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Dmitry Chalikov and Alexander V. Babanin

Abstract

Results of numerical investigations, based on full dynamic equations, are presented for wave breaking in a one-dimensional environment with a wave spectrum. The breaking is defined as a process of irreversible collapse of an individual wave in physical space, and the incipient breaker is a wave that reached a dynamic condition of the limiting stability where the collapse has not started yet but is inevitable. The main attention is paid to documenting the evolution of different wave characteristics before the breaking commences. It is shown that the breaking is a localized process that rapidly develops in space and time. No single characteristic, such as wave steepness, wave height, and asymmetry, can serve as a predictor of the incipient breaking. The process of breaking is intermittent; it happens spontaneously and is individually unpredictable. The evolution of geometric, kinematic, and dynamic characteristics of the breaking wave describes the process of breaking itself rather than indicating an imminent breaking. It is shown that the criterion of breaking, valid for the breaking due to modulation instability in one-dimensional waves trains, is not universal if applied to the conditions of spectral environment. In this context, the development of algorithms for parameterization of breaking for wave prediction models and for direct wave simulations is more important.

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Alexander V. Babanin and AndréJ. van der Westhuysen

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The dissipation term is one of the three most important source functions of the radiative transfer equation employed by all spectral wave models to predict the wave spectrum. In this paper, the issue of physics of such dissipation functions is discussed. It is argued that the physics presently utilized in the models do not adequately describe currently known features of the wave dissipation process, and the dissipation functions, to a great extent, remain a residual tuning term in spite of important experimental progress in wave breaking studies. A recently suggested “saturation-based” dissipation function and its connections with the experimental physics are analyzed in detail.

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Alexander V. Babanin and Brian K. Haus

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This paper is dedicated to wave-induced turbulence unrelated to wave breaking. The existence of such turbulence has been foreshadowed in a number of experimental, theoretical, and numerical studies. The current study presents direct measurements of this turbulence. The laboratory experiment was conducted by means of particle image velocimetry, which allowed estimates of wavenumber velocity spectra beneath monochromatic nonbreaking unforced waves. Observed spectra intermittently exhibited the Kolmogorov interval associated with the presence of isotropic turbulence. The magnitudes of the energy dissipation rates due to this turbulence in the particular case of 1.5-Hz deep-water waves were quantified as a function of the surface wave amplitude. The presence of such turbulence, previously not accounted for, can affect the physics of the wave energy dissipation, the subsurface boundary layer, and the ocean mixing in a significant way.

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Ian R. Young and Alexander V. Babanin

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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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Haoyu Jiang, Alexander V. Babanin, and Ge Chen

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The arrival time of ocean swells is an important factor for offshore and coastal engineering and naval and recreational activities, which can also be used in evaluating the numerical wave model. Using the continuity and pattern of wave heights during the same swell event, a methodology is developed for identifying swell events and verifying swell arrival time in models from buoy data. The swell arrival time in a WAVEWATCH III hindcast database is validated with in situ measurements. The results indicate that the model has a good agreement with the observations but usually predicts an early arrival of swell, about 4 h on average. A histogram shows that about one-quarter of swell events arrive early and three-quarters late by comparison with the model. Many processes that may be responsible for the arrival time errors are discussed, but at this stage it is not possible to distinguish between them from the available data.

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Alexander V. Babanin and Yury P. Soloviev

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The variability of frequency spectra of waves is considered; for example, the dependencies of integral and spectral parameters of waves on wave-development factors and the interrelationships of the parameters are examined. Also studied is the transformation of the frequency spectrum shape in the course of its development, as well as the transition from the spectrum of developing waves to the spectrum of fully developed waves. Data were obtained in situ with common methods during a long-term program in the Black Sea.

The variability of the spectrum of developing waves, as a function of the stage of wave development, is described on the basis of field data using estimates of parameters for the spectrum form of the JONSWAP type. A novel approximation of the equilibrium interval level dependence on the dimensionless peak frequency m is obtained, which includes periods of stable and changeable behavior of the spectrum level. Transformation of the spectrum of wind-generated waves related to the development of the wave field in terms of the JONSWAP spectrum form is obtained. Continuous transition to the Pierson–Moskowitz spectrum is described. An approximation of the dependence of the enhancement coeffiecient γ on wave development stage m is suggested, which describes continuous variation of the coefficient γ for all wave ages. Self-similarity of the spectrum of developing waves is not observed.

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Alexander V. Babanin, Jason McConochie, and Dmitry Chalikov

Abstract

The concept of a constant-flux layer is usually employed for vertical profiling of the wind measured at some elevation near the ocean surface. The surface waves, however, modify the balance of turbulent stresses very near the surface, and therefore such extrapolations can introduce significant biases. This is particularly true for buoy measurements in extreme conditions, when the anemometer mast is within the wave boundary layer (WBL) or even below the wave crests. In this paper, field data and a WBL model are used to investigate such biases. It is shown that near the surface the turbulent stresses are less than those obtained by extrapolation using the logarithmic-layer assumption, and the mean wind speeds very near the surface, based on Lake George field observations, are up to 5% larger. The behavior is then simulated by means of a WBL model coupled with nonlinear waves, which confirmed the observations and revealed further details of complex behaviors at the wind-wave boundary layer.

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Haifeng Zhang, Helen Beggs, Alexander Ignatov, and Alexander V. Babanin

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The nighttime ocean cool skin signal ΔT [defined as skin sea surface temperature (SSTskin) minus depth SST (SSTdepth)] is investigated using 103 days of matchups between shipborne Infrared SST Autonomous Radiometer (ISAR) SSTskin and water intake SSTdepth at ~7.1–9.9-m depths, in oceans around Australia. Before data analysis, strict quality control of ISAR SSTskin data is conducted and possible diurnal warming contamination is carefully minimized. The statistical distribution of ΔT, and its dependencies on wind speed, heat flux, etc., are consistent with previous findings. The overall average ΔT value is −0.23 K. It is observed that the magnitude of the cool skin signal increases after midnight and a coolest skin offset (with an average value of −0.36 K) is found at around dawn. The dependency of ΔT on SST conditions is observed. Direct warm skin events are discovered when the net heat flux direction is from the atmosphere to the ocean, which is more likely to occur at high latitudes when the air is very humid and warmer than the SST. In addition, several cool skin models are validated: one widely used physical model performs best and can capture most skin-effect trends and details; the empirical models only reflect the basic features of the observed ΔT values. If the user cannot apply the physical model (due to, e.g., the algorithm complexity or missing inputs), then the empirical parameterization in the form proposed in a 2002 study can be used. However, we recommend using a new set of parameters, calculated in this study, based on much more representative dataset, and with more rigorous quality control.

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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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W. Erick Rogers, Alexander V. Babanin, and David W. Wang

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A new wind-input and wind-breaking dissipation for phase-averaged spectral models of wind-generated surface waves is presented. Both are based on recent field observations in Lake George, New South Wales, Australia, at moderate-to-strong wind-wave conditions. The respective parameterizations are built on quantitative measurements and incorporate new observed physical features, which until very recently were missing in source terms employed in operational models. Two novel features of the wind-input source function are those that account for the effects of full airflow separation (and therefore relative reduction of the input at strong wind forcing) and for nonlinear behavior of this term. The breaking term also incorporates two new features evident from observational studies; the dissipation consists of two parts—a strictly local dissipation term and a cumulative term—and there is a threshold for wave breaking, below which no breaking occurs. Four variants of the dissipation term are selected for evaluation, with minimal calibration to each. These four models are evaluated using simple calculations herein. Results are generally favorable. Evaluation for more complex situations will be addressed in a forthcoming paper.

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