∎

11institutetext: J. Chen 22institutetext: State Key Laboratory for Turbulence
and Complex System, College of Engineering, Peking University, Beijing,
100871, China
22email<EMAIL_ADDRESS>
# Flow visualization and PIV of wind-waves (2019 Edition)

Chen Junwei

(Received: date / Accepted: date)

###### Abstract

This article presents a flow visualization method for wind-waves, as well as a
technique to measure flow field on two sides of interface by stereoscopic
particle image velocimetry (PIV) simultaneously. The new flow visualization
method applied a special illumination setup to enhance reflection and weaken
refraction on interface, which improves contrast and detail performance of
photos. The concatenation of flow visualization photo along flow direction is
able to demonstrate the scenario from capillary waves to gravity-capillary
waves at the early stage of wind-waves. After that, time-resolved stereoscopic
PIV is employed in vertical planes on both sides of interface with two camera
pairs. Two kinds of tracking particles with different scattering performance
are spread in air or water separately. Then interface detection algorithm is
designed to separate different particles and determine interface position.
Adaptive min-max normalization and near-wall image preprocessing is used to
improve near-wall and main stream PIV result. Finally, clip arts of results
show the flow field in the same time in air and water near interface.

###### Keywords:

Wind-waves Flow visualization PIV Simultaneous measurement

##  1 Introduction

Wind-waves are common phenomenon in nature and attract a perpetual enthusiasm
from fluid scientists. Over the past several decades, there are abundant
literature on such phenomenon along with promotion by the evolved progress of
techniques. The interface itself, the development of waves, flow on both sides
of interface as well as their interaction is important in understanding wind-
waves.

Flow visualization is the most direct method in wind-waves experiment, but its
result contains even more details comparing to quantitative measurements, as
there is no conversion from image to elevation field of interface. Some case
of flow visualization is deduced in laboratory or natural environment, such as
Banner and Phillips (1974), Su (1982), Kawamura and Toba (1988), Banner and
Peirson (1998). Jähne et al. (1994) have introduced a stereo-photography
method and then calculated slope of interface in field of view. Different
approaches are applied to measure two-dimensional elevation field of air-water
interface, such as intrusive or non-intrusive gauge array (Hammack et al.
1989; Bock and Hara 1995), background oriented schlieren (Moisy et al. 2009;
Morris 2004; Fouras et al. 2008; Gomit et al. 2013), structured light (Tsubaki
and Fujita 2005; Cobelli et al. 2009) and volume reconstruction of particles
floating on the surface of water (Douxchamps 2005; Turney et al. 2009; Turney
and Banerjee 2013; Aubourg et al. 2019). Some of these measurement are
combined with PIV on the interface or on a horizontal plane near surface.

PIV is a widely used measurement method using plenty of tiny particles in
fluid as tracers and calculate the velocity of particles within areas on the
image. Many studies have improved the experimental arrangement and algorithm
of PIV towards high-dimensional and more reliable results. Reul et al. (1999)
measured air flow over a breaking wave. Siddiui et al. (2001) obtained current
flow field with an additional profile camera to record interface, infrared
visualization is executed in the same time. Misra et al. (2006) and Dussol et
al. (2016) detected interface position in PIV image via the distribution of
particles, while Andre and Bardet(2014), Buckley and Veron (2017), Vollestad
et al. (2019) via laser-induced fluorescence. Young and Hyung (2011), Park et
al. (2015) found interface by matching texture to photo, which is only
feasible in the situation of quasi-one-dimensional interface. Actually,
Buckley and Veron (2017) has listed nearly 60 articles about PIV of wind-
waves. However, flow measurements near an arbitrary interface are still
challenging for several reasons. The location of interface position is a
pivital problem as regard to the correctness of results. Besides, high shear
region near interface requires a robust algorithm. Furthermore, the volatile
interface generates strong reflection light and nonuniform refraction light
that will deteriorate the image quality in experiments.

Since surface gravity waves strongly couple to adjacent winds and currents
(Sullivan and McWilliams 2010), it is a natural idea to measure flow field on
both sides of interface simultaneously. This paper presents a sketch of
applying stereoscopic PIV in wind and current near the interface of wind-waves
with two camera pairs working concurrently, which includes experimental setup,
interface detection and appropriate PIV algorithm. Besides, a simple but
effective method is introduced, which produces high-contrast and more detailed
flow visualization of interface. The paper is organized in the following way.
Flow field setup and visualization method is given in Sect. 2. PIV image
acquisition (Sect. 3) and processing (Sect. 4) follow, the latter one includes
interface detection procedure and PIV algorithm special for experimental case
in this article. Finally the result and discussion are in Sect. 5.

