Publications

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2012
Zhang, Y, Zhang X.  2012.  Ocean haline skin layer and turbulent surface convections. Journal of Geophysical Research-Oceans. 117   10.1029/2011jc007464   AbstractWebsite

The ocean haline skin layer is of great interest to oceanographic applications, while its attribute is still subject to considerable uncertainty due to observational difficulties. By introducing Batchelor micro-scale, a turbulent surface convection model is developed to determine the depths of various ocean skin layers with same model parameters. These parameters are derived from matching cool skin layer observations. Global distributions of salinity difference across ocean haline layers are then simulated, using surface forcing data mainly from OAFlux project and ISCCP. It is found that, even though both thickness of the haline layer and salinity increment across are greater than the early global simulations, the microwave remote sensing error caused by the haline microlayer effect is still smaller than that from other geophysical error sources. It is shown that forced convections due to sea surface wind stress are dominant over free convections driven by surface cooling in most regions of oceans. The free convection instability is largely controlled by cool skin effect for the thermal microlayer is much thicker and becomes unstable much earlier than the haline microlayer. The similarity of the global distributions of temperature difference and salinity difference across cool and haline skin layers is investigated by comparing their forcing fields of heat fluxes. The turbulent convection model is also found applicable to formulating gas transfer velocity at low wind.

Zhang, X.  2012.  Contribution to the global air-sea CO2 exchange budget from asymmetric bubble-mediated gas transfer. Tellus Series B-Chemical and Physical Meteorology. 64   10.3402/tellusb.v64i0.17260   AbstractWebsite

Quantifying air-sea gas exchange is an essential element for predicting climate change due to human activities. Air-sea gas exchanges take place through both the sea surface and bubbles formed during wave breakings. Bubble-mediated gas transfers are particularly important at high wind regions. Bubble-mediated gas transfers are separated into symmetric and asymmetric transfers. Their transfer fluxes are respectively proportional to the gas concentration difference between the atmosphere and ocean surface water, and to the atmospheric gas concentration alone. To quantify the role of asymmetric transfers in the global carbon dioxide (CO2) transfer budget, a parameterisation scheme of asymmetric transfer is developed, which is constrained by gas equilibrium supersaturation in the ocean surface. By establishing a bound for the global mean gas equilibrium supersaturation in ocean surface water, we found that the global ocean uptake by bubble-mediated asymmetric gas transfer is a substantial part of the total air-sea CO2 uptake budget (over (2)0%). It is found that, over the past half century, the global asymmetric ocean CO2 uptake has increased about a total of 40% on a steadily trend, as a consequence of the increasing atmospheric CO2 concentrations.

2011
Cox, C, Zhang X.  2011.  Contours of slopes of a rippled water surface. Optics Express. 19:18789-18794. AbstractWebsite

The appearance of a horizontal array of linear lamps below the water surface when viewed from above is approximately in the form of contours of one component of the water surface slope. The degree of approximation is a fraction of one percent when this method is used to describe the slopes of a wind ruffled surface. An extension of the method to image both components of slope requires two arrays of lamps pulsed alternately and in synchronism with a fast camera. (C) 2011 Optical Society of America

2010
Cai, WJ, Hu XP, Huang WJ, Jiang LQ, Wang YC, Peng TH, Zhang X.  2010.  Alkalinity distribution in the western North Atlantic Ocean margins. Journal of Geophysical Research-Oceans. 115   10.1029/2009jc005482   AbstractWebsite

