Wavy Water Surface Research Articles

Analyzing Visible Light Communication Through Air–Water Interface

In underwater wireless networks (UWNs), conventionally there is no direct communication between an underwater node and a remote command center. A floating base-station is often used to serve as an interface to a UWN; such a base-station would typically have both acoustic and radio modems to communicate with underwater nodes and off-shore centers, respectively. Although employing an airborne base-station would avoid the logistically-complicated surface nodes deployment, communication across the air-water interface becomes the main challenge since it involves two mediums. This paper promotes a novel way to interconnect UWNs to airborne base-stations through visible light communication (VLC) links. The paper analyzes the viability of VLC across the air-water interface by determining the coverage area and intensity inside the water for a light transmitter placed in the air. We show that enough intensity can be achieved for VLC communication even in the presence of a wavy water surface. We then provide guidelines for using single and multiple light sources to establish robust VLC links under rough environmental conditions like high water current and turbidity. Our approach is validated using simulation and a lab experiment is done to validate the simulation result for flat water surfaces.

The Role of the Effect of Shadowing of Some Wavy Regions by Other Wavy Regions in the Formation of an Image of Snell’s Window

The shadowing of some regions of a wavy water surface by other regions can significantly influence the backscattered signal not only in the problem of remote monitoring of a water reservoir at grazing angles (e.g., in radar), but also in the problems of underwater vision. In this work, we present the results of a theoretical study of this phenomenon with respect to the model of underwater imaging of the sky (Snell’s window) near the image boundary. The numerical-simulation method is used to develop the statistically mean image of Snell’s window, which allows for the shadowing effects, and the corrected formula of the estimate of a wave parameter, namely, the water-surface slope variance, is obtained using the value of blurring of the boundary of Snell’s window.

Synthetic imaging through wavy water surface with centroid evolution.

Imaging through a wavy water surface is a challenging task, as the wavy water surface introduces anisoplanatism effects difficult to model and track. A typical recovery method is usually involving multiple-stage processing on a pre-acquired image sequence. A new progressive restoration scheme is demonstrated, it can run simultaneously with image acquisition and mitigate both distortion and blur progressively. This method extends the anisotropic evolution in lucky region fusion with a novel progressive optical flow based de-warping scheme, centroid evolution. A comparison has been made with other state-of-art techniques, the proposed method can create comparable results, even with much less frames acquired. Experiments with real through-water scenes have also proved the effectiveness of the method.

Method to reduce motion artifacts of sequential imaging polarimetry: long enough exposures minimize polarization blurs of wavy water surfaces.

Researchers studying the polarization characteristics of the optical environment prefer to use sequential imaging polarimetry, because it is inexpensive and simple. This technique takes polarization pictures through polarizers in succession. Its main drawback is, however, that during sequential exposure of the polarization pictures, the target must not move, otherwise so-called motion artifacts are caused after evaluation of the polarization pictures. How could these disturbing motion artifacts be minimized? Taking inspiration from photography, our idea was to take the polarization pictures with an exposure that is long enough so that the changes of the moving/changing target can be averaged and, thus, motion artifacts are reduced, at least in a special case when the motion has a stable mean. In the laboratory, we demonstrated the performance of this method when the target was a wavy water surface. We found that the errors of the measured degree and angle of polarization of light reflected from the undulating water surface decreased with increasing exposure time (shutter speed) and converged to very low values. Although various simultaneous polarimeters (taking the polarization pictures at once) are available that do not suffer from motion artifacts, our method is much cheaper and performs very well, at least when the target is a wavy water surface.

The study of the effects of sea-spray drops on the marine atmospheric boundary layer by direct numerical simulation

The detailed knowledge of turbulent exchange processes occurring in the atmospheric marine boundary layer are of primary importance for their correct parameterization in large-scale prognostic models. These processes are complicated, especially at sufficiently strong wind forcing conditions, by the presence of sea-spray drops which are torn off the crests of sufficiently steep surface waves by the wind gusts. Natural observations indicate that mass fraction of sea-spray drops increases with wind speed and their impact on the dynamics of the air in the vicinity of the sea surface can become quite significant. Field experiments, however, are limited by insufficient accuracy of the acquired data and are in general costly and difficult. Laboratory modeling presents another route to investigate the spray-mediated exchange processes in much more detail as compared to the natural experiments. However, laboratory measurements, contact as well as Particle Image Velocimetry (PIV) methods, also suffer from inability to resolve the dynamics of the near-surface air-flow, especially in the surface wave troughs. In this report, we present a first attempt to use Direct Numerical Simulation (DNS) as tool for investigation of the drops-mediated momentum, heat and moisture transfer in a turbulent, droplet-laden air flow over a wavy water surface. DNS is capable of resolving the details of the transfer processes and do not involve any closure assumptions typical of Large-Eddy and Reynolds Averaged Navier-Stokes (LES and RANS) simulations. Thus DNS provides a basis for improving parameterizations in LES and RANS closure models and further development of large-scale prognostic models. In particular, we discuss numerical results showing the details of the modification of the air flow velocity, temperature and relative humidity fields by multidisperse, evaporating drops. We use Eulerian-Lagrangian approach where the equations for the air-flow fields are solved in a Eulerian frame whereas the drops dymanics equations are solved in a Largangain frame. The effects of air flow and drops on the water surface wave are neglected. A point-force approximation is employed to model the feed-back contributions by the drops to the air momentum, heat and moisture transfer.