##  2 Flow visualization

###  2.1 Flow field setup

Wind waves are generated in the wind-water tunnel at Peking University. This
wind-wave tunnel is a combination of the low-turbulent water channel and an
elementary wind tunnel. The close-loop water channel has two test sections and
the second one measures 6 m x 40 cm x 40 cm. The wind tunnel is mounted over
water tunnel and wind begins to interact with water from one metre at the
second test section. A 40 cm x 30 cm honeycomb filter at the outlet of wind
tunnel straightens the wind. Wind speed varies from 0 to 6.0 m/s and water
speed is up to 0.60 m/s. As wind accelerates water near surface but the total
flow of water is controlled by the console of water tunnel, there will be
backward flow at bottom region when total flow is insufficient. In most cases
of our experiments, water speed is adapted to wind speed to make the bottom
region of water nearly stall.

###  2.2 Visualization method

Figure 1: Schematic of flow visualization

The plane-view visualization of interface was usually snatched from the air
side in previous articles. And the line-of-sight is tilt from vertical to make
photo become more stereoscopic with fair contrast.

However, when watching up from the underwater side, the contrast of image will
be significantly improved. Comparing to refraction, reflection is more
sensitive to small undulation of liquid surface because of its higher
deflection angle. On the other side, refractive index of water is larger than
that of air. When the camera is filming interface from somewhere above the
interface, part of light below the interface will refracts there and be
recorded whatever the tilt angle of line-of-sight is. In contrast, if camera
were below the interface and watched upwards, the energy ratio of reflection
to refraction will increase dramatically as the incident angle approaches to
that of total reflection, i.e. the camera will record mostly reflection light
and the contrast of photo is improved. This can be explained by reflectivity-
or transmissivity-power-ratio derived from Fresnel equations.

Fig. 1 shows a schematic diagram of the experimental arrangement for flow
visualization. A screen covered by white paper sits in one side of wind-water
tunnel and faces toward the object interface. A sodium-vapour lamp illuminates
the screen where light diffused reflects. A PCO sCMOS camera (16 bit
grayscale, 2560 x 2160 $pixel^{2}$ at 50 fps) is in the other side of wind-
water tunnel. The field of view (FOV) is set to be approximately 100 cm x 40
cm using a 28 mm lens and 20 cm x 40 cm using a 60 mm lens. The camera has a
pitch angle about $45^{\circ}$ upwards to improve the contrast of image as
mentioned above. LaVision v4.2 Scheimpflug adapter is used and the aperture of
lens is properly reduced to help the image system focus on the interface.

A bi-lineal mapping function is used to correct the perspective distortion.
Several points are marked with their position both in raw image and real world
to fit the mapping function, and then a trapezoidal shape region of raw image
is dewarped into a rectangle shape image with uniform scale.

Fig. 2 shows interface under different wind speed. The FOV is about 20 cm x 40
cm. Flow is from left to right, and the upper and lower margin of flow field
happen to show the height variation of interface. Wind waves are changing from
capillary waves to gravity-capillary waves when wind speed increases. Many
tiny wavelets in the downstream of the wave crests can be seen clearly, which
is called ’incipient breaking’ by Phillips and Banner (1974). In order to show
the transition process from capillary waves to gravity-capillary waves at the
early stage of wind-waves, three successive sections of interface
visualization measured independently are concatenated together. Fig. 3
demonstrate interface between 50 cm and 300 cm from beginning. The flow is
from left to right. Also, perspective distortion is corrected.

Figure 2: Flow visualization at 260cm from the downstream of wind tunnel. The
flow is from left to right and the width of flow field is 40cm. The Wind speed
is a 3.1m/s; b 5.0m/s; c 5.2m/s; d 6.0m/s. Figure 3: Flow visualization of
interface from 50cm to 300cm on the downstream of the exit of wind tunnel.
Independent measurements over three successive sections are concatenated
together. The flow is from left to right.

##  3 PIV image acquisition

Stereoscopic PIV is employed simultaneously in air and water. Four Phantom
v2512 (12 bit grayscale, 25600 fps at full resolution 1280 x 800 $pixel^{2}$,
72 GB internal RAM) fast-speed cameras are used to grab particle images in air
and water. A ZKLASER DPQ-527-60PIV-DF Nd:YLF laser shades 1 mm light sheet
vertically upwards from the bottom of wind-water tunnel. The energy of laser
is 6 mJ per pulse at 10000 Hz. As Fig. 4 shows, camera A and B focus on flow
field above the interface while C and D focus on that below the interface. The
cameras have about 10∘ pitch angle to surmount the relief of interface beyond
the focusing plane so that near surface region can be snatched without
obstacle. The angle between two cameras in each group is about 60∘ to balance
stereo-PIV error in three direction (Prasad 2000; Bhattacharya et al. 2016).
200 mm lens are mounted on Scheimpflug adapter and fields of view are set to
be approximately 5 cm x 3 cm on each camera and the interface always traverses
the picture. Laser and all cameras follow the same time sequence generated by
LaVision PTU. Sampling rate is from 8000 fps to 15000 fps, which is adapted to
wind speed. Besides, two acrylic prisms filled with water are stuck on the
lateral face of wind-water tunnel. The prisms have a 30∘ edge. In this way,
the scattered light of particles in water will have small incident angle as
far as possible when it refracts to air and reach camera aftermath, so that
the blur of each particle spot will be reduced (Prasad and Jensen 1995). The
aperture for camera A and B is 1/4 and for C and D is 1/5.6. Each case takes
10000 frames during experiment.