Total alkalinity (TA) distribution and its relationship with salinity (S) along the western North Atlantic Ocean (wNAO) margins from the Labrador Sea to tropical areas are examined in this study. Based on the observed TA-S patterns, the mixing processes that control alkalinity distribution in these areas can be categorized into a spectrum of patterns that are bracketed by two extreme mixing types, i.e., alongshore current-dominated and river-dominated. Alongshore current-dominated mixing processes exhibit a segmented mixing line with a shared mid-salinity end-member. In such cases (i.e., Labrador Sea, Gulf of Maine, etc.), the y-intercept of the high salinity segment of the mixing line is generally higher than the local river alkalinity values, and it reflects the mixing history of the alongshore current. In contrast, in river-dominated mixing (Amazon River, Caribbean Sea, etc.), good linear relationships between alkalinity and salinity are generally observed, and the zero salinity intercepts of the TA-S regressions roughly match those of the regional river alkalinity values. TA-S mixing lines can be complicated by rapid changes in the river end-member value and by another river nearby with a different TA value (e. g., Mississippi-Atchafalaya/Gulf of Mexico). In the wNAO margins, regression intercepts and river end-members have a clear latitudinal distribution pattern, increasing from a low of similar to 300 mu mol kg(-1) in the Amazon River plume to a high value between similar to 500-1100 mu mol kg(-1) in the middle and high latitude margins. The highest value of similar to 2400 mu mol kg(-1) is observed in the Mississippi River influenced areas. In addition to mixing control, biological processes such as calcification and benthic alkalinity production may also affect ocean margin alkalinity distribution. Therefore, deriving inorganic carbon system information in coastal oceans using alkalinity-salinity relationships, in particular, those of generic nature, may lead to significant errors.

2007
Zhang, X, Cai WJ.  2007.  On some biases of estimating the global distribution of air-sea CO2 flux by bulk parameterizations. Geophysical Research Letters. 34   10.1029/2006gl027337   AbstractWebsite

It is important to examine the parameterizations used in calculating air-sea exchange fluxes as they are essential in developing global carbon models and in carbon budget calculations. We quantify the potential biases involved in the parameterizations. Adopting a non-zero gas transfer velocity for low wind areas results in a significant increase in the CO2 flux in equatorial regions with a net increase of +0.2 Pg C yr(-1) in the total sea-air global flux. The ocean "cool skin temperature'' effect on CO2 flux estimation is found to be an order of magnitude smaller than early estimations. The previously unknown salty-skin effect has an opposite contribution that cancels the cool-skin effect. Comparing different wind speeds derived from satellite data and Global Circulation Models (GCM), the most significant divergence is found at the low wind equatorial regions regarding the CO2 flux estimation.

2005
Zhang, X.  2005.  Short surface waves on surface shear. Journal of Fluid Mechanics. 541:345-370.   10.1017/s0022112005006063   AbstractWebsite

The problem of short wind waves propagating oil surface wind drift is considered here. Under the assumption of small monochromatic Surface waves oil a steady and horizontally Uniform Surface shear of in inviscid fluid, the governing equation becomes the well-known Rayleigh instability equation. Perturbation Solutions exist for the surface-wave problem; however, the conditions for these approximations are violated in the case of short wind waves on wind drift shear. As an alternative approach, the piecewise-linear approximation (PLA) is explored. A proof is given for the rate of convergence of the piecewise-linear approximation for solving the Rayleigh equation Without limitations oil boundary conditions. The artificial modes of the piecewise-linear flow system are also discussed. The method is numerically efficient and highly accurate. Applying this method, the linear instability of various boundary-layer flows is examined. Short waves propagating with surface shear-flows are stable, while it is possible for waves that are travelling against a shear current to become unstable when the surface speed of the shear is greater than the wavespeed in stagnant fluid. PLA is also applied to examine the applicability of other perturbation approaches to the problem of propagation of short waves oil wind drift shear. it is found that the existing approximations cannot fit the whole range of short wind waves. To bridge the gap, new approximations are derived from an implicit form of the exact dispersion relation based upon the variational principle.

