九州大学大学院総合理工学府報告第 40 巻 第 1 号 1-6 頁 平成 30 年 9 月

Engineering Sciences Reports, Kyushu University
Vol. 40, No. 1, pp. 1-6, SEP, 2018

Laboratory Experiments on the Transition ofWind-Driven Water Surface
Daisuke MIYAZAKI*1 Yuji SUGIHARA*2,† Yoshihiro NAKAMURA*3
Michio SANJOU*4 and Takaaki OKAMOTO*4
E-mail of corresponding author: sugihara@esst.kyushu-u.ac.jp†(Received July 5, 2018, accepted July 6, 2018)
In order to investigate the transition process of the wind-driven water surface, laboratory experiments
were made in a wind-water tunnel with a pipe for the circulation of water. In addition to visual observationof the water surface, measurements of the wind speed, the wind wave and the drift current in water werecarried out in the present experiments. We focused on the relationship between the transition process andsome wind-wave parameters, and examined if what kind of parameter is effective for identifying the wave
breaking. The behavior of the drift current velocity in water was found to be varied by the occurrence of the
micro wave breaking on the surface. It was concluded that the drift current velocity gives an important
aspect of the momentum transfer across the water surface, so that it becomes a significant index to describe
the transition process of the wind-driven water surface.
Key words: Wind wave, Wave breaking, Drift current, Transition process, Friction Velocity,

Wind-water tunnel experiment1.

Introduction

The exchange mechanism of the momentum
or gases across the ocean surface is governedby turbulence dynamics coupled to the wave
breaking phenomenon.
Such a dynamics
varies obviously depending on the aspect of thewind-driven water surface, corresponding towind velocity and wave field conditions. The
transition of the water surface with increase of
the wind velocity is mostly as follows: thewater surface first shifts from the completesmooth surface to the capillary wave surface.
In the next stage, the gravitational
wind-driven waves occur on the surface, andsuch waves reach the wave breaking when
exceeding a certain critical condition. The
surface with violently-breaking waves becomesthe completely rough surface. The transition
process is complexly intertwined with themomentum transfer between the atmosphereand the ocean, and it is regarded as a certain
critical phenomenon for the occurrence of the
ING SHOJI, Co., Ltd.
Department of Earth System Science and Technology
Department of Earth System Science and Technology,
Graduate Student*4 Department of Civil and Earth Resources Engineering,
Kyoto University
*1
*2
*3

wave breaking. Thus, it is important to findout dimensionless parameters to identify thetransitional process, especially the wave
breaking.
Many studies have been made to investigate
the transition process of the wind-driven water
surface. Developing wind-waves trend to beequilibrated locally with wind1), 2). Such wave
fields are well known to satisfy Toba’s
3/2-power law, which is a similarity law
covering a wide range of wind waves. Toba
and Koga3) proposed a parameter suitable forexpressing the occurrence of the wave
breaking. It is called the windsea Reynolds
number4), and defined by the following
relation:
RB 

u*2

 p a,(1)where u* is the friction velocity on airside, athe kinematic viscosity of air, and p the
spectral-peak wave angular frequency. In a
range of RB > 103, the wind-driven water
surface becomes violently-breaking waves withthe generations of bubbles and water spray.
Also, Mitsuyasu5) found that the aspect of thewind-driven water surface varies around u*＝

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Laboratory Experiments on the Transition of Wind-Driven Water Surface

0.2m/s, and that the relations of the mean
wind speed and the wave spectrum with thefriction velocity vary around u*＝0.2m/s. The
value corresponds approximately to the mean
wind speed of approximately 8m/s, which iswell known to that at the occurrence of thewhitecaps on the ocean surface.
The purpose of this study is to examine thetransition process of the wind-driven water
surface. Laboratory experiments were madein a wind-water tunnel with a pipe for thecirculation of water. In addition to visualobservation
of
the
water
surface,measurements of the wind speed, the wind
wave and the drift current in water werecarried out in the experiments.
We
investigated the relationship between thetransition process and some wind-wave
parameters, and examined the validities of theparameters for identifying the wave breaking.

2.

Experimental Procedure

Laboratory experiments were performed ina wind-water tunnel with a pipe for thecirculation of water, at the Graduate School ofEngineering, Kyoto University.
Figure 1
shows aschematic
diagramoftheexperimental apparatus. The tank was 16m

long, 0.4 m wide, and 0.50 m deep. The
wind-driven water flow can circulate throughthe pipe, so that no return flow appears in thewater tank. Tap water was used in theexperiments, and the water depth was kept at
0.25 m in all cases.
Measurements werecarried out at the fetch of 8.0 m, which denotes
the distance taken leeward from the upwindedge in the tunnel. The vertical profile of thewind speed was measured by using a hot-wireanemometer. In addition, the displacement of
the water surface was measured using acapacitance wave gage. The significant wave
height Hs, the spectral-peak wave period Tp,
and the spectral-peak angular frequency pwere calculated from the data of the surface
displacement.
The flow rate of the drift
current in water driven by the wind stress wasmeasured using an electromagnetic flowmeterattached to the circular pipe.
Experimental parameters are summarizedin Table 1, where Ur is a reference wind speed
at the fetch of the wind-water tunnel, andu*and u*w are the friction velocities on airsideand waterside, respectively.
Also, U10
indicates the mean wind speed at the height of
10 m from the water surface. The value has
been calculated by fitting the logarithmic law
to the profile of wind speed near the water

Fig. 1 Experimental apparatus
Table 1 Experimental parameters
case
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18

U r(m/s)u *(m/s)u *w(m/s) U 10(m/s)