Figure 4: Camera and laser setup for PIV and FOV of each camera. Air and water
is flowing from left to right in all pictures. a Presentation of experimental
setup. b A 3D sketch of imaging system. c field of view of each camera.
Perspective distortion is a little exaggerated. Notice that image taken by
camera A and B will turn over vertically to make the flow from left to right.

Two kinds of particles are added into air and water. The choice of particles
is under synthetical consideration among following performance, light
intensity of spots in image, difference of two kinds of particles to be
separated and less impact on wind-waves while floating on interface. Hollow
acrylic particles, 11 $\mu$m in mean diameter, from Potter Industries are
introduced into water. Again, this particles are poured into water very gently
along streamwise to supply more particles just beneath the interface. Fume
composed of particles, about 1-3 $\mu$m in diameter, is injected at the
upstream of wind tunnel by a server fan.

The calibration of two camera groups is done separately on LaVision DaVis 10.
A LaVision 058-5 calibration plate, which has 2 level on each side and 5 mm
between two neighbour spots, mounts on a dock, where it can only move upward
or downward if the dock were fixed. The first level of calibration plate
coincides with light sheet and the height of calibration plate is set to a
proper position. Each camera takes 100 pictures of calibration plate and
calculates average intensity of pictures to reduce noise. The calibration
generates 3rd-order polynomial functions for mapping things between raw image
and real world. The scale factor above the interface is about 28.0 pixel/mm
and below the interface is about 28.5 pixel/mm in images corrected into real
world. To improve calibration quality, water level is changed temporally so
that more points are recorded. Also, photos for self-calibration are grabbed.
Particles in air are replaced with about 10-$\mu$m water droplets from Eau
Thermale, in lower particle density.

Photos taken by four cameras in the same time are shown in Fig. 5. Fig. 5a and
b are particle images of air flow while c and b are of water flow. Fig. 5a and
b have been turned over vertically because the cameras are in the other side
of wind-water tunnel. Concave black shading occurs in the left side or right
side of pictures because the lens have tilting angle up to 10∘ to meet
Scheimpflug criterion and the 42 mm CMOS chip is too large for the 200 mm lens
used. Nonetheless, such shading has little influence on stereo PIV calculation
for the FOV of two cameras in one group may not overlap in some edge area
hence velocity will not be calculated there.

Figure 5: Images taken by four cameras at the same time. a to d are images
taken by camera A to D.

##  4 PIV Image processing

The algorithm of interface detection and PIV is illustrated schematically in
Fig. LABEL:fig:6. Interface detection includes four steps while PIV includes
three steps. There is a sequential order between interface detection and PIV,
because PIV image preprocessing will use interface data.

It would be better to do self-calibration before processing. For calibration
in stereoscopic PIV, apart from velocity calculation errors (Wieneke 2005),
near-wall results may be incorrect for the non-coincidence of interface in
wind-waves experiments. The easiest way to inspect calibration quality is to
show stereoscopic image pair in a single picture, for instance, putting image
taken by camera A in red channel and image taken by camera B in green channel
of a pseudo colour picture, see Fig. 6a, then observe whether interface in red
and green channel coincide or not.

###  4.1 Interface detection

Before interface detection, the content in picture of each camera should be
clarified first. There are two kinds of particles in the picture focusing on
air flow, fume in air and acrylic particle in water, acrylic particles are
much brighter than fume because their diameter is larger. There is only
acrylic particles on the picture focusing on water flow, scatter light of
particles directly recorded by camera spread below the interface while that
reflected by the interface almost appear above the interface. The scattering
of particles follows Mie scattering law (Raffel et al. 2018). As light shades
upward in the experiment setup mentioned above, light scattering oblique
upward is generally more powerful than that scattering oblique downward. This
explains why particles image focusing on water flow has different light
intensity on two sides of interface.

Edge detection is frequently utilized in wall and free surface detection, in
which drastic change of light intensity, such as profile of particles and
solid wall, is found in images. However, particles spread on both side of
interface in our case. It is difficult to recognize interface from edge
detection result. Instead of that, threshold is applied by comparing to images
as two kinds of particles have different light intensity and size in picture
of air flow. The process of first frame is a little different to successive
frames with respect to time-series enhancement, but they are similar on the
whole. There are generally four steps in interface detection, and the first to
the third step are operated on corrected images about air flow.

