Experimental investigation of multiphase hydrodynamics of the ocean-atmosphere boundary layer within laboratory modelling

. Laboratory modelling of the processes of interaction between the atmosphere and ocean in the boundary layers is one of the most interesting from the point of view of the features of the hydrophysical experiment. The main characteristics that need to be controlled in these experiments include, first of all, the air velocity field over the rough surface waves and the underwater flow, as well as the shape of the free surface. However especial features as spray of droplets, the bubbles in the water and foam generated during the breaking of waves should also be taken into account when modelling extreme weather conditions associated with strong winds. Thus, from the point of view of experimental hydrodynamics, we are dealing with a multiphase turbulent flow with a free boundary. For purpose of experimental study on the wind-wave flume, an integrated approach is required that allows simultaneous measurements of the velocity flow fields, the sizes of droplets and bubbles, the shape of waves and parameters of foam coverage. Contact methods often do not allow for universality. This review study describes developing approaches to the use of optical methods for performing these studies. Presented results were obtained in experiments carried out on several wind-wave flumes. To study the processes of fragmentation of the water surface leading to the formation of droplets an foam, high-speed multi-angle video taking is used in combination with the shadow imaging method.


Introduction
The boundary layer between the atmosphere and hydrosphere (first of all the world ocean is meaning) of our planet is characterized by a huge number of various physical processes.From [1] a schematic representation is given, systematizing the numerous physical processes of the interaction of the atmosphere and the hydrosphere (see Fig. 1).

Fig. 1.
Picture illustrating air-sea interaction from the website of Center on Air-Sea Interaction and Marine Atmospheric Sciences at Woods Hole Oceanographic Institution (see https://www2.whoi.edu/site/casimas/) It is clear from it that all physical processes in the atmosphere and hydrophysical processes of the ocean cannot be separated from each other, and they are closely interconnected.For example, the wind in the marine boundary layer of the atmosphere accelerates the waves, while the aerodynamic drag coefficient (characterizing the momentum exchange in the boundary layer) from the sea surface depends on the wave parameters, which vary greatly not only in space but also in time, unlike similar processes over a solid land surface.Depending on the amplitude of the wind speed and the scale of its spatiotemporal variability, characterizing the fetch parameter, regular wave collapse can occur, with the formation of whitecap zones and foam crests, the generation of sprays and the involvement of air in water with the formation of bubbles that float and break the surface, also lead to splashing.Small micron-sized droplets carried away by the wind can levitate for a considerable time in the air, rising to considerable heights and forming a marine aerosol.Large drops, on the other hand, fall back onto the water surface and can "give birth" to small sprays.Spray significantly intensifies heat transfer compared to a smooth water surface, and therefore they are called "fuel" for hurricanes.Foam, also formed during the breaking of waves, also strongly affects the exchange of momentum and heat in the boundary layer.The collapse of waves under the influence of wind leads to the generation of turbulent flows and the intensification of mixing in the surface layer.This is one of the main mechanisms of the formation of the temperature distribution -stratification in the water column, which in turn determines the temperature regime of the ocean, heat transfer with the atmosphere.Various relationships and chains can still be built quite a lot, but it is obvious that from the point of view of the tasks of experimental research of the processes of interaction between the atmosphere and the hydrosphere, the main problem is the need to simultaneously measure as many physical characteristics as possible with high spatial and temporal resolution, in a wide range of conditions including extreme (storms, hurricanes, etc.). it is quite difficult to solve this problem during in situ measurements.Therefore it is actively resorted to laboratory modeling, creating large-scale experimental facilities -wind-wave channels, see Fig. 2. At these facilities they are trying to realize conditions close to natural.However, in addition to realizing the conditions, it is also necessary to provide measurements of various quantities characterizing physical processes in the air flow, at the interface and processes in the water layer.Now, if we consider this problem from the point of view of a laboratory aero/hydrodynamic experiment, we can conclude that it is necessary to study the turbulent process of wind-wave interaction, dealing with a complex dynamic interface between the liquid (water) and gas (air) phases.Among the main problems, it should be highlighted: 1) the need for measurements in air and water close to the interface, which varies significantly in space and time depending on the characteristics of the wind and waves 2) the need for measurements with high spatial and temporal resolution to obtain the necessary ensemble of data for subsequent statistical processing 3) the multiphase nature of the air and water flows due to the formation of sprays and underwater bubbles in strong winds with regular breaking waves.Such studies on wind-wave facilities require significant modernization and adaptation of standard, as well as the development of new methods of laboratory aero/hydrodynamic experiment.Optical methods based on visualization of flows compares favorably point measurements.It allows simultaneous observations in significant volumes of continuous media with high spatial resolution, and also do not introduce disturbances into the medium under study.Another important advantage of optical measurement methods is universality, which consists in the possibility of their application (without significant change) for the study of different processes, the characteristic spatial and temporal scales of which vary over a wide range.The present work is devoted to the history of development and application of these methods and recent results for the comprehensive study of the processes of interaction of the air flow with an rough water surface under laboratory modeling of extreme weather conditions, primarily associated with strong winds.Field measurements in such conditions are very difficult.That is why this study with laboratory modeling focused on the measurements of sprays and foam coverage under which are the features of the boundary layer under severe conditions, the measurements of which are often more complicated than the measurements of the characteristics of flows in the surface water layer.At high wind speeds, regular wave breaking begins with the fragmentation of the water surface, leading to the generation of sprays and the formation of foam on the surface.The first part of the work is devoted to the study of the processes of generation of spray droplets from the rough surface, and their characteristics.The background of research and the current state are described.The second is to study the characteristics of the foam and methods for its artificial creation in laboratory experiments (the results of recent studies are presented).

