Measurements of Waves in a Wind-wave Tank Under Steady and Time-varying Wind Forcing

Since ancient times, it has been well known that waves on water surfaces are excited by wind. The current understanding of the physical mechanisms that govern this process is far from satisfactory. Numerous theories attempting to describe wind-wave generation were proposed over the years^1,2,3,4, however their reliable experimental validation is not yet available. Measurements of random wind-waves in the ocean are extremely challenging due to unpredictable wind that may vary quickly in direction as well as in magnitude. Laboratory experiments have the advantage of controllable conditions that enable prolonged and repeatable measurements.

Under steady wind forcing in the laboratory environment, wind-waves evolve in space. Early laboratory experiments on waves under steady forcing performed decades ago were limited to instantaneous surface elevation measurements^5,6,7,8. More recent studies also employed various optical techniques to measure instantaneous water surface inclination angle, such as LSG^9,10. Those measurements allowed getting some limited qualitative information on the three-dimensional structure of wind-wave fields. When wind forcing is unstable, as it is in field experiments, additional complexity is introduced to the problem of water waves' excitation by wind, since the statistical parameters of the resulting wave field vary not just in space but in time as well. The attempts made so far to describe wave evolution patterns qualitatively and quantitatively under time-dependent forcing were only partially successful^{11,12,13,14,15,16}. The relative contribution of different plausible physical mechanisms that may lead to excitation and growth of waves due to wind action remains largely unknown.

Our experimental facility was designed with the purpose of enabling the accumulation of accurate and diverse statistical information on the variation of wind-wave field characteristics under either steady or unsteady wind forcing. Two major factors facilitated carrying out these detailed studies. First, the modest size of the facility results in relatively short characteristic evolution scales in time and space. Second, the whole experiment is fully controlled by a computer, thus enabling the performance of experimental runs under different experimental conditions automatically and practically without human intervention. These features of the experimental set-up are of crucial importance in performing experiments on waves excited from rest by impulsive wind.

Spatial growth of wind-waves under steady forcing has been studied in our facility for a range of wind velocities¹⁷. Results were compared with growth rate estimates based on the Miles¹⁸ theory as presented by Plant¹⁹. The comparison revealed that the experimental results differ notably from the theoretical predictions. Additional important parameters were also obtained in¹⁷, such as mean pressure drop in the test section, as well as the absolute values and phases of characteristic static pressure fluctuations. The shear stress at the air-water interface is essential for characterization of momentum and energy transfer between wind and waves^17,19. Therefore, detailed measurements of the logarithmic boundary layer and the turbulent fluctuations in the air flow above water waves were performed at numerous fetches and wind velocities²⁰. The values of the friction velocity u_* at the air-water interface determined in this study were used to obtain dimensionless statistical parameters of the wind-waves measured in our facility²¹. These values were compared with the corresponding dimensionless parameters obtained in larger experimental installations and field experiments. It was demonstrated previously²¹ that with proper scaling, the important characteristics of the wind-wave field obtained in our small-scale facility do not differ significantly from the corresponding data accumulated in larger laboratory installations and open sea measurements. These parameters include spatial growth of the representative wave height and wave length, the shape of the frequency spectrum of the surface elevation, as well as the values of higher statistical moments.

The subsequent studies carried out in our facility^22,23 showed that wind waves are essentially random and three-dimensional. To get a better insight into the 3D structure of wind waves, an attempt was made to perform quantitative time-dependent measurements of water surface elevation over an extended area using stereo video imaging²². Due to inadequate computer power available at present and processing algorithms that are not yet sufficiently effective, these attempts proved to be only partially successful. However, it was demonstrated that combined use of a conventional capacitance-type wave gauge and the LSG provides valuable information on the spatial structure of wind waves. Simultaneous application of both those instruments enables independent measurements with high temporal resolution of the instantaneous surface elevation and of the two components of the instantaneous surface slope²³. These measurements allow estimation of both the dominant frequency and dominant wave length of the waves, as well as providing insight into the wave structure in the direction normal to the wind. A pitot tube, which can be moved vertically by a computer-controlled motor, complements the set of sensors and is used for measurements of wind velocity.