Figure 6: Procedure of interface detection before spatial and temporal
smoothing, the flow is from left to right. a Original pictures to be processed
are showing in pseudo-colour form, Images grabbed by camera A and B is turned
over vertically and perspective distortion is corrected. b Pictures after
preprocessing for interface detection. c After comparing with threshold,
’true’ pixels are highlighted. d Interface position is detected and
preliminary smoothed, then showed in red or green line.

####  4.1.1 Image preprocessing

As acrylic particles in water are much bigger than fume particles in air and
their scattering direction is more forward, acrylic particle spots are about
ten times brighter than fume particles as well as occupy morn pixels in the
image taken by camera A and B. Besides, for wind waves in early stage, water
is not much accelerated, wind flow is much faster than water flow. If the
sample rate were adapted to airflow, particles in water are nearly stall
between two adjacent frames. It is recommended to calculate time-series
sliding minimum for every three images, in this way, particles in air are
weakened while particles in water are almost preserved.

Then, due to different sizes of two kinds of particles in image, the grayscale
morphological opening, which consists of grayscale morphological erosion and
dilation in sequence, is applied to particle image. Erosion is to eliminate
the edge of bright area by seeking the dimmest pixel in the neighbourhood of
one pixel and then replacing the latter. Besides, dilation does the contrast
way and extend bright area. If the parameter of grayscale morphological
opening is proper, fume particles will be removed in erosion as far as
possible, while acrylic particles will be reduced in erosion and then
recovered in dilation. Image before and after preprocessing is shown in Fig.
6a and 6b.

####  4.1.2 Interface detection via local threshold

After pre-processing, images are compared with threshold to separate region
contain acrylic particles from region contain fume particles, then it yields
binary images. As mentioned above, some margin area of images may be dim. A
local threshold set is applied to this situation, i.e. the threshold near dim
area is lower than that in ordinary area. However, if a smaller camera sensor
or a lens with larger aperture were used, a constant threshold is adequate.

Morphological opening is applied to binary image, which is to clear sporadic
’true’ pixels above the interface, the result is shown as highlight area in
Fig. 6c. Aftermath, row position is determined by seeking the first ’true’
pixel in every column. The raw position is not smooth due to discreteness of
particle image, so the preliminary smoothing, which contains median and
Gaussian filter, is applied before temporal and spatial smoothing in the next
step, the result is shown in Fig. 6d.

There is an additional procedure in binary image processing special for the
successors of first frame. Upper margin of ’true’ pixels is limited by the
interface in previous frame, hence can not exceed it too much. To make the
algorithm more robust, it is recommended to set limitation alternately, i.e.
interface on camera A is the source of limitation in next frame on camera B,
and vise versa. The reason is bright taint above interface caused by
conglomeration of fume particles, reflected light from interface, off-plane
particles, converging and diverging light passed through interface are less
probable to arise in the same place on two cameras simultaneously.

Figure 7: Phase speed of interface. Blue dots represent phase speed detected
from camera A and Green dots from camera B. Red line is phase speed after
smoothing.

####  4.1.3 Spatial and temporal smoothing

In this step, interface position is smoothed using data in several vicinity
frames. Albeit the interface is changing all the time, its shape is nearly
frozen when moves downstream so that phase-locked averaging can be applied to
smooth the interface. Phase speed of waves should be calculated before
averaging. It is calculated by finding correlation peak of interface position
between two frames. As the phase speed is about 1.2 pixel/frame, see Fig. 7,
numerical error will be significant if two adjacent frames were used. The gap
is chosen from 25 frames to 250 frames. Due to many spikes in the series of
displacement, median filter and Gaussian filter are applied to smooth the
data.

For the interface position series $\boldsymbol{s}(\boldsymbol{x},t)$, where
$\boldsymbol{x}$ are series of x-coordinate, t is time and every element in
$\boldsymbol{s}$ corresponding to element in $\boldsymbol{x}$ at the same
place. Let phase speed to be $\boldsymbol{v}_{\phi}(t)$ and the time interval
to be $\Delta$t, than interface moves
$\Delta\boldsymbol{x}(t)\approx\boldsymbol{v}_{\phi}(t){\Delta}t$ in a time
interval. If 2N + 1 frames were used to smooth the interface, and suppose that
phase speed didn’t change in short time, then smoothed interface in $t_{0}$ is

$\boldsymbol{s}_{e}(\boldsymbol{x}_{e},t_{0})=\overline{\boldsymbol{s}(\boldsymbol{x}+n\Delta\boldsymbol{x}(t_{0}),t_{0}-n\Delta
t)},$ (1)

where $\boldsymbol{x}_{e}$ is extension of $\boldsymbol{x}$ to the sides,
$\boldsymbol{s}_{e}$ is interface position on $\boldsymbol{x}_{e}$, and n is
from -N to N. The averaging will omit terms without value. Since interface
position is discredited and averaging is conducted at every elements in
$\boldsymbol{x}_{e}$, one-dimensional interpolation has to be done before.
Interface position in all frames before and after phase-locked averaging is
shown in Fig. 8, where higher brightness means relatively higher position. The
interface is more smooth and extended to two sides by 200 pixels in Fig. 8b.
There are many tiny wavelets behind wave crest, which can be seen in Fig. 2
too, but some small amplitude wavelets are still smeared out.