Polarized X-band Doppler radar scatterometer for investigation of microwave scattering of the wavy water surface in laboratory conditions

The paper describes an experimental model of continuous wave X-band Doppler radar scatterometer (sine frequency modulation) designed for physics investigation of radio waves scattering from sea surface in controlled conditions. The prototype is developed and fabricated at the IAP RAS. Its main feature is adaptation to the conditions of a laboratory modeling in the wind-wave flumes to investigate the dependence of the normalized radar cross-section (NRCS) on the wind speed. The design of the microwave and antenna systems allows measurement of scattered radiation power and its Doppler spectrum both at linear co- and cross-polarizations (in a sequential switching mode). This is important from the viewpoint of studying the waves at high wind speeds. The detailed description of the design and its specifications are presented. Also the problems of calibration and results of experimental operation on the high-speed wind-wave flume of IAP RAS are discussed.

Polarization Patterns of Transmitted Celestial Light under Wavy Water Surfaces

This paper presents a model to describe the polarization patterns of celestial light, which includes sunlight and skylight, when refracted by wavy water surfaces. The polarization patterns and intensity distribution of refracted light through the wave water surface were calculated. The model was validated by underwater experimental measurements. The experimental and theoretical values agree well qualitatively. This work provides a quantitative description of the repolarization and transmittance of celestial light transmitted through wave water surfaces. The effects of wind speed and incident sources on the underwater refraction polarization patterns are discussed. Scattering skylight dominates the polarization patterns while direct solar light is the dominant source of the intensity of the underwater light field. Wind speed has an influence on disturbing the patterns under water.

Direct numerical simulation of a turbulent stably stratified air flow above a wavy water surface

The influence of the roughness of the underlaying water surface on turbulence is studied in a stably stratified boundary layer (SSBL). Direct numerical simulation (DNS) is conducted at various Reynolds (Re) and Richardson (Ri) numbers and the wave steepness ka. It is shown that, at constant Re, the stationary turbulent regime is set in at Ri below the threshold value Ric depending on Re. At Ri > Ric, in the absence of turbulent fluctuations near the wave water surface, three-dimensional quasiperiodical structures are identified and their threshold of origin depends on the steepness of the surface wave on the water surface. This regime is called a wave pumping regime. The formation of three-dimensional structures is explained by the development of parametric instability of the disturbances induced by the surface water in the air flow. The DNS results are quite consistent with prediction of the theoretical model of the SSBL flow, in which solutions for the disturbances of the fields of velocity and temperature in the wave pumping regime are found to be a solution of a two-dimensional linearized system with the heterogeneous boundary condition, which is caused by the presence of the surface wave. In addition to the turbulent fluctuations, the three-dimensional structures in the wave pumping regime provide for the transfer of impulse and heat, i.e., the increase in the roughness of the water–air boundary caused by the presence of waves intensifies the exchange in the SSBL.

Numerical simulation of small-scale mixing processes in the upper ocean and atmospheric boundary layer

The processes of turbulent mixing and momentum and heat exchange occur in the upper ocean at depths up to several dozens of meters and in the atmospheric boundary layer within interval of millimeters to dozens of meters and can not be resolved by known large- scale climate models. Thus small-scale processes need to be parameterized with respect to large scale fields. This parameterization involves the so-called bulk coefficients which relate turbulent fluxes with large-scale fields gradients. The bulk coefficients are dependent on the properties of the small-scale mixing processes which are affected by the upper-ocean stratification and characteristics of surface and internal waves. These dependencies are not well understood at present and need to be clarified. We employ Direct Numerical Simulation (DNS) as a research tool which resolves all relevant flow scales and does not require closure assumptions typical of Large-Eddy and Reynolds Averaged Navier-Stokes simulations (LES and RANS). Thus DNS provides a solid ground for correct parameterization of small-scale mixing processes and also can be used for improving LES and RANS closure models. In particular, we discuss the problems of the interaction between small-scale turbulence and internal gravity waves propagating in the pycnocline in the upper ocean as well as the impact of surface waves on the properties of atmospheric boundary layer over wavy water surface.

