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William J. Plant and Mark A. Donelan

Abstract

We describe here a method for recovering directional ocean surface wave spectra obtained from height and slope measurements made over a small area, the iterative deconvolution method (IDM). We show that IDM is a more reliable method for estimating directional wave spectra than more common spectral estimation techniques by comparing it with the widely used maximum entropy method (MEM). IDM is based on the observation that pitch–roll buoys produce directional spectra that are the true spectra convolved with an angular windowing function and are therefore much broader than the true spectra. We test IDM against simulated data and find that it does a better job of retrieving the known input spectra than does MEM, which often produces false double peaks or incorrect angular widths. We compare IDM recoveries to spectra obtained using a nonstandard processing technique, the wavelet directional method (WDM) on data from a compact array of wave staffs on Lake Ontario. We find that IDM produces directional wave spectra very nearly identical to those obtained using WDM, verifying both techniques. Finally, we processed standard NDBC buoy directional spectra and showed that IDM recovers ocean wave spectra that narrow in the Strait of Juan de Fuca and that follow a changing wind in the expected manner. Neither of these phenomena are reliably obtained using MEM due to its tendency to produce false bimodal peaks and peaks that are too narrow.

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George L. Mellor, Mark A. Donelan, and Lie-Yauw Oey

Abstract

A surface wave model is developed with the intention of coupling it to three-dimensional ocean circulation models. The model is based on a paper by Mellor wherein depth-dependent coupling terms were derived. To be compatible with circulation models and to be numerically economical, this model is simplified compared to popular third-generation models. However, the model does support depth and current refraction, deep and shallow water, and proper coupling with depth-variable currents.

The model is demonstrated for several simple scenarios culminating in comparisons of model calculations with buoy data during Hurricane Katrina and with calculations from the model Simulating Waves Nearshore (SWAN); for these calculations, coupling with the ocean was not activated.

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Ivan B. Savelyev, Brian K. Haus, and Mark A. Donelan

Abstract

A quantitative description of wind-wave momentum transfer in high wind conditions is necessary for accurate wave models, storm and hurricane forecasting, and models that require atmosphere–ocean coupling such as circulation and mixed layer models. In this work, a static pressure probe mounted on a vertical wave follower to investigate relatively strong winds (U 10 up to 26.9 m s−1 and U 10/Cp up to 16.6) above waves in laboratory conditions. The main goal of the paper is to quantify the effect of wave shape and airflow sheltering on the momentum transfer and wave growth. Primary results are formulated in terms of wind forcing and wave steepness ak, where a is wave amplitude and k is wave number. It is suggested that, within the studied range (ak up to 0.19), the airflow is best described by the nonseparated sheltering theory. Notably, a small amount of spray and breaking waves was present at the highest wind speeds; however, their effect on the momentum flux was not found to be significant within studied conditions.

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Dahai Jeong, Brian K. Haus, and Mark A. Donelan

Abstract

Controlled experiments were conducted in the Air–Sea Interaction Saltwater Tank (ASIST) at the University of Miami to investigate air–sea moist enthalpy transfer rates under various wind speeds (range of 0.6–39 m s−1 scaled to equivalent 10-m neutral winds) and water–air temperature differences (range of 1.3°–9.2°C). An indirect calorimetric (heat content budget) measurement technique yielded accurate determinations of moist enthalpy flux over the full range of wind speeds. These winds included conditions with significant spray generation, the concentrations of which were of the same order as field observations. The moist enthalpy exchange coefficient so measured included a contribution from cooled reentrant spray and therefore serves as an upper limit for the interfacial transfer of enthalpy. An unknown quantity of spray was also observed to exit the tank without evaporating. By invoking an air volume enthalpy budget it was determined that the potential contribution of this exiting spray over an unbounded water volume was up to 28%. These two limits bound the total enthalpy transfer coefficient including spray-mediated transfers.

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William M. Drennan, Hans C. Graber, and Mark A. Donelan

Abstract

Over the past four decades much effort has been directed toward determining a parameterization of the sea surface drag coefficient on readily measurable quantities, such as mean wind speed and atmospheric stability. Although such a parameterization would have obvious operational advantages, the considerable scatter present between experiments, or within any one experiment, indicates that it is not easily achievable. One likely candidate for much of the scatter is the underlying wave field. Unfortunately, few campaigns over the years have included spectral measurements of the waves. Among those that have, the results are inconclusive.

Here data are presented from the Surface Wave Dynamics Experiment and High Resolution Remote Sensing Program campaigns in which 3-m discus buoys were instrumented with K-Gill and sonic anemometers and complete motion packages to measure the direct (eddy correlation) stress and, concurrently, the directional ocean wave spectrum. These data are examined for the effects of swell on the drag coefficient. It is found that much of the scatter in the drag coefficient can be attributed to geophysical effects, such as the presence of swells or nonstationary conditions.