Figure 8: Relative interface height a before and b after spatial and temporal
smoothing, greyscale represent relative interface height. The interface is
extended by 200 pixels in two sides as well as smoothing.

####  4.1.4 Applying interface position to all cameras

In step 1-3, the interface in images about air flow have been detected. In
this step, the detected interface are applied to images about water flow.
Also, self-calibration and perspective correction are required first. As the
scale factor for two calibration system on other side of interface is not
always the same, the interface series detected should be amplified or reduced
to adjust the scale factor of calibration for water flow. Then move the
interface to the borderline in picture, where particle intensity is different
on two sides.

Fig. 9 shows two scenery of interface detection result, and it works stably in
both upstream and downstream of wave crests. The accuracy of interface
detection method mentioned above is about 5 pixels in our experimental case.
This method is a bit time-consuming for its multiple image morphological
processing and interpolation, because the algorithm must be stable enough to
deal with thousands of frames. The processing time for 10000 frames is about 3
hours on a quad-core platform via MATLAB.

Figure 9: Interface detection results, image of a and b are taken in at the
same time, while c and d are taken in another time. Flow is from left to right
in all images and white line represent interface detected.

###  4.2 PIV processing

Adaptive min-max normalization is applied to images taken by camera A and B.
Assume that the light intensity distribution of an image, I(x, y) can be
characterized by two components: (1)source illumination incident on the scene
being viewed, and (2)illumination reflected by the objects in the scene
(Gonzales and Woods 2007). For particle images with noise, intensity
distribution can be decomposed by

$I(x,y)=I_{illu}(x,y)I_{part}(x,y)+I_{noise}(x,y),$ (2)

where $I_{illu}$ is distribution of illumination, $I_{part}$ is reflectance by
tracking particles and $I_{noise}$ is noise. The ideal situation is $I_{illu}$
is uniform and $I_{part}$ is homogeneous. Quality of image is deteriorated if
either of them were dissatisfied. For non-uniform illumination, there are
plenty of methods to rescue the image, such as min-max normalization
introduced by Westerweel (1993). Adaptive min-max normalization combines two
min-max normalization results with different filter size together. Suppose
that normalization result of raw image by filter size n is $f_{n}\\{I\\}$, and
$\widetilde{I}$ is multiply smoothed image, in which undulance of particles
can not been seen. Then adaptive min-max normalization is

$f_{a,b}^{\star}=\left\\{\begin{matrix}f_{a}\\{I\\},\quad\sigma(\widetilde{I})>H,\\\
f_{b}\\{I\\},\quad\sigma(\widetilde{I})<H,\end{matrix}\right.$ (3)

where $a<b$, $\sigma(\widetilde{I})$ is standard deviation of $\widetilde{I}$
of every pixel with its several vinicity pixels, and H is threshold.

Figure 10: Correlation result are compared from images without or with
adaptive min-max normalization. a is origin image of stereoscopic pair, while
is b is the adaptive min-max normalization result of a. c is correlation
result without image preprocessing, and d is correlation result of method in
Sect. 4.2.

In classical PIV measurement, particle images are divided into a series of
interrogation windows, and the particle distribution in interrogation window
is one of the factors influencing vector calculation. Simply mask out
particles on the other side of interface may not be a good precessing method,
because it will cause a typical problem, lack or even absence of particles on
other side in the interrogation window across the interface (Park et al. 2015;
Theunissen et al. 2008). Optimal synthetic particles is applied to fill the
other side of fixed or translating wall in order to improve velocity
prediction in high-shear boundary layer (Zhu et al. 2013; Jia et al. 2017).
Due to particles spreading in both phase and inclined camera mounting in the
experimental setup in this article, particles are filled in both sides of
interface in image, as mentioned above. The way for near-wall velocity
calculation is to keep particles in other side of interface and treat them as
optimal synthetic particles. Particles below the interface in images about air
flow are simply kept after adaptive min-max normalization. Reflected particles
above the interface in images about water flow act like mirror particles, they
have same tangential velocity and opposite normal speed to their original
part. Such mirror particles are processed as SP (Stationary particles) mode
(Zhu et al. 2013), their intensity is reduced to one-third of the original.