Investigation of spray within laboratory modelling of the interaction between atmosphere and hydrosphere
Sea sprays are typical element of the marine atmospheric boundary layer and important environmental effect.Difficulties of direct measurements in hurricane conditions and insufficient knowledge about the mechanisms of the spume droplet's formation are the main reasons for insufficient knowledge on the SSGF, which characterizes the size distribution of droplets injected from a unit of surface in a unit of time, leading to significant uncertainties in estimations of sea sprays influence on the marine atmospheric boundary layer [2,3].For example, the empirical function of spray generation may differ by six orders of magnitude based on different observation reports (see a review of experimental data in [4,5]).Even the spray-generation mechanisms in extreme winds remained undetermined up to present time.Such difficulties are primarily associated with the problems of obtaining a sufficient amount of empirical data not only in field, but also in laboratory modeling.The development of methods for measuring the characteristics of sprays in laboratory modeling can be considere be considered as competition between point methods and panoramic methods based on visualization and photo/video filming.Initially, the main source of information about the quantitative characteristics of the spray of droplets generated during fragmentation of the water surface within wind-wave interaction was the measurement results basing on the point methods (see Fig. 3).In [6], the technique of electric wire microgauges was used, similar to hot-wire anemometric sensors, the principle of which was to register an abrupt increase in voltage (decrease in resistance) when droplets hit the sensor.In a similar study [7], a sensor was used based on charge transfer during the contact action of a drop on a wire under high voltage, which causes charge transfer and a voltage drop.In [8], a laser-optical sensor was proposed that works in light when shaded by droplets crossing its beam.It allows to to evaluate not only the size, but also the speed of the droplet in contrast to the previous ones.The electronic and optical sensors listed above had rather low accuracy and allowed measuring only sufficiently large particles (low threshold from 50-100 μm depending on the work), although they outperformed the measurement methods based on photo / video shooting in similar experiments at the same time.The measurements were also carried out for weak to moderate winds (the equivalent wind speed U 10 at a height of 10 m is less than 15 m/s), when the spray concentration was low.Also the were always performed above the wave crests, i.e. the area of throughs remained unexplored.Significant progress was achieved using the PDA method [9], which was developed at the end of the 80s.Unlike the LDA method (a modification of which is), PDA made it possible to measure size of microparticles in a continuous medium (multiphase flows) in a wide range in addition to measurement velocities.So in [10], droplet sizes were measured in the range of 5-120 μm, with a resolution of only 0.5 μm.Moreover, the wind speed U 10 was already more than 30 m/s. .Photography and video began to be used even before contact and non-contact point measurements.In the early 1950s, high-speed imaging was first used to study the generation of droplets by bursting underwater bubbles in a liquid without flows (see Fig. 4a in [11]).And then, in the well-known [12], Toba used photography to study the processes of generation of droplets by bursting bubbles within laboratory modeling on a wind-wave flume.Koga [13] used the MOET method for visualization.This method is based on sequential pulse exposure of the same image with light of a different range (two pulses of the red and blue range were used), see the example in Fig. 4 b.This made it possible to single out a new mechanism for generating sprays, the so-called projection, which consists in breaking a drop directly from the crest of a breaking wave when growing a liquid thread (sometimes they say filament) along the direction of the wind, which ends with a separation of 1-2 large drops.The distribution of projections by size and speed was obtained.Also, an analysis of the displacement between images in different colors makes it possible to find the velocities of droplets (see Fig. 4 c).It should be noted that despite the high resolution of the film photos used, and the possibility of digitizing the image with subsequent computer processing, which appeared in the 80s, the analysis of such images was very robust.Given the sporadic nature of the occurrence of droplets, with light and moderate winds, the data obtained with filming were often not enough for correct statistical processing in these experiments.Therefore, the information for constructing the spray generation function was taken from the data of point measurements.At the end of the 90s, a great common shift to digital video technology began in a physical experiment.