Spray of droplets torn off by the wind from the crests of waves
plays an important role in the exchange processes between the atmosphere and
the hydrosphere, especially under extreme (stormy) conditions. As was shown in
studies [1-3], it strongly influences on momentum, heat and moisture fluxes. A
quantitative analysis of the spray characteristics in situ is a complicated
problem. That is why for a long time investigations have been carried out in
laboratory conditions on the wind-wave facilities when the air flow rate is
sufficient for fragmentation of the water surface and formation of spray (see
[2-9]). Different
experimental
methods can be divided on point (see for example [4-6]) and
volumetric methods [2, 7-9]. Volumetric methods are based on visualization:
illumination with a laser sheet [7] or shadowgraph method [2, 8, 9] with video
recording, including high-speed filming, which became very popular. It allows
to obtain the data of the spray characteristics and to study in detail the
process of its formation both. It should be noted that regardless of the
methods used, measuring the characteristics of spray (velocity, size) close to the
water surface especially for high and strongly breaking waves caused by severe
wind is a very difficult task.
In [9] the
combination
of multi-view high-speed filming and the shadowgraph visualization within
laboratory experiments on the Thermostratified Wind-Wave Tank (TSWiWaT)
has
helped to study in detail
the typical mechanisms leading to the generation of spray and classify them for
the first time. The dominant mechanism - the so-called bag-breakup
fragmentation was identified based on the comparative analysis of the obtained
statistics of the main phenomena leading to the generation of spray. According
to laboratory experiments in [9] we can estimate that for the whole range of
wind parameters (from calm to severe conditions) the average frequency of
sporadic bag-breakup event was only 1 per 1000 frames of record (on average
over all wind speeds). This strongly complicates detailed investigation of this
phenomenon. In this case the artificial initiation of the phenomenon seems
proper way to solve the problem. A similar approach was previously used in
[10], where a bursting bubbles was artificially generated in a stationary
liquid. However, unlike underwater bubbles, the phenomenon of bag-breakup
fragmentation can be only simulated under conditions of air flow over the water
surface.
This paper describes a specially developed method of artificial
initiation of the phenomenon of bag-breakup fragmentation and spray generation
of the water surface, intended for use in a laboratory experiment to simulate
the wind-wave interaction. The investigations of this phenomenon were carried
out using optical methods based on visualization.
In
the experiments carried
out in [9],
the side view filming for a detailed study of spray generation
process and a qualitative analysis of spray characteristics
have demonstrated
that a
three-dimensional wind wave can obscure the region of formation of the
bag-breakups. Therefore, firstly we solve the problem of artificially
initiating the bag-breakup phenomenon on a smooth water surface without waves.
Taking into account that further experiments should be performed on a wavy
surface with waves we needed experimental results under similar air flow
conditions, i.e. on the same wind-wave facility. The experiments were carried
out at the TSWiWaT of IAP RAS. The air flume of total length of 9 m and
cross-section 0.4 × 0.4 m with the water depth of 1.5 m. The wind speed
on the axis was up to 25 m/s, which corresponds to the equivalent wind speed of
40 m/s recalculating to the standard meteorological height of 10 m for real
conditions. The wind speed in our experiments was measured using a Pitot gauge.
In [9] to study the processes of spray generation a side view of the water
surface was taken with camera
within
a special semi-submerged watertight underwater box
that was
located
perpendicular to the flume wall (see fig. 1 a) at a distance of 7.5 m from the
outlet. This box allows placing
the camera
below
the water level. In this
work a scheme of a special (unusual) experiment at TSWiWaT was developed for
research on an undisturbed water surface. Facility was completely drained and
at the working level of the water surface from the 1st to the 7th sections a
rigid flat plexiglass bottom was installed. A rectangular water reservoir
(20×20×70 cm, aligned along the flume) completely filled with water
was inserted into rigid bottom in the middle of the 8th section (see fig. 1 b).
The surface of the water coincided with the level of the plexiglass bottom.
As it was shown in [9] the bag is blown up by the wind from the
surface disturbance - a small elevation (protrusion) of water with typical
widths about 1 cm. Thus, we needed to provide the artificial initiation of such
a disturbance and ensure high repeatability of its sizes and shape. A special
electronic-hydraulic pulse system was developed for this purpose.
Initial disturbance was artificially created by underwater jet
from a submerged nozzle. The nozzle was placed in vertical orientation 1.5 cm
under water surface. It is assembled of 5 nickel tubes 20×2 mm, lined up
in a row in cross-wind direction. Water entered the nozzle at a pressure of 3
bar via an electronically controlled valve that was opened for a period of 20
ms. Driving signal for the valve was combined with triggers of both cameras in
synchronization system, controlled via microcontroller.