Case-Encapsulated Triboelectric Nanogenerator for Harvesting Energy from Reciprocating Sliding Motion

Reciprocating motion is a widely existing form of mechanical motion in natural environment. In this work we reported a case-encapsulated triboelectric nanogenerator (cTENG) based on sliding electrification to convert reciprocating motion into electric energy. Patterned with multiple sets of grating electrodes and lubricated with polytetrafluoroethylene (PTFE) nanoparticles, the cTENG exported an average effective output power of 12.2 mW over 140 kΩ external load at a sliding velocity of 1 m/s, in corresponding to a power density of 1.36 W/m(2). The sliding motion can be induced by direct-applied forces as well as inertia forces, enabling the applicability of the cTENG in addressing ambient vibration motions that feature large amplitude and low frequency. The cTENG was demonstrated to effectively harvest energy from human body motions and wavy water surface, indicating promising prospects of the cTENG in applications such as portable and stand-alone self-powered electronics.

Laboratory investigation of damping of gravity-capillary waves on the surface of turbulized liquid

Investigation of damping of gravity-capillary waves (GCWs) in the presence of turbulence is a classical hydrodynamic problem which has important geophysical applications, one of which is related with the problem of forming a radar and optical image of a ship wake on wavy water surface. In this work a new method for the laboratory study of surface wave damping in turbulized liquid is described and the results are presented. The damping of standing GCWs by turbulence on the water surface in a tank mounted on a vibration table is studied. GCWs and turbulence are excited using a two-frequency mode of vibration table oscillations. A high-frequency small amplitude signal is used for parametric GCW excitation; a low-frequency large amplitude signal is used for generating turbulence due to water flowing through a fixed perforated grid submerged into the tank. The coefficient of GCW damping is determined by measured threshold of parametric excitation of the waves; turbulence characteristics are determined by the PIV and PTV techniques. Dependences of GCW damping coefficients on their frequency at different turbulence intensities are obtained, estimates for turbulent viscosity are presented, and a comparison with empirical models proposed earlier is performed.

Momentum and buoyancy transfer in atmospheric turbulent boundary layer over wavy water surface – Part 2: Wind–wave spectra

Abstract. Drag and mass exchange coefficients are calculated within a self-consistent problem for the wave-induced air perturbations and mean velocity and density fields using a quasi-linear model based on the Reynolds equations with down-gradient turbulence closure. This second part of the report is devoted to specification of the model elements: turbulent transfer coefficients and wave number-frequency spectra. It is shown that the theory agrees with laboratory and field experimental data well when turbulent mass and momentum transfer coefficients do not depend on the wave parameters. Among several model spectra better agreement of the theoretically calculated drag coefficients with TOGA (Tropical Ocean Global Atmosphere) COARE (Coupled Ocean–Atmosphere Response Experiment) data is achieved for the Hwang spectrum (Hwang, 2005) with the high frequency part completed by the Romeiser spectrum (Romeiser et al., 1997).

Momentum and buoyancy transfer in atmospheric turbulent boundary layer over wavy water surface – Part 1: Harmonic wave

Abstract. The surface-drag and mass-transfer coefficients are determined within a self-consistent problem of wave-induced perturbations and mean fields of velocity and density in the air, using a quasi-linear model based on the Reynolds equations with down-gradient turbulence closure. Investigation of a harmonic wave propagating along the wind has disclosed that the surface drag is generally larger for shorter waves. This effect is more pronounced in the unstable and neutral stratification. The stable stratification suppresses turbulence, which leads to weakening of the momentum and mass transfer.

Specular scattering of light on cloud ice crystals and wavy water surface

Specular scattering is observed as a bright glint formed upon light reflection from cirrus clouds, snow cover, and a wavy water surface. Analytical expressions uniting specular scattering both on a set of particles and on a continuous surface have been obtained. Conditions that make it possible to identify the type of the scattering medium by the form of the differential cross section in problems of remote sensing have been determined.

An experimental investigation on the effects of surface gravity waves on the water evaporation rate in different air flow regimes

Estimating rate of evaporation from undisturbed water surfaces to moving and quiet air has been the topic a vast number of research activities. The obvious presence of various shapes of gravity waves on the water body surfaces was the motivation of this experimental investigation. In this investigation experimental measurements have been done to quantify evaporation rate from wavy water surfaces in free, mixed and forced convection regimes. The effects of a wide range of surface gravity waves from low steepness, round shaped crest with slow celerity, to steep and very slight spilling crest waves, on the water evaporation rate have been investigated. A wide range of \({\text{Gr}}/{\text{Re}}^{2} (0.01 \le {\text{Gr}}/{\text{Re}}^{2} \le 100)\) was achieved by applying different air flow velocities on a large heated wave flume equipped with a wind tunnel. Results reveal that wave motion on the water surface increase the rate of evaporation for all air flow regimes. For free convection, due to the effect of wave motion for pumping rotational airflows at the wave troughs and the dominant effect of natural convection for the air flow advection, the maximum evaporation increment percentage from wavy water surface is about 70 %. For mixed and forced convection, water evaporation rate increment is more sensitive to the air flow velocity for the appearance of very slight spilling on the steep wave crests and the leeward air flow structures.