[14] was one of the first works in which a study of generation of sprays was carried out on a wind-wave flume using digital video equipment.Images were obtained with a resolution of 650 μm, which did not greatly exceed 800 μm in the above-mentioned work [13], and allowed only very large droplets (more than 1 mm) to be correctly identified.The shooting speed of 30 frames per second did not allow to restore the drop shift between the frames and determine its velocity.But in this work, an array of data with the image of breaking waves was almost 20 times higher than in the previous work, which significantly increased the accuracy and brought it closer to point measurements.The work [15] can be considered as milestone study on the development and application of methods based on visualization.For this study data were obtained for a droplet with a size from the threshold of 140 microns for equivalent wind speeds of up to 33 m/s, due to the higher spatial resolution.But most importantly, that due to high-speed filming and a large ensemble of implementations, it was possible for the first time to observe a new mechanism of fragmentation of the water surface under the influence of wind, the so-called bag breakup instability mechanism (see Fig. 5) leading to the formation and breaking of sails, which was previously known only in engineering problems associated with the fragmentation of droplets and jets in air flows.Also the shadow method was used for visualization in [15].Fig. 5. From [15].Images of the surface and spray generation taken with the high speed camera at a rate of 1000 fps.Each imageis 6.38*6.38 cm and separated by 1 ms.The arrow shows a liquid sheet inflated by the airflow and its subsequent fractionation that yields to the generation of small water drops which are transported in the airflow.The 10-m equivalent wind speed is U 10 = 31.3m/s.The main feature of the studies performed by our group in the last three years ( [16][17]) was simultaneous multiview high speed and resolution filming of the water surface (see Fig. 6 a), also with a shadow visualization method with backlighting by powerful LED spotlights.Experiments were carried out on a unique facility of the TSWiWaT.This level is a highest for the present time in experiments on the study of sprays in the conditions of laboratory modeling wind-wave interaction.Basing on the results of [16,17], the classification of phenomena (projections, bursting bubbles, bagbreakup) leading to the generation of sprays was clarified.It was possible to obtain statistics of precisely the phenomena leading to the generation of splashes due to the additional filming of a top view of the water surface illuminated by underwater lights, which was carried out for the first time.It demonstrated that at high wind speeds the bag breakup mechanism is dominant (see Fig. 6 b).
The obtained statistics data allowed us to offer a fundamentally new approach to obtaining the necessary SSGF.It can be obtained as a combination (convolution) of the statistics of phenomena leading to the generation of sprays and statistics of the generation of sprays in a single phenomenon.At the same time, it is rather difficult to study in detail a single phenomenon under natural conditions of wind-wave interaction, even in laboratory modeling, given its sporadic nature and the difficulty of performing measurements, especially at high wind speeds.Therefore, the idea was proposed to artificially initiate these phenomena under controlled conditions for detailed study.In our last study [18], we succeeded in realizing the artificial initiation of the bagbreakup phenomenon in the modified TSWiWaT.Arterially produced bag-breakup phenomenon turned out to be close to that observed under natural conditions of the wind-wave interaction (see the comparison in Fig. 7a, b).New algorithms were developed for identifying droplets, plotting trajectories, and estimating velocities (see Fig. 7  c).However, due to the fact that the phenomenon has a very complex spatial structure, the resolution for observing a drop of size less than 10 μm in the experiments was not enough.Therefore, at present we use the results of previous measurements of droplets induced by bursting bubbles, when they are artificially generated ( see [19]), as well as splashes generated by crushing a liquid filament (see [20]) to construct the SSGF.At the same time, the problems of a detailed study of the bag breakup mechanism and refinement of the SSGF based on it are planned to be solved in subsequent works with the artificial initiation of the phenomena leading to the generation of spray of droplets.