2004
Zhang, X, Harrison S.  2004.  A laboratory observation of the surface temperature and velocity distributions on a wavy and windy air-water interface. Physics of Fluids. 16:L5-L8.   10.1063/1.1631813   AbstractWebsite

Temperature and velocity distributions of the water surface are examined experimentally with infrared imaging techniques. The surface velocity is determined from the movement of the pattern of surface temperature cell. It is found that the mean wind drift is about 30%u(*), much less than the widely cited measurements of 55%u(*). Although many complicated thermal and dynamical processes control the surface temperature, we found that the probability distribution function (PDF) of the standardized water surface temperature does not vary significantly with wind speed. The increasing nonlinear effects of wave orbital motions and wave breaking on surface motion are shown by the similarity and trend of change in the PDFs of the water surface velocity normalized by the wave orbital velocity at different wind speeds. The standard deviation of the speed distribution increases with the wind speed while the basic skewed distribution shape remains. (C) 2004 American Institute of Physics.

Zhang, X, Garbe CS.  2004.  Studying dynamical processes of air-sea exchanges with air-waterinterface image techniques. Recent Res. Devel. Fluid Dynamics. 5:57-87. Abstract

Many interfacial processes contribute to oceanic air-sea interchanges. Conventionally, some of these processes are either simplified for theoretical analysis or parameterized based on dimensional arguments.However, the validity of these approximations over awide range of sea-states is not well established on afirm scientific basis. Hence, numerical simulations and predictions exhibit uncertainties. This skepticism could be restrained if direct observations both in spatial and temporal domains were available. Measurements inthe close vicinity of the air-sea interface have been challenging. The recent technical developments for imaging air-water interface made it possible to exam some small-scale surface processes in detail, and are instrumental to the latest improvement in our ability to qualify air-sea transport processes. Modernoptical, acoustic and electromagnetic instrumentation should lead to significantly improved interface-measurements in the near future

2003
Zhang, X.  2003.  Surface image velocimetry for measuring short wind wave kinematics. Experiments in Fluids. 35:653-665.   10.1007/s00348-003-0721-y   AbstractWebsite

Techniques are developed here for determining the propagation speeds of short wind waves from surface slope images. The surface slope images are taken in experiments at three different wind-wave facilities in Heidelberg, Marseilles, and San Diego. Travel distances of wavelets of different scales are determined from image pairs captured within a very short time interval by both wavelet tracking and coherence analysis methods. It is shown, for the first time by direct measurements, that most of the short wind waves are dispersive.

2002
Zhang, X.  2002.  Enhanced dissipation of short gravity and gravity capillary waves due to parasitic capillaries. Physics of Fluids. 14:L81-L84.   10.1063/1.1519260   AbstractWebsite

The dissipation rate of short, mechanically generated, monochromatic surface waves was measured in order to determine the increased dissipation due to the generation of parasitic capillary waves. As the surface waves propagate freely, the decaying wave elevations were measured by an ultra-thin capacitance wire. Measurements indicate that the dissipation rate increases approximately with the square of the wave slope, AK, and the generation of parasitic capillaries depends on the wavelength of the surface waves. The maximum generation of parasitic capillaries coincides with a surface wave wavelength near 7 cm. Measured data fits a simple parameterized model of the dissipation rate reasonably well. (C) 2002 American Institute of Physics.

1999
Zhang, X.  1999.  Observations on waveforms of capillary and gravity-capillary waves. European Journal of Mechanics B-Fluids. 18:373-388.   10.1016/S0997-7546(99)80035-1   AbstractWebsite