On observing underwater objects through a wavy water surface: A new algorithm for image correction and laboratory experiment

The possibility of correcting refraction distortions in images of the sea bottom or an underwater object observed through a wavy water surface is studied. A fast-operating algorithm of recovering the “regular” image by its random realization and spatial distribution of surface slopes at the instant of observation has been proposed and approbated. A technique of determining surface slopes by the surface image with the following correction of the underwater object image based on the data about the surface slopes has been developed under conditions of a laboratory experiment.

Water Surface Topography Retrieved from Color Images*

Abstract Submerged objects viewed through wavy water surfaces appear distorted by refraction. An imaging system exploiting this effect is implemented using a submerged planar light source designed so that color images reveal features of small-amplitude waves in a wind-wave tank. The system is described by a nonlinear model of image formation based on the geometry of refraction, spectral emission from the light source, radiative transfer through the water and surface, and camera spectral response. Surface normal vector components are retrieved from the color image data using an iterative solution to the nonlinear model. The surface topography is then retrieved using a linear model that combines surface normal data with a priori constraints on elevation and curvature. The high-resolution topographic data reveal small-amplitude waves spanning wavelength scales from capillary through short gravity wave regimes. The system capabilities are demonstrated in the retrieval of test surfaces, and of a case of wind-driven waves, using data collected at high spatial and temporal resolution in a wave tank. The approach of using a physical model of image formation with inverse solution methods provides an example of how surface topography can be retrieved and may be applicable to data from other similar instruments.

Glints from particulate media and wavy surfaces

Glints are bright light spots created by particulate media like cirrus clouds, glaciers, and wavy water surfaces. They are seen around the specular reflection angle. In this paper, the glints from such scattering/reflecting media are described in a unified manner through the probability density for facet tilts. Various kinds of these probability densities for wavy surfaces are defined and classified. The concept of the differential scattering cross section (DSCS) for rough surfaces instead of the conventional bidirectional reflectance distribution function (BRDF) is introduced for characterization of the glints. The simple equations connecting the DSCS and the probability densities for facet tilts are derived. It is shown that the glints from particulate media and wavy surface are very similar at small incidence angles and they are significantly different at slant incidence.

Direct numerical simulation of a turbulent wind over a wavy water surface

Parameterization of the wind‐water‐waves interaction is a key problem of the air‐sea system modeling. Of most importance are water waves with sufficiently large steepness, when nonlinear effects related to the boundary layer separation and vortex generation in the wind flow are well pronounced. Known experimental techniques (contact methods and particle image velocimetry) are not yet able to provide a full, detailed understanding of the wind flow in the viscous sublayer and the buffer region. As an alternative, we consider direct numerical simulations (DNS). In the present paper we discuss numerical algorithm and results of DNS of a turbulent wind flow over a wavy water surface. Waves with maximum steepness of ka = 0.2, wave age 0 < c/u* < 10, and Reynolds number Re = 15,000 are considered. Full, 3‐D Navier‐Stokes equations are solved in curvilinear coordinates in a reference frame moving with the wave phase speed c. DNS results show that an instantaneous velocity field is characterized by the presence of well‐pronounced separation zones in the vicinity of the wave crests whereas the average velocity field is nonseparating. We also perform a comparison of the DNS results with the predictions of a theoretical quasi‐linear model of the wind‐wave interaction.

Statistical Parameters of the Air Turbulent Boundary Layer over Steep Water Waves Measured by the PIV Technique

Abstract A turbulent airflow with a centerline velocity of 4 m s−1 above 2.5-Hz mechanically generated gravity waves of different amplitudes has been studied in experiments using the particle image velocimetry (PIV) technique. Direct measurements of the instantaneous flow velocity fields above a curvilinear interface demonstrating flow separation are presented. Because the airflow above the wavy water surface is turbulent and nonstationary, the individual vector fields are conditionally averaged sampled on the phase of the water elevation. The flow patterns of the phase-averaged fields are relatively smooth. Because the averaged flow does not show any strongly nonlinear effects, the quasi-linear approximation can be used. The parameters obtained by the flow averaging are compared with the theoretical results obtained within the theoretical quasi-linear model of a turbulent boundary layer above the wavy water surface. The wave-induced pressure disturbances in the airflow are calculated using the retrieved statistical ensemble of wind flow velocities. The energy flux from the wind to waves and the wind–wave interaction parameter are estimated using the obtained wave-induced pressure disturbances. The estimated values of the wind–wave interaction parameter are in a good agreement with the theory.