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Turbulent entrainment across a density interface is studied in a laboratory wind–wave tank in which a stably stratified system consisting of two homogeneous fluid layers is introduced. The results indicate that the rate of change of the potential energy of the mixing layer is proportional to the rate of work done by the wind. However, only a very small fraction of the work done by the wind is used for interfacial mixing or developing a seasonal thermocline. A formula relating the entrainment rate to the density stratification and the wind-friction velocity is derived from the experimental results.

A boundary-layer survey has been conducted on a rough plate consisting of uniform spherical particles arranged in a random and compact fashion. Strong turbulent mixing was observed in a region within a quarter of the particle size from the top of the particles. Such mixing is important to transfer or transport processes near a rough wall. The data of the normal axis of the present rough surface are found to be located at a distance of 1/50 of the particle diameter below the top of the particles. This reference data are different from that used by Nikuradse, indicating a possible modification of some numerical constants determined by Nikuradse.

A practical procedure is outlined for determining wind-induced drift currents near the free surface, at all fetches, from a single wind-velocity measurement. The wind stress is scaled according to the Froude number and the momentum flux of the wind is considered to be partitioned between the wave drag and the momentum flux of the current. Some coefficients involved in the procedure are derived from the available data; further studies are suggested to refine the present estimation.

Drag reduction caused by ejecting additive solutions from a slot into a pure-water boundary layer on a flat plate has been systematically studied. Results include drag measurements for a plane boundary, smooth and rough, with various openings of the slot and with various concentrations and discharges of the ejected additive solution. Conclusions have been drawn on the additive requirement in external flows and on the ejection technique for an optimum drag reduction.

Turbulent diffusion in high molecular weight additive solutions was measured and compared on a laboratory scale by observing the axisymmetric spreading of a cylindrical turbulent cloud in these solutions of various concentrations. Significant suppression of turbulence in additive solutions was observed. The trend of the results as a function of additive concentrations is similar to that of the additive reduction of turbulent frictional resistance.

The present study consists of wind profile surveys, drift current measurements and water surface observations for a wide range of wind velocities in a wind–wave tank. It is confirmed that the velocity distribution essentially follows the logarithmic law near the water surface and the velocity-defect law toward the outer edge of the boundary layer. The wind stresses and surface roughnesses calculated from these distributions are divided into two groups separated by the occurrence of the wave-breaking phenomenon. For low wind velocities the surface roughness is dictated by ripples, and the wind-stress coefficient varies with U0−½, where U0 is the free-stream wind velocity. The surface roughness is proportional to the average height of the basic gravity wave at higher wind velocities; the stress coefficient is then proportional to U0. In addition, it is found that Charnock's expression (k ∝ u*2/g) holds only at high wind velocities, and that the constant of proportionality determined from the present experiment correlates very well with field observations. A new technique, involving the use of various-sized surface floats to determine the drift current gradient and the surface drift current, has been developed. A good agreement is shown between the gradients obtained from the measured currents and those determined from the wind stresses. Finally, the wind-stress coefficient is shown to be larger than the friction coefficient for turbulent flow along a solid rough surface; the difference is shown to be the wave drag of the wind over the water surface.

An experiment has been conducted modelling a two-dimensional mixed region collapsing in a continuously density-stratified medium. The process of collapse can be divided into three stages. Empirical formulae have been derived to describe the process of the first two stages, during which gravitational effects determine the modelling criterion. The collapse in the final stage is complicated by viscous effects; a ratio between the Froude number and the Reynolds number seems to provide a probable modification of the time scale.The pattern of internal waves generated by the initial impulsive collapse of this mixed region can be represented by moving rays connecting either wave crests or troughs. These rays move away from the collapse centre and at the same time decrease their slopes from the horizontal. A simpler steady-state wave pattern generated by an oscillating plunger has also been studied. Taken together, these experimental results are interpreted to show that the energy density of the collapse is skewed toward high frequencies and is peaked at 8/10 of the Brunt-Väisälä frequency of the medium.

An analysis is given of relevant physical scales on which coupling takes place between long and short waves, and dynamic scales for coupling of wind and waves, in the generation of wind waves. Based on these scales and on a separation criterion, it is argued that the airflow separates from dominant waves in the laboratory and from ripples superimposed on dominant waves in the field. This difference may account for the discrepancy between the laboratory-determined growth rate and that observed in the field. Finally, some consideration is given to observational evidence and critical scales relating to the nonlinear mechanism for wave generation.

