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Christopher J. Zappa, Michael L. Banner, Russel P. Morison, and Sophia E. Brumer

Abstract

A spectral framework for quantifying the geometric/kinematic and dynamic/energetic properties of breaking ocean waves was proposed by Phillips in 1985. Phillips assumed a constant breaking strength coefficient to link the kinematic/geometric breaking crest properties to the associated excess energy and momentum fluxes from the waves to the upper ocean. However, a scale-dependent (spectral) breaking strength coefficient is needed, but is unavailable from measurements. In this paper, the feasibility of a parametric mean effective breaking strength coefficient valid for a wide range of sea states is investigated. All available ocean breaking wave datasets were analyzed and complemented with wave model behavior. Robust evidence is found supporting a single linear parameter relationship between the effective breaking strength and wave age or significant wave steepness. Envisaged applications for the effective breaking strength are described.

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Peter P. Sullivan, Michael L. Banner, Russel P. Morison, and William L. Peirson

Abstract

Turbulent flow over strongly forced steep steady and unsteady waves is simulated using large-eddy simulation (LES) with time t and space x varying wave height h(x, t) imposed as a lower boundary condition. With steady waves, h(x, t) is based on measurements of incipient and active breaking waves collected in a wind-wave flume, while a numerical wave code is used to generate an unsteady evolving wave packet (group). Highly intermittent airflow separation is found in the simulations, and the results suggest separation near a wave crest occurs prior to the onset of wave breaking. The form (pressure) drag is most sensitive to the wave slope, and the form drag can contribute as much as 74% to the total stress. Wind and scalar profiles from the LES display log-linear variations above the wave surface; the LES wind profiles are in good agreement with the measurements. The momentum roughness increases as the water surface changes from wind ripples to incipient breaking to active breaking. However, the scalar roughness decreases as the wave surface becomes rougher. This highlights major differences in momentum and scalar transport over a rough wavy surface. For a rapidly evolving, strongly forced wave group, the form drag is highly correlated with the wave slope, and intermittent separation is found early in the packet evolution when the local wave slope −∂h/∂x(x, t) ≥ 0.22. The packet root-mean-square wave slope is 0.084, but the form drag fraction is 2.4 times larger than a comparably forced steady wave. Thus, a passing wave group can induce unsteadiness in the wind stress.

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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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Wei Chen, Michael L. Banner, Edward J. Walsh, Jorgen B. Jensen, and Sunhee Lee

Abstract

The Southern Ocean Waves Experiment (SOWEX) was an international collaborative air–sea interaction experiment in which a specially instrumented meteorological research aircraft simultaneously gathered marine boundary-layer atmospheric turbulence data and sea surface roughness data over the Southern Ocean, particularly for gale-force wind conditions. In this paper analysis and findings are presented on key aspects of the coupled variability of the wind field, the wind stress, and the underlying sea surface roughness. This study complements the overview, methodology, and mean results published in Part I.

Weakly unstable atmospheric stratification conditions prevailed during SOWEX, with wind speeds ranging from gale force to light and variable. Throughout the SOWEX observational period, the wind field was dominated by large-scale atmospheric roll-cell structures, whose height scale was comparable with the thickness of the marine atmospheric boundary layer (MABL). Well above the sea surface, these coherent structures provide the dominant contribution to the downward momentum flux toward the sea surface. Closer to the sea surface, these organized large-scale structures continued to make significant contributions to the downward momentum flux, even within a few tens of meters of the sea surface.

At the minimum aircraft height, typical cumulative stress cospectra indicated that 10-km averages along crosswind tracks appeared adequate to close the stress cospectrum. Nevertheless, a large-scale spatial inhomogeneity in the wind stress vector was observed using 10- and 20-km spatial averaging intervals on one of the strongest wind days when the mean wind field was close to being spatially uniform. This indicates a departure from the familiar drag coefficient relationship and implies large-scale transverse modulations in the MABL with an effective horizontal to vertical aspect ratio of around 20.

A high visual correlation was found between mean wind speed variations and collocated sea-surface mean square slope (mss) variations, averaged over 1.9 km. A comparable plot of the 10-km running average of the downward momentum flux, observed at heights from 30 to 90 m, showed appreciably lower visual correlation with the wind speed variations and mss variations. The 10–20 km averaging distance needed to determine the wind stress was larger than the local scale of variation of the mss roughness variations. It also exceeded the scale of the striations often observed in synthetic aperture radar imagery under unstable atmospheric conditions and strong wind forcing. This highlights an overlooked intrinsic difficulty in using the friction velocity as the wind parameter in models of the wind wave spectrum, especially for the short wind wave scales.