Due to extreme conditions in the field, there has not been any observational report on three-dimensional waveforms of short ocean surface waves. Three-dimensional waveforms of short wind waves can be found from integrating surface gradient image data (Zhang 1996a). Ocean surface gradient images are captured by an optical surface gradient detector mounted on a raft operating in the water offshore California (Cox and Zhang 1997). Waveforms and spatial structures of short wind waves are compared with early laboratory wind wave data (Zhang 1994, 1995). Although the large-scale wind and wave conditions are quite different, the waveforms are resoundingly similar at the small scale. It is very common, among steep short wind waves, that waves in the capillary range feature sharp troughs and flat crests. The observations show that most short waves are far less steep than the limiting waveform under weak wind conditions. Waveforms that resemble capillary-gravity solitons are observed with a close match to the form theoretically predicted for potential flows (Longuet-Higgins 1989, Vanden-Broeck and Dias 1992). Capillaries are mainly found as parasitic capillaries on the forward face of short gravity waves. The maximum wavelength in a parasitic wave train is less than a centimeter. The profiles of parasitic wave trains and longitudinal variations are shown. The phenomenon of capillary blockage (Phillips 1981) on dispersive freely traveling short waves is observed in the tank but not at sea. The short waves seen at sea propagate in all directions while waves in the tank are much more unidirectional. (C) Elsevier, Paris.

Zhang, X, Klinke J, Jahne B.  1999.  A study of advection of short wind waves by long waves from surface slope images. The wind-driven air-sea interface : electromagnetic and acoustic sensing, wave dynamics and turbulent fluxes. ( Banner ML, Ed.).:92-100., Sydney, A.C.T..: School of Mathematics, University of New South Wales Abstract
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Zhang, X, Klinke J, Cox CS.  1999.  Vortical motines under short wind waves. The wind-driven air-sea interface : electromagnetic and acoustic sensing, wave dynamics and turbulent fluxes. ( Banner ML, Ed.).:277-284., Sydney, A.C.T..: School of Mathematics, University of New South Wales Abstract
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1997
LonguetHiggins, M, Zhang X.  1997.  Experiments on capillary-gravity waves of solitary type on deep water. Physics of Fluids. 9:1963-1968.   10.1063/1.869315   AbstractWebsite

It is shown that capillary-gravity waves of solitary type on deep water can be generated by the resonant excitation of a water surface at a speed close to the phase-speed of free waves. This speed depends upon the wave amplitude. When the source of excitation is removed, the waves are shown to propagate as free solitary waves, damped by viscosity. (C) 1997 American Institute of Physics.

Zhang, X, Cox CS, Wang X.  1997.  Further evaluation of feature correlation for PIV and PTV. Optical Technology in Fluid, Thermal, and Combustion Flow III. 3172( Cha SS, Trolinger JD, Kawahashi M, Eds.)., San Diego, CA   10.1117/12.279750   Abstract

Particle Image Velocimetry and Particle-Tracking Velocimetry have been successfully used for measuring instantaneous velocity fields. Analyzing PIV images involves matching particle images captured sequentially. Correlating interrogation images is commonly used, which determines the non-rotational rigid body motion of interrogation image elements by averaging motions of a sufficient number of particles within the interrogation element. A variety of methods are used for PTV which tracks the motions of individual particles. In PTV applications, particle seeding density is kept low to avoid ambiguity of multiple particles within the interrogation element.PIV allows for higher particle seeking. However, each interrogation element has to be large enough to include a significant number of particles. Both PIV and PTV data processing methods limit the ability of extracting fine spatial scale flow motion from particle image data. The feature-based matching method proposed recently bridges the methods of PIV and PTV. It enables us to track individual particles at higher particle seeding,thus is capable of detecting flow motion at a smaller spatial scale. The feature-based matching method has been evaluated on different data sets. It shows the fine structure of flow field by the motions of each particle and its neighborhoods. Spatially averaged velocity fields are consistent with those calculated from image correlation methods.

