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- Author or Editor: Alexander V. Babanin x
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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.
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.
Abstract
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.
Abstract
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.
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.
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.
Abstract
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
Abstract
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
Abstract
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.
Abstract
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.
Abstract
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.
Abstract
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.
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.
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.
Nighttime Cool Skin Effect Observed from Infrared SST Autonomous Radiometer (ISAR) and Depth TemperaturesAbstract
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.
Abstract
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.
Abstract
Laboratory experiments were performed to investigate the effects of a coflowing current field on the spectral shape of water waves. The results indicate that refraction is the main factor in modulating wave height and overall wave energy. Although the structure of the current field varies considerably, some current-induced patterns in the wave spectrum are observed. In high frequencies, the energy cascading generated by nonlinear interactions is suppressed, and the development of a spectral tail is disturbed, as a consequence of the detuning of the four-wave resonance conditions. Furthermore, the presence of currents slows the downshifting of the spectral peak. The suppression of the high-frequency energy under the influence of currents is more prominent as the spectral steepness increases. The energy suppression is also more accentuated and long-standing along the fetch when the directional spreading of waves is sufficiently broad. This result indicates that the current-induced detuning of resonant conditions is more effective when exact resonances are the primary mechanism of nonlinear interactions than when quasi resonances prevail (directionally narrow cases). Additionally, the directional analysis shows that the highly variable currents broaden the directional spreading of waves. The broadening is suggested to be related to random refraction and scattering of wave rays. The random disturbance of wavenumbers alters the nonlinear interaction conditions and weakens the energy exchanges among wave components, which is expressed in the suppression of the high-frequency energy.
Abstract
Laboratory experiments were performed to investigate the effects of a coflowing current field on the spectral shape of water waves. The results indicate that refraction is the main factor in modulating wave height and overall wave energy. Although the structure of the current field varies considerably, some current-induced patterns in the wave spectrum are observed. In high frequencies, the energy cascading generated by nonlinear interactions is suppressed, and the development of a spectral tail is disturbed, as a consequence of the detuning of the four-wave resonance conditions. Furthermore, the presence of currents slows the downshifting of the spectral peak. The suppression of the high-frequency energy under the influence of currents is more prominent as the spectral steepness increases. The energy suppression is also more accentuated and long-standing along the fetch when the directional spreading of waves is sufficiently broad. This result indicates that the current-induced detuning of resonant conditions is more effective when exact resonances are the primary mechanism of nonlinear interactions than when quasi resonances prevail (directionally narrow cases). Additionally, the directional analysis shows that the highly variable currents broaden the directional spreading of waves. The broadening is suggested to be related to random refraction and scattering of wave rays. The random disturbance of wavenumbers alters the nonlinear interaction conditions and weakens the energy exchanges among wave components, which is expressed in the suppression of the high-frequency energy.
Abstract
This paper studies the impact of the surface waves on the turbulent mixing. The satellite observations of suspended particulate matter (SPM) at the ocean surface as an indicator of turbulent quantities of the flow are used. In a water column, SPM builds a vertical profile depending on settling velocities of the particles and on vertical mixing processes; thus, SPM is a perfect marker to study the turbulent quantities of the flow. Satellite observations in the North Sea show that surface SPM concentrations, in locations of its deposition, grow rapidly and build plume-shaped, long (many kilometers) uninterrupted and consistent structures during a storm. Also, satellites reveal that SPM rapidly sinks to the seabed after the storm peak has passed and wave height decreases (i.e., in the absence of strong turbulence).
The nonbreaking wave-induced turbulence has been discussed, parameterized, and implemented into an equation of evolution of turbulent kinetic energy (TKE) in the frame of mean-flow concept, which can be used in existing circulation models. The ratio between dissipated and total wave energy is used to describe the influence of wave damping on the mean flow. The numerical tests reproduce experiments in a wave tank very well and are supported by observations of SPM in the North Sea. Their results show that the motion of an individual nonbreaking wave includes turbulent fluctuations if the critical Reynolds number for wave motion is exceeded, independent of the presence of currents due to wind or tides. These fluctuations can produce high diffusivity and strongly influence mixing in the upper water layer of the ocean.
Abstract
This paper studies the impact of the surface waves on the turbulent mixing. The satellite observations of suspended particulate matter (SPM) at the ocean surface as an indicator of turbulent quantities of the flow are used. In a water column, SPM builds a vertical profile depending on settling velocities of the particles and on vertical mixing processes; thus, SPM is a perfect marker to study the turbulent quantities of the flow. Satellite observations in the North Sea show that surface SPM concentrations, in locations of its deposition, grow rapidly and build plume-shaped, long (many kilometers) uninterrupted and consistent structures during a storm. Also, satellites reveal that SPM rapidly sinks to the seabed after the storm peak has passed and wave height decreases (i.e., in the absence of strong turbulence).
The nonbreaking wave-induced turbulence has been discussed, parameterized, and implemented into an equation of evolution of turbulent kinetic energy (TKE) in the frame of mean-flow concept, which can be used in existing circulation models. The ratio between dissipated and total wave energy is used to describe the influence of wave damping on the mean flow. The numerical tests reproduce experiments in a wave tank very well and are supported by observations of SPM in the North Sea. Their results show that the motion of an individual nonbreaking wave includes turbulent fluctuations if the critical Reynolds number for wave motion is exceeded, independent of the presence of currents due to wind or tides. These fluctuations can produce high diffusivity and strongly influence mixing in the upper water layer of the ocean.