The velocity vectors are obtained on LaVision DaVis 10 using multi-path cross-
correlations and the final interrogation window is comparable to a 24 x 24
square window whose shape and weight is elliptical Gaussian with lateral-to-
vertical factor 2:1. 75% overlap is applied to improve vector field
resolution, and vector spacing in air flow measurement is 214 $\mu$m while in
water flow measurement is 211 $\mu$m. In vector post-processing, removal-and-
replacement median filter and velocity range limitation are applied to remove
outliers. The empty space after post-processing is filled with calculation
result from time-resolved PIV sliding sum-of-correlation (Scarano and Moore
2012; Sciacchitano et al. 2012) in 5 frames with the same correlation setup
and post-processing procedure as the first round. Due to water flow is much
slower, velocity is calculated at intervals of 5 frames.

Figure 11: PIV results in region above and below the interface, background in
a and c is velocity amplitude and in b and d is z-component of velocity.

##  5 Results and discussion

PIV results are shown in Fig. 11 and Fig. 12, the flow is from left to right
in all pictures. Fig. 11 presents vector field above and below the interface
in a moment, and its background is the amplitude or z-component of velocity.
Fig. 12a is clip art of vector field above and below the interface, where
interaction of wind and current can be seen simultaneously in one picture or
video, while Fig. 12b demonstrates that measurement method in this article
also works passable in the region behind wave crest. As the experiment is held
in a short wind-water tunnel, the wind-waves have not fully developed. Wind
speed is much faster than interface phase speed and interface phase speed is
much faster than water flow speed, as shown in Fig. 7 and Fig. 12. Boundary
layer in air flow near interface is very thin, which can be also seen in Fig.
11, its thickness is about 2 mm at most phase of waves. Despite that,
recirculation zone appears on the downstream of crests, which can be seen in
Figures and Video. Water flow is similar but not exact Stokes waves especially
in the downstream of crests.

Figure 12: PIV results above the interface and below the interface are shown
in one picture, the vector amplification ratio is different in two sides,
Vector amplitude is showed in background with warm-toned colour bar and cold-
toned colour bar for air flow and water flow. Figure 13: A schematic of
experimental setup with two laser of different colour.

Illumination in air deteriorates when light sheet pass through tiny wavelets
on the downstream of wave crests. Due to many convex and concave menisci exist
there, light converges or diverges after passing through the interface, which
has two unfavourable factors, non-uniform strength of light sheet on FOV and
out-of-plane motion of light sheet. As the noise of CMOS is mainly depended on
temperature (Lundberg 2002), noise level is roughly similar in the whole
frame, signal-to-noise ratio increases in some underexposed region. This has
been mended by sliding sum-of-correlation. Besides, heterogeneous illumination
$I_{illu}$ in Eq. (2) introduces weighting to cross-correlation. As $I_{illu}$
goes with interface moving and $I_{illu}$ goes with particles moving, and the
latter is much faster than the former, weighting is nearly unchanged in two
adjacent frames, which tends to emphasis on zero displacement. As is known to
all, classical stereoscopic PIV uses two cameras and calculates velocity field
in the perspective of each camera, then reconstructs three-component velocity
field. The final result will not be right as long as one part in
reconstruction is error. Fig. 10c shows the worst situation, PIV without image
preprocessing results in many spurious vectors. $I_{illu}$ can be equalized by
min-max normalization, actually, normalization with filter length 3, 5 and 7
pixels have been tried, filter of short length adjusts the illumination light
to be uniform effectively, but the upper and lower envelops of light intensity
in processing change too fast, thus introduce more noise to image, while
filter of long length does not introduce so much noise to image, but does not
work well when $I_{illu}$ varies too violently. Adaptive min-max normalization
is a combination of that with short and long filter length, and produces
better results(Fig. 10d).

Yet, pre- and post-processing can not remedy out-of-plane motion of light
sheet. It brings equivalent z-component velocity of particles, we can only
remove corresponding spurious vectors. There is a way to completely solve this
problem, which is to use two sets of illumination system. See Fig. 13, red and
green (for example) laser illuminate region on one side of interface and
filters on cameras can block unwanted light. In present experimental setup
with only monochromatic laser, shading light upwards can reduce impact because
wind is much faster than interface, illumination changes not so much comparing
to particles moving in air.

##  6 Conclusions

A flow visualization method for wind-waves is proposed in this article.
Reflection on water side replaces that on air side of interface in flow
visualization. In this way, reflected light from interface is recorded with
diversion due to the undulation of interface, while refracted light pass
through interface will be very weak because of higher refractive index in
water and proper exit angle of light. The contrast of photos increases, and
more details like tiny wavelets on the downstream of crest are reserved in
this minor technical change, which is better than present visualization method
and quantitative measurement results. By concatenating visualization photos in
different stages from upstream to downstream, the scenery from capillary waves
to gravity-capillary waves in the early stage of wind-waves is able to be
seen.