Cox, CS, Zhang X.  1997.  Optical methods for study of sea surface roughness and microscale turbulence. Optical Technology in Fluid, Thermal, and Combustion Flow III. 3172( Cha SS, Trolinger JD, Kawahashi M, Eds.)., San Diego, CA   10.1117/12.279735   Abstract

The shape of the ocean surface on a millimeter scale controls the scattering of microwave radiation, hence the measurement of oceanic properties by remote sensing. In addition the micro-turbulence immediately adjacent to the sea surface brings about transfers of momentum, soluble gases such as CO2, and heat or water vapor through the lowermost layers of air and the water immediately below. Although these processes are of vital importance to our understanding of the oceans and climate, they have not been adequately studied at sea. Recent developments of optical techniques have greatly simplified measurements of small scale fluid motions and have made them accessible to measurement from a small raft in the open sea. A contributing factor in these developments is the availability of high power, high efficiency visible light diode lasers and high resolution CCD arrays. Optical methods have the advantage that they do not influence the delicate motions of capillary waves at the sea surface, nor are they intrusive in the motions of small turbulent eddies. Our light source for study of turbulence below the water surface is a diode bar laser array. Light generated by the laser array is refracted into a fan shaped light sheet of approximate dimensions 50 by 20 by 2 mm to illuminate particles in the water. Sea water is sufficient transparent to this deep red light that particle tracking and particle image velocimetry can be carried out. The laser and a CCD camera in their water proof containers are so compact that they do not materially interfere with the water flow despite being mounted below the sea surface.

Dabiri, D, Zhang X, Gharib M.  1997.  Quantitative visualization of three-dimensional free surface slope and elevations. Atlas of Visualization III. ( of Japan V, Ed.).:1-22., Oxford: Pergamon Press Abstract

A new technique that integrates optics, colorimetry, and digital image processing is developed to measure the three-dimensional surface slope and elevation for time-evolving flows.

1996
Zhang, X.  1996.  An algorithm for calculating water surface elevations from surface gradient image data. Experiments in Fluids. 21:43-48.   10.1007/BF00204634   AbstractWebsite

2-D water surface gradient data can be measured by a 2-D gradient detector (Zhang and Cox 1991; Zhang et al. 1993). An algorithm for the reconstruction of water surface elevation from measured surface gradient data is described in some detail. The boundary and noise effects are explored.

Zhang, X, Dabiri D, Gharib M.  1996.  Optical mapping of fluid density interfaces: Concepts and implementations. Review of Scientific Instruments. 67:1858-1868.   10.1063/1.1146990   Abstract

Several ideas of color encoding for surface slope measurements are systematically explored and reviewed to develop a new set of fundamental concepts. It is shown that different systems, such as shadowgraphs, Schlieren optics, and our water surface gradient detectors, can also be universally described through the concepts of sun glitter functions, incident light‐source encoding, and observer encoding. These concepts provide a more precise way of mathematically formulating and physically interpreting the flow visualization images, thereby providing quantitative results. It is this new system of concepts that uncover the quantitative potential of these optical methods. The measurement abilities of various existing optical systems are thus enhanced from qualitative observation or visualization to the well‐defined quantitative measurement. This is a critical step forward. The concepts can also be further extended to measure fluid flows with multiple density layers or flows with continuous density variations. As an example of implementation, the method of measuring a water‐surface gradient is extended into a reflective approach of detecting small changes of surface slope at an air–water interface. In this process, fluid surface slopes (surface gradients) are first optically mapped into color space. An array of lenses is used to transform the rays of an optical light source into a series of colored parallel light beams by passing the light through a group of two‐dimensional color palettes at the focal planes of the lens array. This system of parallel light beams is used to illuminate a free surface of water. The reflected rays from the free surface are captured by a charge‐coupled device color camera located above the surface. The slopes are derived from the color images after the calibration, and surface elevations are obtained by integrating the slopes. This technique is then applied to observe free‐surface deformations caused by near‐surface turbulence interacting with the free surface.