Fig. 1. Scheme of experiments at TSWiWaT a) usual wind-wave
conditions b) with artificial initiation of a disturbance from which a bag is
formed for rigid flat surface c) with artificial initiation of a disturbance on
the wavy surface. Designations: 1) TSWiWaT body 2) rigid surface 3) water
surface with waves 4) artificial disturbance on the surface from which the
bag-breakup develops 5) opaque screen 6) LED light sources 7) wire wave gauge
8) nozzle of the surface disturbance generating system 9) water reservoir
20×20×70 cm 10) watertight semi-submerged box 11) NAC HX-3
high-speed camera.
One of the main requirements for the system of artificial
initiation of a disturbance on the surface is the repeatability of its shape.
To check this, a high-speed filming of the process of disturbance initiation
was performed without air flow in the flume.
Similarly to
[9],
the
video was captured from
the side by a NAC Memrecam HX-3 high-speed camera installed in a watertight box
using a shadow method with illuminating LED lamps located behind the opposite
flume wall with an opaque screen at it. The frame rate was 3990 frames per
second, exposure 50
μs.
Each record from the side camera consisted of 700 frames (175
ms). Resolution was 2560×960 pixels, dimensions of the filming area
(161×60 mm).
An example of images of the disturbance for different time of
evolution is shown in Figure 2a. The visible contour of the disturbance was
automatically determined with help of algorithms for image processing taken
from the [11], where the form of surface waves with small scale breakings on
the crest was determined using Canny method. In Figure 2b and c the time
dependences of the width
W
and heights
H
of the disturbance on
the water surface are shown for ten consecutive cases of initiation performed
with a time step of 30 seconds. The
H
was chosen as the maximal distance
from the surface level to the top of the disturbance, and we used a
height-averaged width
W. Time dependencies are plotted from the moment
of 60 ms (trigger delay) after valve opening (start of inducing artificial
water elevation) until the moment of reaching the maximal
H
of water
surface elevation. Curves are very close to each other, and this can prove that
the high repeatability of the form of artificially initiated disturbance
created by the developed system.
Fig. 2. a) Tree consecutive images of an artificially initiated
surface disturbance with contour determination and denoting
W
and
H
parameters. An automatically determined contour is shown and the height and
width are indicated b) Time dependence of the height
H
for ten
successive realizations c) Time dependence of the width
W
for the same
realizations
The results have demonstrated that the
bag-breakups began to form regularly at speeds about 15 m/s. Fig.
3 shows a comparison of the images obtained in this work, and images of studies
of the bag-breakup occurred sporadically in the work [9]. The comparison
confirmed that it is possible to reproduce the phenomenon of bag-breakup spray
generation using artificial perturbation, including the stages of inflation,
membrane rupture, and rim fragmentation. This allowed the further development
of the system for conditions of rough surface. Earlier in [9] it was noted that
in sporadic regime bag-breakups are mainly formed on the crests of waves. Thus,
we had to ensure the operation of the system of artificial initiation of
disturbances on the surface at the required phase of the wave (at crests). A
resistive wire wave gauge, which located close to the observation area, at a
distance of 5 cm was used to obtain wave parameters (see Fig. 1c). The
operation of electronic-hydraulic system was synchronized with adjusted time
delay on the basis of signal from wave gauge.
(a)
(b)
Fig. 3. Set of frames of high-speed filming of the formation of a
bag-breakup in experiments at TSWiWaT. a) with artificial disturbance of the
surface, in the absence of waves according to the results of these studies b)
sporadical formation of a bag-breakup taken from [9]
Thus,
solely
matching
of
the images
was not
sufficient
and we should quantitatively
compare the main characteristics of artificial (in our case) and sporadically
occurred bag-breakups. To this purpose we processed the images of the
bag-breakups in the manner similar to what proposed in [12] to obtain parameters
of maximal size of the membrane before the rupture and lifetime of the
bag-breakups. The main difference was that in previous investigation top view
images were processed, but in our case the side images.