Methods of laboratory modelling and measurements phenomena of foam coverage over the water surface
Foam (or whitecapping), like spray, is almost always present on the sea surface, with the exception of only very weak waves and wind.In its characteristics, it is very different from both water and air, which determines its special role in the processes of exchange between the atmosphere and the sea surface.The main mechanism for the formation of foam is a strong breaking of the waves (macrobreaking).It leads to intensive air entrainment, the formation of underwater bubbles and their whipping into foam.Foam is also formed due to large-scale near-surface currents, for example, Langmuir circulation.By combining various factors, the relative area of the foam coverage increases sharply in hurricane winds (U10 more than 30 m/s) and exceeds 70% (see the results of field measurements in [21]).In [22], basing on the results of [21], a quantitative model was proposed for describing the contribution of foam to momentum exchange, in which the aerodynamic roughness parameter due to the foam coverage was determined through the size distribution of the bubbles.However, such data obtained in natural conditions are characterized by a large scatter, which complicates their use in the development of theoretical models.Therefore, in the present work, a system for the artificial generation of foam was first developed, as well as a technique for measuring the characteristics of the foam (relative coverage area and bubble sizing) specifically for research in laboratory modeling.
Experiments to study the characteristics of the foam in the framework of laboratory modeling were carried out at the TSWiWaT.The general scheme of the experiments is presented in Fig. 8 a.In conditions of clean water, as well as small accelerations, it is difficult to ensure generation of foam.Therefore, to create a stable foam with the necessary density on the surface of the water, a special device (foam generator) was developed (Fig. 8 b).The device consisted of two diffusers (tubes 35 cm long with a diameter of 1 cm with side holes with a diameter of 2 mm with a pitch of 7 mm) connected by side surfaces to each other, wrapped in foam rubber.The device was located horizontally, perpendicular to the channel, with a depth of less than 5 mm.The distance from the beginning of the flume (air flow inlet) is 1.2 m.A solution of a foaming substance enters through one of the diffusers under a pressure of a height of 1.5 m, compressed air (1.5 atm) is supplied through a second diffuser to force the solution of the foaming substance through a layer of foam.As a result, finely dispersed foam forms on the surface of the water.During the experiments, the level of the solution of the substance and the pressure of the compressed air were kept constant, which ensured a constant foam rate.A special series of measurements aimed at assessing the effect of the foam generator on surface waves in the case when only compressed air is supplied to the system showed that changes in the parameters of surface waves compared to a completely disabled foam generation system are insignificant.
The foam characteristics were measured in the seventh section of the channel (6.5 m acceleration) for 6 different values of the equivalent wind speed U10 from 12 to 34 m/s.To visualize the foam on the surface of the water, we used the shadow method of visualizing processes on the rough surface of the water with backlight under the water, which has proven itself in studying the statistics of spray generation phenomena (see earlier), the general scheme is shown in Fig. 8 (a).More detailed description of the experimental setup please find in [23].The fraction of the surface area covered with foam was calculated on the basis of the number of pixels darker than a certain threshold.To eliminate the influence of noise and small optical inhomogeneities, the original images were divided into regions, in each of which the average brightness was calculated, ie, the resolution of the frames decreased 50 times on each side.
Using reference records made without wind, one background image was calculated as the median value for each pixel.A background image was subtracted from each frame, then a histogram common to all frames was constructed, i.e. distribution of areas of all images by brightness.For each histogram, one can calculate the fraction of regions with brightness below the threshold, which naturally depended on the choice of the threshold.
To determine the threshold, a direct calculation of the foam coverage area using morphological image processing was performed.It was carried out in several stages shown on Fig 10 a-f.The background was subtracted from the original image and cropping was carried out; the image was binarized with a fixed threshold; the morphological opening with the structural element "disk" of 1 px was performed followed by the morphological closure with a "disk" of 21 px; closed regions of the image were filled with flood-fill operation.The ratio of the number of pixels found to the total number of pixels was taken as the fraction of the surface area covered with foam.Based on this analysis, a relative coverage was found for sequences of frames from several records in experiments with artificial foam at U10 = 12 m/s.For each record, a relative brightness threshold is selected for analysis by histograms, which gives the corresponding coverage.Then this threshold value averaged over several over all realizations for U 10 = 12 m/s was used for all cases of wind speeds.
Information about the characteristic size of the foam bubbles was obtained additionally to data on the area of foam coverage.From each record, several frames were selected, on which the foam is clearly visible.Areas were identified on which the bubbles merge (located in several layers) and others unsuitable for automatic determination of the area.For the remaining areas of the images after the preliminary filtering, all circles were found (see Fig. 10 g) by two-stage circular Hough transform (see [24]) and their distribution in radius was calculated.