As the second topic of this article, a PIV arrangement for wind-waves is
introduced, in which flow field above and below the interface can be measured
simultaneously by stereoscopic PIV. This arrangement utilized two kinds of
tracking particles (smoke and hollow acrylic particles) with different
scattering performance to make their size and intensity diverse in photos. The
content of photos grabbed by four cameras is analyzed, in the photo of air
flow, there are smoke particles above the interface and hollow acrylic
particles below the interface, while in the photo of water flow, there are
acrylic particles in both side of interface, but particles above the interface
are mirror image of interface with higher brightness. Interface detection is
first applied on the photos focusing on air flow, then adapted to photos
focusing on water flow after spatial and temporal smoothing. Adaptive min-max
normalization and near-wall image preprocessing is applied before PIV
correlation. The final result of flow field in two phase is shown in one
figure in the end.

The imperfection of PIV illumination in experiment is discussed. The quality
of light sheet deteriorate after passing through the interface. To radically
overcome this problem, it is recommended to make use of two light sources in
different colour and illuminate regions on each side of interface
individually.

Acknowledgments This research is supported by the National Natural Science
Foundation of China under grant numbers 109103010062, 10921202, 11632002, and
11602005.

## References

  * (1) André MA, Bardet PM (2014) Velocity field, surface profile and curvature resolution of steep and short free-surface waves. Exp fluids 55(4):1709. https://doi.org/10.1007/s00348-014-1709-5
  * (2) Banner ML, Peirson WL (1998) Tangential stress beneath wind-driven air-water interfaces. J Fluid Mech 364:115-145. https://doi.org/10.1017/S0022112098001128
  * (3) Banner ML, Phillips OM (1974) On the incipient breaking of small scale waves. J Fluid Mech 65(4):647-656. https://doi.org/10.1017/S0022112074001583
  * (4) Bhattacharya S, Charonko JJ, Vlachos PP (2016) Stereo-particle image velocimetry uncertainty quantification. Meas Sci Technol 28(1):015301. doi:10.1088/1361-6501/28/1/015301
  * (5) Bock EJ, Hara T (1995) Optical measurements of capillary-gravity wave spectra using a scanning laser slope gauge. J Atmos Oceanic Technol 12(2):395-403. https://doi.org/10.1175/1520-0426
  * (6) Buckley MP, Veron F (2017) Airflow measurements at a wavy air-water interface using PIV and LIF Exp Fluids 58(11):161. https://doi.org/10.1007/s00348-017-2439-2
  * (7) Cobelli PJ, Maurel A, Pagneux V, Petitjeans P (2009) Global measurement of water waves by Fourier transform profilometry. Exp Fluids 46:1037-1047 https://doi.org/10.1007/s00348-009-0611-z
  * (8) Douxchamps D, Devriendt D, Capart H, Craeye C, Macq B, Zech Y (2005) Stereoscopic and velocimetric reconstructions of the free surface topography of antidune flows. Exp Fluids 39:533-551. https://doi.org/10.1007/s00348-005-0983-7
  * (9) Dussol D, Druault P, Mallat B, Delacroix S, Germain G (2016) Automatic dynamic mask extraction for PIV images containing an unsteady interface, bubbles, and a moving structure. C R Mec 344(7):464-478. https://doi.org/10.1016/j.crme.2016.03.005
  * (10) Fouras A, LoJacono D, Sheard GJ, Hourigan K (2008) Measurement of instantaneous velocity and surface topography in the wake of a cylinder at low Reynolds number. J Fluids Struct 24:1271-1277. https://doi.org/10.1016/j.jfluidstructs.2008.06.013
  * (11) Gonzalez RC , Woods RE (2007) Digital Image Processing (3rd Edition). Prentice-Hall, New Jersey. https://doi.org/10.1109/IEMDC.2013.6556306
  * (12) Hammack J, Scheffner N, Segur H (1989) Two-dimensional periodic waves in shallow water. J Fluid Mech 209:567-589. https://doi.org/10.1017/S0022112089003228
  * (13) Hecht E (2012) Optics (4th Edition). Addison Wesley, Boston. https://doi.org/10.1364/NP.2012.NW3D.5
  * (14) Jähne B, Klinke J, Waas S (1994) Imaging of short ocean wind waves: a critical theoretical review. JOSA A, 11(8):2197-2209. https://doi.org/10.1364/JOSAA.11.002197
  * (15) Jeon YJ, Sung HJ (2011) PIV measurement of flow around an arbitrarily moving body. Exp fluids 50(4):787-798. https://doi.org/10.1007/s00348-010-0855-7
  * (16) Jia LC, Zhu YD, Jia YX, Yuan HJ, Lee CB (2017) Image pre-processing method for near-wall PIV measurements over moving curved interfaces. Meas Sci Technol 28(3):035201. https://doi:10.1088/1361-6501/aa574c