Based on the compiled data of thirty independent oceanic observations, this article systematically presents the wind-stress coefficient, the surface roughness, and the boundary layer flow regime at the air-sea interface under various wind conditions. The air flow near the water surface is shown to be aerodynamically rough or in the transition region except at a very low wind velocity (U10 < 3 m/sec). Both the wind-stress coefficient and the surface roughness are found to increase with the wind velocity when U10 is less than 15 m/sec and to reach a saturated value for U10 greater than 15 m/sec. From the oceanic wave observations, the presence of this discontinuity at U10 = 15 m/sec is found to be due to an increase in the wind velocity (measured at the significant wave amplitude above the mean water level) beyond the average wave phase velocity. This finding provides a well-defined separation for the often quoted terms ‘light’ and ‘strong’ winds. The compiled data also show that the surface roughness is governed by the amplitude of the short gravity waves. Charnock's relationship is shown to be applicable to most of the oceanic data and Charnock's proportionality constant is determined, η/(u*2/g) = 0.0156. Finally, two approximate formulas for the windstress coefficient C10 = 0.5 × U101/2 × 10−3 for light wind and C10 = 2.6 × 10−3 for strong wind are suggested for oceanic applications.

Following the verification of the logarithmic nature of the wind profile and the establishment of a non-dimensional expression relating the shear velocity and surface roughness, a Froude number is proposed for scaling the wind stress at the air-water interface. A correlation curve for wind stresses determined at all fetches is presented and is shown to interrelate successfully the available data compiled from 42 independent investigations consisting of 12 laboratory studies and 30 oceanic observations.

The longitudinal dispersion coefficient in a wide channel is calculated under various combinations of streamflow and wind conditions. The effect of wind, which produces drift currents in the stream, on dispersion has hitherto been neglected. The results obtained here, especially the difference in dispersion coefficients obtained under upstream and downstream wind conditions, may partially explain the wide scatter of field data. This difference further indicates the importance of choosing the ejection site on the basis of the prevailing wind conditions and of considering environmental conditions beyond stream factors alone.

The intrusion of salt water into tideless estuaries is of great interest to hydraulic and coastal engineers. Extensive laboratory studies on two important aspects of the problem were carefully conducted by Keulegan. His first series of experiments on the arrested salt wedge (a still form which is established as the intrusion ceases) have a direct bearing on the natural occurrence. His second series of experiments on the motion of saline fronts in still water extends the understanding of the mechanism governing density currents. Considering his other findings from these experiments, two of Keulegan’s most important results are regrouped herein by replacing the water depth with the hydraulic radius as the length scale in the Reynolds number which characterizes the resistance to intrusion. This regrouping seems to offer a much better correlation of results obtained from experiments conducted in channels with various width-depth ratios.

An optical instrument, utilizing a light reflection principle, has been designed which is capable of determining not only surface slope, but also surface curvature distribution. This instrument has been successfully tested in laboratory studies of wind generated waves. Some sample results are included to illustrate the applicability of the instrument.

A laser and phototransistor unit has been developed to measure spray produced in a laboratory wind wave tank. Under a given wind velocity, the droplet concentration is found to decrease in a power law form with the elevation above mean water surface; the exponent varies inversely with the friction velocity of the wind. At a given elevation, the droplet concentration increases exponentially with the wind velocity, and the spray at a higher elevation above the water surface initiates at a greater wind velocity. The droplet-size distribution curves drop off very rapidly and similarly for diameters greater than 200 μ. The speed of the droplet approaches the wind velocity, and the spray stress is negligible in comparison with the wind stress.

Extending previously proposed Froude scaling of wind stress coefficients, the paper suggests the appropriate anemometer heights for different wind fetches, and proposes a procedure of obtaining the wind stress by a single wind velocity measurement at this suggested anemometer height. The procedure consists of first estimating the fetch Renynolds number and then obtaining a tentative anemometer height from a prepared figure. Setting the anemometer at this height, an accurate wind velocity is measured; from this measurement and knowledge of the wind fetch, a corrected anemometer height can then be determined. Having the wind velocity measured at this final anemometer height, the wind stress coefficient can be obtained from another prepared figure.

Further analysis of Untersteiner and Badgley's data indicates that the wind boundary layer over the upper surface of sea ice is generally in either the transition region or the hydrodynamically rough regime. The upper surface is actually rougher hydrodynamically at lower wind velocities, which suggests that surface configurations of floes may change with wind conditions. The current boundary layer developed along the lower surface of the sea ice is always in the hydrodynamically rough regime. Finally, the large deviation of results obtained from different sites indicates that the roughness length and resistance coefficient of sea ice may vary with the macroscale of the boundary layer and the surface condition of the floes.