1995
Zhang, X.  1995.  Capillary-gravity and capillary waves generated in a wind-wave tank - observations and theories. Journal of Fluid Mechanics. 289:51-82.   10.1017/s0022112095001236   AbstractWebsite

Short water surface waves generated by wind in a water tunnel have been measured by an optical technique that provides a synoptic picture of the water surface gradient over an area of water surface (Zhang & Cox 1994). These images of the surface gradient can be integrated to recover the shape of the water surface and find the two-dimensional wavenumber spectrum. Waveforms and two-dimensional structures of short wind waves have many interesting features: short and steep waves featuring sharp troughs and flat crests are very commonly seen and most of the short waves are far less steep than the limiting wave forms; waveforms that resemble capillary-gravity solitons are observed with a close match to the form theoretically predicted for potential flows (Longuet-Higgins 1989); capillaries are mainly found as parasitics on the downwind faces of gravity waves, and the longest wavelengths of those parasitic capillaries found are less than 1 cm; the phenomenon of capillary blockage (Phillips 1981) on dispersive freely travelling short waves is also observed. The spectra of short waves generated by low winds show a characteristic dip at the transition wavenumber between the gravity and capillary regimes, and the dip becomes filled in as the wind increases. The spectral cut-off at high wavenumbers shows a power law behaviour with an exponent of about minus four. The wavenumber of the transition from the dip to the cut-off is not sensitive to the change of wind speed. The minus fourth power law of the extreme capillary wind wave spectrum can be explained through a model of energy balances. The concept of an equilibrium spectrum is still useful. It is shown that the dip in the spectrum of capillary-gravity waves is a result of blockage of both capillary-gravity wind waves and parasitic capillary waves.

Zhang, X.  1995.  Color tomography for 3D fluid density inversion. Optical Techniques in Fluid, Thermal, and Combustion Flow. 2546( Cha SS, Trolinger JD, Eds.)., San Diego, CA   10.1117/12.221536   Abstract

The optical method of imaging fluid surface gradient is extended to measure multiple fluid interfaces of refractive index changes. The density of a fluid is a function of the fluid's refractive index. This method may be applied to the study of such flows that are associated with density changes caused by either compressibility, thermal effects, or mixing of fluids of different densities. A lens is used to transform the rays of an optical light source into a series of colored parallel light beams by passing the light through a slide of 2D color patterns at the focal planes of the lens. This system of parallel light beams is used to illuminate through the test section of a fluid volume. The out- going rays of refracted light of different directions are instantaneous recorded by multiple cameras located far away from the test section. The different camera captures different light rays. To observed colors of rays provide measurements of the total volume refraction of the rays. According to ray tracing equations, the images of total fluid volume refraction are then used to estimate the fluid isopycnal surfaces. The color tomography proposed here inverts fluid isopycnal surfaces through the measurements of integrated volume refraction rather than the traditional radiological tomography which studies the body properties through measuring the absorption in the ray-path, or seismic and ocean acoustic tomography which inverts the properties of earth or ocean water body by detecting the travel times of rays between sources and receivers.

Zhang, X, Cox CS.  1995.  Feature correlation for particle image velocimetry: an application of pattern recognition. Optical Techniques in Fluid, Thermal, and Combustion Flow. 2546( Cha SS, Trolinger JD, Eds.).   10.1117/12.221508   Abstract

Particle Image Velocimetry (PIV) has been used successfully for measuring instantaneous two dimensional velocity fields. Analyzing PIV images involves matching particle images captured sequentially. In the usual practice, correlation (auto- or cross-correlation) is used to find the displacement (hence velocity) of the particles within a large number of small 'interrogation areas' in the field of view. An image correlation within an interrogation area is inherently sensitive to the rotation and distortion of the fluid flow within the area, and is also sensitive to the brightness of particles. It can only find the mean spatial offset of particles weighted by their brightness. Rotation, dilation and distortion of fluid flow within the interrogation region and intensity changes of particles introduced correlation errors or bias. As a consequence, the size of the interrogation area and the time interval between images must be kept small to avoid these problems. A feature-recognition method is proposed here for analyzing PIV images. It first extracts structural features of the particle pattern after their locations have been isolated from images. A preliminary process is to replace the particle images by the Cartesian coordinates of particle centers. In this way the brightness of particle images plays no further part, and the point positions are used to establish structural features: topological relations between each point and its neighbors. The interrogation area is defined by a limited number of neighboring points. The size and shape of each interrogation area varies with the distribution of neighbors. A fit to motion, rotation and distortion among the neighbors is then carried out in the space of topological relations of successive images. In this way changes of structural features define fluid spatial translation, rotation, and deformations within each interrogation region. Measurement of feature space in two successive images demands knowledge of the locations of corresponding points derived from individual particles in the two images. Classification of point correspondences, despite confusingly discordant displacements from one image to the next, can be made by taking advantage of physical limitations on the possible movement of particles between the two images. It is found that feature space search and correlation is a much more efficient procedure than correlation operations in the two dimensional image domain.