  * (17) Kawamura H, Toba Y (1988) Ordered motion in the turbulent boundary layer over wind waves. J Fluid Mech 197:105-138. https://doi.org/10.1017/S0022112088003192
  * (18) Lundberg KH (2002) Noise sources in bulk CMOS. http://web.mit.edu/klund/www/papers/UNP_noise.pdf. Accessed 9 August 2019
  * (19) Misra SK, Thomas M, Kambhamettu C, Kirby JT, Veron F, Brocchini M (2006) Estimation of complex air-water interfaces from particle image velocimetry images. Exp Fluids 40(5):764. https://doi.org/10.1007/s00348-006-0113-1
  * (20) Moisy F, Rabaud M, Salsac K (2009) A synthetic Schlieren method for the measurement of the topography of a liquid interface. Exp Fluids 46:1021-1036 https://doi.org/10.1007/s00348-008-0608-z
  * (21) Morris NJW (2004) Image-based water surface reconstruction with refractive stereo. Master’s thesis, Department of Computer Science, University of Toronto
  * (22) Park J, Im S, Sung HJ, Park JS (2015) PIV measurements of flow around an arbitrarily moving free surface. Exp Fluids 56(3):56. https://doi.org/10.1007/s00348-015-1920-z
  * (23) Phillips OM, Banner ML (1974) Wave breaking in the presence of wind drift and swell. J Fluid Mech 66(4):625-640. https://doi.org/10.1017/S0022112074000413
  * (24) Prasad AK, Jensen K (1995) Scheimpflug stereocamera for particle image velocimetry in liquid flows. Appl Opt 34:7092-7099. https://doi.org/10.1364/AO.34.007092
  * (25) Prasad AK (2000) Stereoscopic particle image velocimetry. Exp Fluids 29(2):103-116. https://doi.org/10.1007/s003480000143
  * (26) Raffel M, Willert CE, Scarano F, Kähler CJ, Wereley ST, Kompenhans J (2018) Particle image velocimetry: a practical guide. Springer. https://doi.org/10.1007/978-3-319-68852-7
  * (27) Reul N, Branger H, Giovanangeli JP (1999) Air flow separation over unsteady breaking waves. Phys Fluids 11(7):1959-1961. https://doi.org/10.1063/1.870058
  * (28) Scarano F, Moore PD (2011) An advection-based model to increase the temporal resolution of PIV time series. Exp Fluids 52:919-933. https://doi.org/10.1007/s00348-011-1158-3
  * (29) Sciacchitano A, Scarano F, Wieneke B (2012) Multi-frame pyramid correlation for time-resolved PIV. Exp Fluids 53(4):1087-1105. https://doi.org/10.1007/s00348-012-1345-x
  * (30) Siddiqui MK, Loewen MR, Richardson C, Asher WE, Jessup AT (2001) Simultaneous particle image velocimetry and infrared imagery of microscale breaking waves. Phys Fluids 13(7):1891-1903. https://doi.org/10.1063/1.1375144
  * (31) Su MY (1982) Three-dimensional deep-water waves. Part 1. Experimental measurement of skew and symmetric wave patterns. J Fluid Mech 124:73-108. https://doi.org/10.1017/S0022112082002419
  * (32) Sullivan PP, McWilliams JC (2010) Dynamics of winds and currents coupled to surface waves. Annu Rev Fluid Mech 42. https://doi.org/10.1146/annurev-fluid-121108-145541
  * (33) Theunissen R, Scarano F, Riethmuller ML (2008) On improvement of PIV image interrogation near stationary interfaces. Exp Fluids 45:557-572. https://doi.org/10.1007/s00348-008-0481-9
  * (34) Tsubaki R, Fujita I (2005) Stereoscopic measurement of a fluctuating free surface with discontinuities. Meas Sci Technol 16:1894-1902 https://doi.org/10.1088/0957-0233/16/10/003
  * (35) Turney DE, Anderer A, Banerjee S (2009) A method for threedimensional interfacial particle image velocimetry (3D-IPIV) of an air-water interface. Meas Sci Technol 20(4):045403-1-045403-12 https://doi.org/10.1088/0957-0233/20/4/045403
  * (36) Turney DE, Banerjee S (2013) Air-water gas transfer and near-surface motions. J Fluid Mech 733:588-624. https://doi.org/10.1017/jfm.2013.435
  * (37) Vollestad P, Ayati AA, Angheluta L, LaCasce JH, Jensen A (2019) Experimental investigation of airflow above waves in a horizontal pipe. Int J Multiphase Flow 110:37-49. https://doi.org/10.1016/j.ijmultiphaseflow.2018.08.008
  * (38) Westerweel J (1993) Digital image particle velocimetry-theory and application. Delft University of Technology, Delft
  * (39) Wieneke B (2005) Stereo-PIV using self-calibration on particle images. Exp Fluids 39(2):267-280. https://doi.org/10.1007/s00348-005-0962-z
  * (40) Zhu YD, Yuan HJ, Zhang CH, Lee CB (2013) Image-preprocessing method for near-wall particle image velocimetry (PIV) image interrogation with very large in-plane displacement. Meas Sci Technol 24(12):125302. https://doi.org/10.1088/0957-0233/24/12/125302