The evaporation due to spray, produced in a laboratory wind-wave tank, is calculated from the measured droplet concentration and is found to increase drastically with the wind velocity.

The thickness of the oceanic thermal layer is considered to be one-half of the viscous-sublayer thickness, which decreases as the wind velocity increases. The thermal-layer thickness is estimated to be between 4 and 0.25 mm for light winds and between 0.25 and 0.1 mm for strong winds.

A series of measurements of the turbulent drag on a flat plate using homogeneous solutions of high-molecular-weight additives, and a series of visual studies concerning diffusion and entrainment of jets with additive solutions flowing into a turbulent stream of pure Water have been conducted. The experiments include tests with additive solutions of various concentrations and different channel velocities. The drag reduction obtained in these experiments is generally lower than that for pipe flows without taking into account differences in experimental Reynolds numbers; however, the maximum reduction occurs at about the same concentration (50–100 ppmw) in both cases. A comparison between the ejection study (studies with additive solutions ejected into a pure water boundary layer) data and the present results indicates very poor mixing between the ejected fluid and its surroundings. Photographs of submerged jets confirm that additives suppress turbulent diffusion. The flat plate results also suggest that for efficient drag reduction, the solution ejected into the boundary layer should be dilute and that the rate of ejection should be comparable to the discharge within the inner boundary layer (the wall controlled region). These findings suggest that smaller amounts of additive are needed for ejection than are usually estimated, and therefore brighten the hope for the practical application of additives to achieve drag reduction in external flaw cases, such as on a ship hull.

Drag reduction caused by ejecting additive solutions from a slot into a pure-water boundary layer on a flat plate was systematically studied. Results include drag measurements for a plane boundary, smooth and rough, with various openings of the slot and with various concentrations and discharges of the ejected additive solution. Conclusions were drawn on the additive requirement in external flows and on the ejection technique for an optimum drag reduction.

The effects on evaporation rates of the suppression of small waves by monolayers, which heretofore have been neglected, are considered to be a major mechanism for retarding evaporation under wind.

The sudden rise of spray droplet concentration and the occurence of the wind-stress discontinuity are found at about the same wind velocity of 15 m/sec.

A criterion proposed earlier for determining airflow separation from wind waves and a previously determined relationship between surface roughness and wind stress are herein correlated. The results indicate that the airflow boundary layer is developed due to the form drag provided by wavelets (surface roughness) superimposed on big waves. Based on the magnitudes of surface roughness, viscous‐sublayer thickness and critical height, the mechanisms of wind‐wave generation are discussed.

The measured mean‐square slope of the sea surface is shown to vary logarithmically with the wind velocity, and the rates of variation change with different boundary‐layer regimes of the wind. Based on mean‐square slope data, the form of a newly proposed equilibrium wind‐wave spectrum for the capillary range is verified, the spectral coefficients for both gravity and capillary ranges are determined, and the cutoff wavenumber for the slope data is shown to be much smaller than the neutrally stable wavenumber obtained from laminar model. Finally, an approximate correlation is presented between the mean‐square slope and the roughness height of the sea surface, implying that the growth of small waves is mainly due to the direct action of the wind.

The microstructure of the wind-disturbed water surface, characterized by surface-slope and surface-curvature distributions, is studied in a laboratory tank with a newly developed optical instrument. Some features of these distributions under various wind and wave conditions are systematically presented. It is also shown that wind waves arise at about the time when the airflow boundary layer becomes turbulent. At lower wind velocities, the formation of parasitic waves causes a skewed slope distribution; at high wind velocities, the wave breaking causes a peaked slope distribution. With a turbulent wind, similar variation of the mean-square slope with the shear velocity is shown in the present laboratory results and in older oceanic data, suggesting that the laboratory facility may be able to simulate the microstructure of the air–sea interface.

Glitter photographs illustrate an important phenomenon on interactions between short and long waves: long waves sweep through short waves, causing the short waves to break on the forward face of the long wave crests.DOI: 10.1111/j.2153-3490.1971.tb00582.x

The curvature distribution of the wind-disturbed water surface in a laboratory tank is observed from different angles with an optical instrument. The distribution is generally skewed with greater radius of curvature at steeper viewing angles from the normal to the mean water surface. As the wind velocity increases, the average radius of curvature decreases: rapidly at low wind velocities when waves are effectively excited by wind, and gradually at high wind velocities when waves approach saturated state.