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

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

Abstract

This paper demonstrates that it is practical to measure turbulent air-sea fluxes from a discus buoy. It proposes a method to correct the measured wind flow, for velocities induced by angular and axial movements of the anemometer, allowing the estimation of the momentum flux from a floating platform. Discus buoys modified for the measurement of momentum flux were deployed during the Surface Wave Dynamics Experiment and the High Resolution Remote Sensing Programme. Successful evaluation of the wind stress was carried out in moderate sea conditions: wind speed and significant wave height, respectively, reaching 12 m s−1 and 4.25 m. Friction velocities calculated using the eddy-correlation method are shown to agree well with those determined from the less direct inertial dissipation method in conditions where the latter method is applicable.

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Shuyi S. Chen, James F. Price, Wei Zhao, Mark A. Donelan, and Edward J. Walsh
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