Alexander V. Babanin

Global Trends in Wind Speed and Wave Height

Wind speeds over the world’s oceans have increased over the past two decades, as have wave heights. Studies of climate change typically consider measurements or predictions of temperature over extended periods of time. Climate, however, is much more than temperature. Over the oceans, changes in wind speed and the surface gravity waves generated by such winds play an important role. We used a 23-year database of calibrated and validated satellite altimeter measurements to investigate global changes in oceanic wind speed and wave height over this period. We find a general global trend of increasing values of wind speed and, to a lesser degree, wave height, over this period. The rate of increase is greater for extreme events as compared to the mean condition.

Semiempirical Dissipation Source Functions for Ocean Waves. Part I: Definition, Calibration, and Validation

Abstract New parameterizations for the spectral dissipation of wind-generated waves are proposed. The rates of dissipation have no predetermined spectral shapes and are functions of the wave spectrum and wind speed and direction, in a way consistent with observations of wave breaking and swell dissipation properties. Namely, the swell dissipation is nonlinear and proportional to the swell steepness, and dissipation due to wave breaking is nonzero only when a nondimensional spectrum exceeds the threshold at which waves are observed to start breaking. An additional source of short-wave dissipation is introduced to represent the dissipation of short waves due to longer breaking waves. A reduction of the wind-wave generation of short waves is meant to account for the momentum flux absorbed by longer waves. These parameterizations are combined and calibrated with the discrete interaction approximation for the nonlinear interactions. Parameters are adjusted to reproduce observed shapes of directional wave spect...

Breaking Probability for Dominant Waves on the Sea Surface

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 aerod...

Wave-Follower Field Measurements of the Wind-Input Spectral Function. Part II: Parameterization of the Wind Input

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, U10/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 winddriven 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.

Breaking probabilities for dominant surface waves on water of finite constant depth

This paper extends our previous study of the breaking probability of dominant deep water gravity surface waves into the finite water depth environment. It reports a unified behavior of the mean breaking statistics once the effects of finite water depth are taken into account. The shallow water wave data that form the basis of this study were acquired at a field experiment site at Lake George, New South Wales, Australia. The breaking events were detected through visual observation of videotaped records of the wave field in combination with acoustic signatures of the breaking waves from a collocated hydrophone. Following Banner et al. [2000], we argue that when constant finite depth bottom influence is operative, nonlinear hydrodynamical effects associated with energy and momentum fluxes within deforming wave groups remain the primary determinant of breaking onset. This underpins our proposed finite depth water parameterization for the environmental dependence of dominant wave breaking probability, given by the average number of breakers passing a fixed point per dominant wave period. The additional influence of bottom interaction with the wind drift current shear and wind forcing are also included in our finite constant depth formulation. This is a natural extension of our recently proposed deep water dependence and reduces to it as the significant wave height becomes much smaller than the water depth. In common with the deep water case we propose that there exists a threshold of the significant peak steepness below which negligible dominant wave breaking occurs. The available data show encouraging agreement with our proposed dependence, with a correlation coefficient approaching 0.9.

On the existence of water turbulence induced by nonbreaking surface waves

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.

Field Investigation of Transformation of the Wind Wave Frequency Spectrum with Fetch and the Stage of Development

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 fm 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 devel...

Spectral Distribution of Energy Dissipation of Wind-Generated Waves due to Dominant Wave Breaking

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 fun...

Weakly turbulent laws of wind-wave growth

The theory of weak turbulence developed for wind-driven waves in theoretical works and in recent extensive numerical studies concludes that non-dimensional features of self-similar wave growth (i.e. wave energy and characteristic frequency) have to be scaled by internal wave-field properties (fluxes of energy, momentum or wave action) rather than by external attributes (e.g. wind speed) which have been widely adopted since the 1960s. Based on the hypothesis of dominant nonlinear transfer, an asymptotic weakly turbulent relation for the total energy e and a characteristic wave frequency ω* was derived eω 4 g 2 αss = ω 3 .de/dt g 2 ) 1/3 g 2 g2 ) The self-similarity parameter α ss was found in the numerical duration-limited experiments and was shown to be naturally varying in a relatively narrow range, being dependent on the energy growth rate only. In this work, the analytical and numerical conclusions are further verified by means of known field dependencies for wave energy growth and peak frequency downshift. A comprehensive set of more than 20 such dependencies, obtained over almost 50 years of field observations, is analysed. The estimates give α ss very close to the numerical values. They demonstrate that the weakly turbulent law has a general value and describes the wave evolution well, apart from the earliest and full wave development stages when nonlinear transfer competes with wave input and dissipation.

NOTES AND CORRESPONDENCE An Experiment on the Nonbreaking Surface-Wave-Induced Vertical Mixing

Abstract Mixing induced by nonbreaking surface waves was investigated in a wave tank by measuring the thermal destratification rate of the water column. One experiment without waves and four experiments with waves of amplitudes ranging from 1.0 to 1.5 cm and wavelength from 30 to 75 cm were conducted. Water temperature variations at depths from 4 to 12 cm below the surface were measured. In the layer from 4 to 7 cm, the originally dense isothermal lines disperse soon after the waves are generated, whereas the vertical gradient from 9 to 12 cm is maintained for a relatively long time. The time span, during which the water temperature becomes well mixed, changes from about 20 h for the case with no waves to tens of minutes for the case with waves, and it decreases with increasing wave amplitude and wavelength. A one-dimensional diffusion numerical model with wave-induced mixing parameterization shows consistent results with the measurement. The study demonstrates that the mixing induced by nonbreaking waves...