In Figure
4 we see a
good agreement between the results. Our data are well fitted with the
dependencies of the average values of maximal size and lifetime of the bags on
friction velocity
u
* proposed in [12] within the error bars.
|
(à)
|
(b) (c)
|
Fig. 4. a) the image of the bag with illustrating the processing
to define the size (radius) of the bag membrane in the moment of rupture b)
comparing our results of determining the averaged radius of bag membrane for
the moment of its rupture with data previously obtained in [12] (c) the same
comparison for the averaged bag lifetime
The results of present investigation demonstrated that previously
observed sporadic events of bag-breakup fragmentation on the free water surface
under the action of air flow could be induced artificially in control time and
space area for the condition of laboratory experiments. The shadow imaging
method combined with high-speed filming allowed to demonstrate quality and
quantity similarity between the artificial and observed in vivo bag-breakup
events. It was possible to reproduce all the main stages of this phenomenon: 1)
inflation of a thin membrane surrounded by a thicker rim, 2) rupture of the
membrane, leading to the formation of small droplets, 3) fragmentation of the
rim with the formation of large droplets. Also, special processing of the frame
sequences allowed to obtain main integral parameters of bag-breakups: averaged
lifetime and maximal size of the membrane before the rupture. It’s turned out
to be very close to the similar results with obtained for sporadic bag-breakups
events. The developed method can be used further for detailed studies of the
processes of spray generation due to the phenomenon of bag-breakup
fragmentation of the water surface not only at TSWiWaT, but also at other
experimental facilities.
This work was supported by the Russian Science Foundation project
19-17-00209 (development of software for image processing) and project
21-19-00755 (development of the hardware part of the artificial disturbance
generation system), Russian Foundation Basic Research project 19-05-00249
(development of an optical system), work of A.A. Kandaurov was partially
supported by the President's grant for young scientists
ÌÊ-5503.2021.1.5. The
experiments were carried out at unique scientific facility "Complex of
large-scale geophysical facilities of IAP RAS".
1. Andreas, E. L., A review of the
sea spray generation function for the open ocean// Adv. Fluid Mech., vol.
33, pp. 1–46, 2002.
2. Veron, F., Ocean Spray //Annu.
Rev. Fluid Mech., vol. 47, pp. 507–538, 2015.
doi.org/10.1146/annurev-fluid-010814-014651
3. Komori, S. et al., Laboratory
Measurements of Heat Transfer and Drag Coefficients at Extremely High Wind
Speeds // J. Phys. Oceanogr., vol. 48, pp. 959–974, 2018.
doi.org/10.1175/JPO-D-17-0243.1
4. Lai, R. J. & Shemdin, O. H.,
Laboratory study of the generation of spray over water // J. Geophys.
Res., vol. 79, pp. 3055–3063, 1974.
doi.org/10.1029/JC079i021p03055
5. Wu, J., Spray in the atmospheric
surface layer: Laboratory study // J. Geophys. Res., vol. 78, pp. 511–519,
1973.
doi.org/10.1029/JC078i003p00511
6. Fairall, C. W., Banner, M. L.,
Peirson, W. L., Asher, W. & Morison, R. P., Investigation of the
physical scaling of sea spray spume droplet production// J. Geophys. Res.,
vol. 114, pp. C10001, 2009. doi.org/10.1029/2008JC004918
7. Anguelova, M., Barber, R. P. and
Wu, Laboratory observation of spume drops produced by wind tearing of wave
crests // J. Phys. Oceanogr., vol. 29, pp. 1156-1165, 1999.
doi:10.1175/1520-0485(1999)029<1156:SDPBTW>2.0.CO;2
8. Koga, M., Direct production of
droplets from breaking wind-waves —its observation by a multi-colored
overlapping exposure photographing technique // Tellus, vol. 33, pp.
552–563, 1981. doi.org/10.3402/tellusa.v33i6.10776
9. Y. I. Troitskaya, O. S.
Ermakova, A. A. Kandaurov, D. S. Kozlov, D. A. Sergeev, and S. S.
Zilitinkevich, Fragmentation of the ‘bag-breakup’ type as a mechanism of
the generation of sea spray at strong and hurricane winds // Dokl. Earth
Sci., vol. 477, no. 1, pp. 1330–1335, 2017.
doi.org/10.1134/S1028334X17110174
10. Lhuissier, H. & Villermaux,
E., Bursting bubble aerosols, J. Fluid Mech., vol. 696, pp. 5–44, 2012.
doi.org/10.1017/jfm.2011.418
11. Kandaurov, A.A., Troitskaya,
Y.I., Sergeev, D.A., Vdovin, M.I., Baidakov, G.A. Average velocity field
of the air flow over the water surface in a laboratory modeling of storm
and hurricane conditions in the ocean // Izvestiya - Atmospheric and Ocean
Physics, 2014, vol.50, I.4, pp. 399-410. doi.org/10.1134/S000143381404015X
12. Troitskaya, Y. I. Troitskaya,
Y.I., Ermakova, O.S., Kandaurov, A.A., Sergeev D.A., Kozlov D.S.,
Zilitinkevich S.S. Non-monotonous dependence of the ocean surface drag
coefficient on the hurricane wind speed due to the fragmentation of the
ocean-atmosphere interface// Doklady Earth Sciences, 2017, vol. 477, pp.1373–1378
doi.org/10.1134/S1028334X17110265
