the secondary influence of wind forcing and background current shear improved the correlation only marginally to 0.81.

The applicability of the breaking probability dependence found for the dominant waves was investigated for higher-frequency bins up to twice the spectral peak frequency f p . The Black Sea data were used for this analysis, in which shorter breaking wave statistics were also measured. It was found that the maximum of the composite breaking frequency distribution gradually shifts from about 1.6f p for lower values of the peak steepness parameter to f p for higher values of this parameter. The breaking probability in a comparable higher frequency band has a similar dependence on significant steepness to that found for the dominant waves.

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Ali Tamizi
,
Jose-Henrique Alves
, and
Ian R. Young

Abstract

A series of numerical experiments with the WAVEWATCH III spectral wave model are used to investigate the physics of wave evolution in tropical cyclones. Buoy observations show that tropical cyclone wave spectra are directionally skewed with a continuum of energy between locally generated wind-sea and remotely generated waves. These systems are often separated by more than 90°. The model spectra are consistent with the observed buoy data and are shown to be governed by nonlinear wave–wave interactions that result in a cascade of energy from the wind-sea to the remotely generated spectral peak. The peak waves act in a “parasitic” manner taking energy from the wind-sea to maintain their growth. The critical role of nonlinear processes explains why one-dimensional tropical cyclone spectra have characteristics very similar to fetch-limited waves, even though the generation system is far more complex. The results also provide strong validation of the critical role nonlinear interactions play in wind-wave evolution.

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Cesar B. Rocha
,
William R. Young
, and
Ian Grooms

Abstract

This study investigates the representation of solutions of the three-dimensional quasigeostrophic (QG) equations using Galerkin series with standard vertical modes, with particular attention to the incorporation of active surface buoyancy dynamics. This study extends two existing Galerkin approaches (A and B) and develops a new Galerkin approximation (C). Approximation A, due to Flierl, represents the streamfunction as a truncated Galerkin series and defines the potential vorticity (PV) that satisfies the inversion problem exactly. Approximation B, due to Tulloch and Smith, represents the PV as a truncated Galerkin series and calculates the streamfunction that satisfies the inversion problem exactly. Approximation C, the true Galerkin approximation for the QG equations, represents both streamfunction and PV as truncated Galerkin series but does not satisfy the inversion equation exactly. The three approximations are fundamentally different unless the boundaries are isopycnal surfaces. The authors discuss the advantages and limitations of approximations A, B, and C in terms of mathematical rigor and conservation laws and illustrate their relative efficiency by solving linear stability problems with nonzero surface buoyancy. With moderate number of modes, B and C have superior accuracy than A at high wavenumbers. Because B lacks the conservation of energy, this study recommends approximation C for constructing solutions to the surface active QG equations using the Galerkin series with standard vertical modes.

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Mark A. Donelan
,
Alexander V. Babanin
,
Ian R. Young
, and
Michael L. Banner

Abstract

Nearly all of the momentum transferred from wind to waves comes about through wave-induced pressure acting on the slopes of waves: known as form drag. Direct field measurements of the wave-induced pressure in airflow over water waves are difficult and consequently rare. Those that have been reported are for deep water conditions and conditions in which the level of forcing, measured by the ratio of wind speed to the speed of the dominant (spectral peak) waves, is quite weak, U 10/cp < 3. The data reported here were obtained over a large shallow lake during the Australian Shallow Water Experiment (AUSWEX). The propagation speeds of the dominant waves were limited by depth and the waves were correspondingly steep. This wider range of forcing and concomitant wave steepness revealed some new aspects of the rate of wave amplification by wind, the so-called wind input source function, in the energy balance equation for wind-driven water waves. It was found that the exponential growth rate parameter (fractional energy increase per radian) depended on the slope of the waves, ak, vanishing as ak → 0. For very strong forcing a condition of “full separation” occurs, where the airflow detaches from the crests and reattaches on the windward face leaving a separation zone over the leeward face and the troughs. In a sense, the outer flow does not “see” the troughs and the resulting wave-induced pressure perturbation is much reduced, leading to a reduction in the wind input source function relative to that obtained by extrapolation from more benign conditions. The source function parameterized on wave steepness and degree of separation is shown to be in agreement with previous field and laboratory data obtained in conditions of much weaker forcing and wave steepness. The strongly forced steady-state conditions of AUSWEX have enabled the authors to define a generalized wind input source function that is suitable for a wide range of conditions.

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Alexander V. Babanin
,
Michael L. Banner
,
Ian R. Young
, and
Mark A. Donelan

Abstract

This is the third in a series of papers describing wave-follower observations of the aerodynamic coupling between wind and waves on a large shallow lake during the Australian Shallow Water Experiment (AUSWEX). It focuses on the long-standing problem of the aerodynamic consequences of wave breaking on the wind–wave coupling. Direct field measurements are reported of the influence of wave breaking on the wave-induced pressure in the airflow over water waves, and hence the energy flux to the waves. The level of forcing, measured by the ratio of wind speed to the speed of the dominant (spectral peak) waves, covered the range of 3–7. The propagation speeds of the dominant waves were limited by the water depth and the waves were correspondingly steep. These measurements allowed an assessment of the magnitude of any breaking-induced enhancement operative for these field conditions and provided a basis for parameterizing the effect. Overall, appreciable levels of wave breaking occurred for the strong wind forcing conditions that prevailed during the observational period. Associated with these breaking wave events, a significant phase shift is observed in the local wave-coherent surface pressure. This produced an enhanced wave-coherent energy flux from the wind to the waves with a mean value of 2 times the corresponding energy flux to the nonbreaking waves. It is proposed that the breaking-induced enhancement of the wind input to the waves can be parameterized by the sum of the nonbreaking input and the contribution due to the breaking probability.

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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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Qingxiang Liu
,
W. Erick Rogers
,
Alexander V. Babanin
,
Ian R. Young
,
Leonel Romero
,
Stefan Zieger
,
Fangli Qiao
, and
Changlong Guan

Abstract

The observation-based source terms available in the third-generation wave model WAVEWATCH III (i.e., the ST6 package for parameterizations of wind input, wave breaking, and swell dissipation terms) are recalibrated and verified against a series of academic and realistic simulations, including the fetch/duration-limited test, a Lake Michigan hindcast, and a 1-yr global hindcast. The updated ST6 not only performs well in predicting commonly used bulk wave parameters (e.g., significant wave height and wave period) but also yields a clearly improved estimation of high-frequency energy level (in terms of saturation spectrum and mean square slope). In the duration-limited test, we investigate the modeled wave spectrum in a detailed way by introducing spectral metrics for the tail and the peak of the omnidirectional wave spectrum and for the directionality of the two-dimensional frequency–direction spectrum. The omnidirectional frequency spectrum E(f) from the recalibrated ST6 shows a clear transition behavior from a power law of approximately f −4 to a power law of about f −5, comparable to previous field studies. Different solvers for nonlinear wave interactions are applied with ST6, including the Discrete Interaction Approximation (DIA), the more expensive Generalized Multiple DIA (GMD), and the very expensive exact solutions [using the Webb–Resio–Tracy method (WRT)]. The GMD-simulated E(f) is in excellent agreement with that from WRT. Nonetheless, we find the peak of E(f) modeled by the GMD and WRT appears too narrow. It is also shown that in the 1-yr global hindcast, the DIA-based model overestimates the low-frequency wave energy (wave period T > 16 s) by 90%. Such model errors are reduced significantly by the GMD to ~20%.

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