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Mark A. Donelan, William M. Drennan, and Kristina B. Katsaros

Abstract

During the Surface Wave Dynamics Experiment, direct measurements of momentum, heat, and water vapor fluxes were obtained from a mast on the foredeck of a SWATH (small water-plane area, twin hull) ship in deep water off the state of Virginia. Directional wave spectra were obtained simultaneously from a 6- or 3-wire wave-staff array mounted at the bow of the ship. One hundred and twenty-six 17-minute runs of flux and wave data obtained with the ship steaming slowly into the wind are examined for the effects of the relative direction of the wind sea and background swell on the momentum transfer. The adequacy of the inertial dissipation method, which depends on the high-frequency turbulent fluctuations for evaluating the wind stress, is also examined for any effects of swell.

The results show that the presence of counter- and cross-swells can result in drag coefficients that are much larger than the value for a pure wind sea. The eddy correlation and inertial dissipation methods for measuring wind stress are found to diverge during the complex sea conditions. The authors interpret the latter observations as an indication that the traditional inertial dissipation method, in which the pressure and transport terms in the kinetic energy balance equation are assumed to be in balance, may be unsuitable for use in a marine boundary layer disturbed by swell.

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Naoya Suzuki, Takuji Waseda, Mark A. Donelan, and Takeshi Kinoshita

Abstract

There exists considerable disagreement among the observed values of the drag coefficient C D. To develop a model of C D, the wind stress generally will be calculated from the eddy correlation method. A buoy is suitable to measure the wind stress in many sea surface conditions. However, the motion correction is very difficult because the anemometer measures the wind components, including the motion of the buoy. In this study, as a first approach, the motion of a prototype buoy system with a three-axis sonic anemometer and a six-axis motion sensor installed in the small-size GPS observation buoy was investigated. The wave tank is in the ocean engineering basin of the Institute of Industrial Science, University of Tokyo, Japan. The imposed conditions were wave periods from 1.1 to 2.5 s; wind speeds of 0, 2, and 5 m s−1; and the wave spectrum was either regular or irregular. The motion of the buoy was measured in 120 cases. For all the wave periods and without wind, the wind velocity measured by the sonic anemometer and the velocity of the anemometer motion calculated from the motion sensor data showed good agreement. Also, in the condition with wind speeds of 2 and 5 m s−1, the motion-corrected wind velocity, obtained by deducting the velocity of the anemometer motion from the wind velocity measured by the anemometer, yielded the true wind velocity with better-than-average (4.3%) accuracy. The friction velocity from corrected wind velocity components shows agreement with the friction velocity measured from a fixed sonic anemometer within expected intrinsic error. The buoy system is expected to be able to measure the wind stress in the field. The next stage is to do comprehensive field tests.

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Kimmo K. Kahma, Mark A. Donelan, William M. Drennan, and Eugene A. Terray

Abstract

Measurements of pressure near the surface in conditions of wind sea and swell are reported. Swell, or waves that overrun the wind, produces an upward flux of energy and momentum from waves to the wind and corresponding attenuation of the swell waves. The estimates of growth of wind sea are consistent with existing parameterizations. The attenuation of swell in the field is considerably smaller than existing measurements in the laboratory.

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Shuyi S. Chen, Wei Zhao, Mark A. Donelan, and Hendrik L. Tolman

Abstract

The extreme high winds, intense rainfall, large ocean waves, and copious sea spray in hurricanes push the surface-exchange parameters for temperature, water vapor, and momentum into untested regimes. The Coupled Boundary Layer Air–Sea Transfer (CBLAST)-Hurricane program is aimed at developing improved coupling parameterizations (using the observations collected during the CBLAST-Hurricane field program) for the next-generation hurricane research prediction models. Hurricane-induced surface waves that determine the surface stress are highly asymmetric, which can affect storm structure and intensity significantly. Much of the stress is supported by waves in the wavelength range of 0.1–10 m, which is the unresolved “spectral tail” in present wave models. A directional wind–wave coupling method is developed to include effects of directionality of the wind and waves in hurricanes. The surface stress vector is calculated using the two-dimensional wave spectra from a wave model with an added short-wave spectral tail. The wind and waves are coupled in a vector form rather than through the traditional roughness scalar. This new wind–wave coupling parameterization has been implemented in a fully coupled atmosphere–wave–ocean model with 1.67-km grid resolution in the atmospheric model, which can resolve finescale features in the extreme high-wind region of the hurricane eyewall. It has been tested in a number of storms including Hurricane Frances (2004), which is one of the best-observed storms during the CBLAST-Hurricane 2004 field program. This paper describes the new wind–wave coupling parameterization and examines the characteristics of the coupled model simulations of Hurricane Frances (2004). Observations of surface waves and winds are used to evaluate the coupled model results.

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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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