All those studies made clear that randomness and three-dimensionality of wind waves result in significant variability of the measured parameters even for steady wind forcing and a single measuring location. Thus, prolonged measurements with duration commensurate with the characteristic time scales of the measured wave field are needed to accumulate sufficient information for extracting reliable statistical quantities. To gain valuable physical insight into the mechanisms governing spatial variation of the wave field, it is imperative to carry out measurements at numerous locations and for as many values of the wind flow rate as possible in the test section. To achieve this goal, it is thus highly desirable to apply an automated experimental procedure.

Experiments on waves excited by unsteady wind forcing introduce an additional level of complexity. In such studies, it is imperative to relate the instantaneous measured parameters to the instantaneous level of the wind speed. Consider experiments on waves excited from rest by a nearly impulsive wind forcing as an important example. In this case, numerous independent measurements are needed of the wind-wave field evolving under the action of wind that varies in time following the same prescribed pattern²⁴. Meaningful statistical parameters, expressed as a function of time elapsed since the initiation of air flow, are then calculated by averaging the data extracted from the accumulated ensemble of independent realizations. This undertaking may involve tens and hundreds of hours of continuous sampling. The total duration of experimental sessions required to accomplish such an ambitious task renders the whole approach unfeasible, unless the experiment is fully automated. No such fully computerized experimental procedure in wind-wave facilities has been developed until recently. That is among the main reasons for the lack of reliable statistical data on wind waves under unsteady forcing.

Since the facility used for the experiment is not constructed from commercially available, off-the-shelf hardware, a brief description of its main parts is provided here.

Figure 1. Schematic (not to scale) view of the experimental facility. 1 – blower; 2 – inflow settling chamber; 3 – outflow settling chamber; 4 – silencer boxes; 5 – test section; with a 6 – beach; 7 – heat exchanger; 8 – honeycomb; 9 – nozzle; 10 – wavemaker; 11 – flap; 12 – instrument carriage; 13 – wave gauge driven by a stepper motor; 14 – Pitot tube driven by a stepper motor. Please click here to view a larger version of this figure.

The experimental facility consists of a closed loop wind tunnel mounted over a wave tank (a schematic view is shown in Figure 1). The test section is 5 m long, 0.4 m wide, and 0.5 m deep. The sidewalls and floor are made of 6 mm thick glass plates and are enclosed within a frame made of aluminum profiles. A 40-cm long flap provides a smooth expansion of the airflow cross-section from the nozzle to the water surface. Wave energy absorbing beach made of porous packing material is located at the far end of the tank. A computer-controlled blower allows attaining mean air flow velocity in the test section up to 15 m/s.

The custom-made capacitance-type 100 mm-long wave gauge is made of anodized tantalum. 0.3 mm wire is mounted on a vertical stage driven by a PC-controlled step motor designed for wave gauge calibration. A Pitot tube with a diameter of 3 mm is used for measuring the dynamic pressure in the central airflow part of the test section.

The LSG, measuring instantaneous 2D water surface slope, is installed on a frame detached from the test section that can be positioned at any location along the tank (Figure 2). LSG consists of four main parts: a laser diode, a Fresnel lens, a diffusive screen, and a Position Sensing Detector (PSD) assembly. The laser diode generates a 650 nm (red), 200 mW focusable laser beam with diameter of about 0.5 mm. The 26.4 cm diameter Fresnel lens with focal length of 22.86 cm directs the incoming laser beam to the 25 x 25 cm² diffusive screen located in the back focal plane of the lens.

Figure 2. Schematic view of the Laser Slope Gauge (LSG). 1 – laser diode; 2 – Fresnel lens; 3 – diffusive screen; 4 – Position Sensor Detector (PSD). Please click here to view a larger version of this figure.

This protocol describes the procedure that allows performing experiments in which numerous parameters characterizing unsteady waves are measured simultaneously under time-dependent wind forcing. The procedure can be adjusted to any desired dependence of wind velocity on time that can be attained in view of the technical limitations of the experimental facility. The present protocol describes specifically experiments in which in every realization, wind starts nearly impulsively over initially calm water. The steady wind forcing then lasts for long enough that the wind-wave field everywhere in the test section attains quasi-steady state. The wind eventually is shut down, again nearly impulsively. At all stages, multiple wave parameters are recorded. The procedure that allows computation of numerous statistically representative ensemble-averaged quantities characterizing the instantaneous local wind-wave field is novel, and was developed in the course of recent experiments carried out in our facility^22,23,24.