1994
Zhang, X, Cox CS.  1994.  Measuring the 2-dimensional structure of a wavy water-surface optically - a surface gradient detector. Experiments in Fluids. 17:225-237.   10.1007/BF00203041   AbstractWebsite

A new method of measuring the slopes of a water surface covered with short waves is developed. A camera is placed far above the water surface looking downward so that it receives only approximately vertical rays of light emerging from the water surface from a source below. A large lens is positioned horizontally underwater. A plane light source in the form of a translucent colored screen is placed horizontally in the focal plane below this lens. Corresponding to each value of water surface slope, regardless of observer position, there is one and only one point of origin on the color screen from which light rays can enter the camera. When the color screen has a suitable two-dimensional color pattern, we are able to detect the gradient of the surface elevation throughout the field of view of the camera. This refraction slope detector has been used to find statistical properties of short wind waves in a wind-wave channel where a broad angular beam width of capillary ripples and short gravity waves contribute to the surface slopes. In these experiments waves were generated by winds ranging from 5 m/s to to m/s at a fetch of 24 m. The wavenumber spectra of short wave slopes have two distinguishing features: a dip at the capillary-gravity transition and steep slopes in the capillary range. Surface shapes resembling the shape of solitary capillary-gravity waves have been found from profiles of wave elevation deduced by integration of the elevation gradient.

Zhang, X.  1994.  Wave-number spectrum of very short wind-waves - an application of 2-dimensional Slepian windows to spectral estimation. Journal of Atmospheric and Oceanic Technology. 11:489-505.   10.1175/1520-0426(1994)011<0489:wsovsw>2.0.co;2   AbstractWebsite

A multitaper 2D spectral estimation method is developed for increasing the degree of freedom of the estimation. The core of this method is 2D Slepian eigen windows that are optimum in the sense of minimizing the spectral leakage. Wavenumber spectra of very short wind wave slopes are calculated by this method. The advantages of the multitaper technique are shown by obtaining smooth wavenumber spectra from a limited amount of image data. The data used for the spectral estimation were measured in the laboratory with a water surface gradient detector developed by the authors. Important features of the spatial distribution of short-wave energy are newly revealed: The widening of angular spreading of energy density spectra is not monotonic with increasing wavenumber. There is a local plat region of minimum angular spreading in the spectral band of parasitic capillary waves that suggests that there is another upstream of energy cascade in spite of the energetic gravity-wave spectral peak. The input energy of parasitic waves from energetic long gravity waves with a narrow angular distribution is dominant over energy e down from spectrally close short waves with a broad angular distribution. The omnidirectional energy spectra also show features related to the change of energy spreading. There is a local wave energy maximum of parasitic waves and a local wave energy minimum of gravity-capillary waves.

Zhang, X, Cox CS.  1994.  The spectrum of capillary-gravity and capillary wind waves observed in a wave tank. The Air-Sea Interface : radio and acoustic sensing, turbulence and wave dynamics. ( Donelan MA, Hui WH, Plant WJ, Eds.).:357-365., Miami, Fla.: Rosenstiel School of Marine and Atmospheric Science, University of Miami Abstract
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