Conclusion
The history of the development of methods for studying the processes of fragmentation of the water surface under wind forcing demonstrates that methods based on visualization of flows and photo/video filming helped us to study microphysics of boundary layer within laboratory modeling for severe conditions.It allow to identify and study in detail the main phenomena that lead to the generation of sprays and obtain information about the characteristics of the foam in contrast to point methods.Multi-angle high speed video filming with a shadow method of visualization, including a top view of the rough surface with backlighting from under water, provided data on statistics of the main phenomena leading to spray generation (projection, bubbles, bagbreakup), as well as data on the area of foam coverage and bubbles size.However, it should be noted that for further advancement in the direction of obtaining information about the SSGF, when taking measurements under conditions of artificial initiation of the phenomena leading to spray generation, it is advisable to use a combined approach that combines visualization methods (high-speed filming with the shadow method) and the most advanced point measurement methods (e.g.PDA).This will provide statistics on the size and velocity of the droplets formed during various types of single phenomena of surface fragmentation and spray generation, which will supplement the previously obtained statistics of the phenomena themselves.

Fig. 2 .
Fig. 2. Panorama view on the most known wind-wave flumes: a) SUSTAIN, University of Miami b) Large Air-Sea Interactions Facility (LASIF) Marsei University France c) TSWiWaT, IAP RAS, Russia d) Kyoto University High Speed Wind Wave Facility e) AEOLOTRON -circle wind-wave tank in University Heidelberg.

Fig. 4 .
Fig. 4. a) Form [11].Bursting bubbles produced sprays b) From [13] photographs of projections obtained with MOET technique.Wind direction is from left to right.Successive two images are shown by blue and red colors.One division of the photographed measure (right end) is 1 cm.Fetch F = 16 m, representative wind velocity V=.16 m/s, flushing interval t = 5 ms.c) Movements directly produced droplets along the representative wave.Each droplet in the figure indicates actual size traced from photographs.Arrows indicate the droplet velocity vector in a coordinate moving with the phase speed of the wave.

Fig. 6 а
Fig. 6 а) Schematic diagram of experimental setup on TSWiWaT, from [16], b) Dependence of the specific numbers (per unit time per unit area) of the spraygenerating phenomena on the wind speed.Blue circles indicate bursting of floating bubbles, black the liquid filaments, and red the bag breakup events is adapted from [17].

Fig. 7 a
Fig. 7 a) bag-breakup on the real wavy surface b) artificially induced bag-breakup c) trajectories of the droplets generated by bag-breakup.

Fig. 10 .
Fig. 10.Fig. 10 (a-f) sequences of stages of morphological analysis of the images to determine the relative foam coverage (g) an example of bubble determination.
-00209); designing of methods of measurements including: optical and visualization scheme, methods of measurements of the air flow and wave field parameters were supported by Russian Foundation of Basic Research (No 21-55-52005, 20-05-00322); the development of the software was supported by the Grant of the President no.MK -5503.2021.1.5,and the work under processing of the video was supported by Russian Science Foundation (Agreement No.21-19-00755).