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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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Juan M. Restrepo, Jorge M. Ramírez, James C. McWilliams, and Michael Banner

Abstract

Whitecapping affects the Reynolds stresses near the ocean surface. A model for the conservative dynamics of waves and currents is modified to include the averaged effect of multiple, short-lived, and random wave-breaking events on large spatiotemporal scales. In this study’s treatment, whitecapping is parameterized stochastically as an additive uncertainty in the fluid velocity. It is coupled to the Stokes drift as well as to the current velocity in the form of nonlinear momentum terms in the vortex force and the Bernoulli head. The effects of whitecapping on tracer dynamics, mass balances, and boundary conditions are also derived here. Whitecapping also modifies the dynamics and the size of the sea surface boundary layer. This study does not resolve the boundary layer, however, the authors appeal to traditional viscosity parameterizations to include these diffusive effects, modified for the context of wave–current interactions.

The parameterized breaking velocity field is endowed with empirical rules that link their generation in space and time to properties and dynamics of wave groups. The energy convergence rate of wave groups is used as an indicator for the onset of wave breaking. A methodology is proposed for evaluating this criterion over an evolving random Gaussian model for the ocean surface. The expected spatiotemporal statistics of the breaking events are not imposed, but rather computed, and are found to agree with the general expectation of its Poisson character. The authors also compute, rather than impose, the shear stress associated with the breaking events and find it to agree with theoretical expectations.

When the relative role played by waves and breaking events on currents is compared, this study finds that waves, via the vortex force, purely advect the vorticity of currents that are essentially only dependent on transverse coordinates. The authors show that currents will tend to get rougher in the direction of steady wind, when whitecapping is present. Breaking events can alter and even suppress the rate of advection in the vortex force. When comparing the rates of transport, the waves will tend to dominate the short term and the whitecapping of the long-term rate.

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

Abstract

An experimental study of wind energy and momentum input into finite-depth wind waves was undertaken at Lake George, New South Wales, Australia. To measure microscale oscillations of induced pressure above surface waves, a high-precision wave-follower system was developed at the University of Miami, Florida. The principal sensing hardware included Elliott pressure probes, hot-film anemometers, and Pitot tubes. The wave-follower recordings were supplemented by a complete set of relevant measurements in the atmospheric boundary layer, on the surface, and in the water body. This paper is dedicated to technical aspects of the measurement procedure and data analysis. The precision of the feedback wave-following mechanism did not impose any restrictions on the measurement accuracy in the range of wave heights and frequencies relevant to the problem. Thorough calibrations of the pressure transducers and moving Elliott probes were conducted. It is shown that the response of the air column in the connecting tubes provides a frequency-dependent phase shift, which must be accounted for to recover the low-level induced pressure signal. In the finite-depth environment of Lake George, breaking waves play an important role in the momentum exchange between wind and waves, as will be shown in a subsequent paper.

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Michael L. Banner, Wei Chen, Edward J. Walsh, Jorgen B. Jensen, Sunhee Lee, and Chris Fandry

Abstract

The Southern Ocean Waves Experiment (SOWEX) was an international collaborative air–sea interaction experiment in which a specially instrumented meteorological research aircraft simultaneously gathered atmospheric turbulence data in the marine boundary layer and sea surface topography data over the Southern Ocean for a wide range of wind speeds. The aim was to increase present knowledge of severe sea state air–sea interaction. This first paper presents an overview of the experiment and a detailed discussion of the methodology and mean results. A companion paper describes the findings on variability of the wind speed and wind stress and their relationship to variations in the underlying sea surface roughness.

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Ian R. Young, Michael L. Banner, Mark A. Donelan, Cyril McCormick, Alexander V. Babanin, W. Kendall Melville, and Fabrice Veron

Abstract

A field experiment to study the spectral balance of the source terms for wind-generated waves in finite water depth was carried out in Lake George, Australia. The measurements were made from a shore-connected platform at varying water depths from 1.2 m down to 20 cm. Wind conditions and the geometry of the lake were such that fetch-limited conditions with fetches ranging from approximately 10 km down to 1 km prevailed. The resulting waves were intermediate-depth wind waves with inverse wave ages in the range 1 < U 10/Cp < 8. The atmospheric input, bottom friction, and whitecap dissipation were measured directly and synchronously by an integrated measurement system, described in the paper. In addition, simultaneous data defining the directional wave spectrum, atmospheric boundary layer profile, and atmospheric turbulence were available. The contribution to the spectral evolution due to nonlinear interactions of various orders is investigated by a combination of bispectral analysis of the data and numerical modeling. The relatively small scale of the lake enabled experimental conditions such as the wind field and bathymetry to be well defined. The observations were conducted over a 3-yr period, from September 1997 to August 2000, with a designated intensive measurement period [the Australian Shallow Water Experiment (AUSWEX)] carried out in August–September 1999. High data return was achieved.

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