1.75
2.31
2.88
3.44
4.04
4.58
5.14
5.70
6.31
6.89
7.39
7.83
8.31
8.67
9.06
9.44
9.50
9.83

0.017
0.023
0.035
0.040
0.067
0.081
0.140
0.153
0.223
0.407
0.520
0.584
0.598
0.959
1.333
1.401
1.712
1.757

5.92E-04
7.91E-04
1.20E-03
1.38E-03
2.32E-03
2.78E-03
4.81E-03
5.27E-03
7.67E-03
1.40E-02
1.79E-02
2.01E-02
2.06E-02
3.30E-02
4.58E-02
4.81E-02
5.88E-02
6.04E-02

1.75
2.48
2.73
3.39
4.29
5.38
6.87
7.32
8.89
12.6
13.8
14.4
15.9
21.6
26.6
27.6
31.0
31.6

H s(m)
9.39E-04
2.71E-03
5.36E-03
1.01E-02
1.42E-02
1.81E-02
2.19E-02
2.69E-02
2.91E-02
3.39E-02
3.68E-02
4.05E-02
4.67E-02
4.98E-02
5.45E-02
5.87E-02
6.23E-02
6.75E-02

T p(s)Q (l/s)

0.298
0.312
0.377
0.388
0.400
0.427
0.427
0.441
0.457
0.474
0.492
0.492
0.512
0.533
0.582

0.19
0.32
0.51
0.80
0.96
1.23
1.48
1.69
2.00
2.29
2.63
2.96
3.32
3.69
4.03
4.37
4.65
4.86

Surface aspect
Complete smooth surface
Capillary wave〃
Gravitational wind-wave〃
Micro wave breaking [MB]〃〃Wave breaking [B]〃〃Wave breaking with bubble [BB]
〃
〃
〃
〃
〃

平成 30 年度

九州大学大学院総合理工学報告

surface. We should note that the value of u*w
has been obtained from the following relation:au*  wu*w
2

2

(1)

第 40 巻第1号

3

different between laboratory water surfaces
and actual ocean surfaces at high wind speeds.

3.

Results and Discussion

with a and w being the densities of air andwater, respectively.
The above relationmeans the continuity of the momentum
transfer across the water surface. The valuesof p in the cases of 1 to 3 couldn’t be obtained
from the spectra. Table 1 also gives the
aspects of the wind-driven water surface
identfied by visual observation. In this study,
the patterns of the wave breaking wereclassified on the basis of the scale of the wind
waves. The slightly-breaking waves due tothe instability of the wave train are called themicro wave breaking, which is expressed by
the symbol of MB （ Micro Breaking ） . In
addition, the wave breaking with no clearlyvisible bubbles is expressed by B（Breaking），
and the symbol of BB（Breaking with Bubble）
gives the violent wave-breaking with thegeneration of visible bubbles. It should be
noted that in wind-water tunnel experiments,
the sale of the wind-driven wave must be
limited in the width of the wind-water tunnel,
so that properties of the wind waves may be

3.1 Transition of Wind-Driven Water Surface(a) Ur = 2.31m/s（U10 = 2.48m/s, u* = 0.023m/s）(d) Ur = 6.31m/s（U10 = 8.89m/s, u* = 0.223m/s）[B](b) Ur = 3.44m/s（U10 = 3.39 m/s, u* = 0.040m/s）(e) Ur = 8.31m/s（U10 = 15.9m/s, u* = 0.598m/s）[BB](c) Ur = 4.58m/s（U10 = 5.38m/s, u* = 0.081m/s）[MB](f) Ur = 9.44m/s（U10 = 27.6m/s, u* = 1.401m/s）

Figures 3 (a)-(f) show typical patterns of
the wind-driven water surfaces photographed
under the conditions of various wind speeds,
where the shutter speed of camera was 100 fps
in a range of Ur < 6.31 m/s, and otherwise thespeed was 125 fps.
Features of thewind-driven water surface observed at eachwind speed, i.e., the transition process, are as
follows:(a) Ur = 2.31 m/s（U10 = 2.48 m/s, u* = 0.023m/s）: capillary wave occurs on the surface.
(b) Ur = 3.44 m/s（U10 = 3.39 m/s, u* = 0.040m/s）：Gravitational wind-wave is observed.
(c) Ur = 4.58 m/s（U10 = 5.38 m/s, u* = 0.081m/s）：the instability of wave train occurs,
and the micro breaking of wave crest isobserved [MB].
(d) Ur = 6.31 m/s（U10 = 8.89 m/s, u* = 0.223m/s ） ： definitely breaking waves are
obviously shown, and the water surface
may become incomplete rough one, but the
bubbles in the water are indistinct [B].

Fig. 2 Visualized transition process of wind-driven water surface

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Laboratory Experiments on the Transition of Wind-Driven Water Surface

1.00E+01

Ud/u*ｗ

Q[l/s]

1.00E+01

1.00E+00

1.00E-01
1.00E-03

1.00E-02

1.00E-01

1.00E+00

1.00E+00

1.00E-01
1.0E-5

1.00E+01

1.0E-4

1.0E-3

Relation between Q and u*

Fig. 4

1.0E-1 1.0E+0 1.0E+1 1.0E+2

Relation between Ud/u*w and Kew

1.00E-051.00E-041.00E-031.00E-021.00E-011.00E+001.00E+011.00E+02
1.0E+04
10,0001.00E-03 1.00E-02 1.00E-01 1.00E+00 1.00E+01 1.00E+02 1.00E+03
1.0E+04

1.0E+031,000

1.0E+03

1.0E+02100

1.0E+0110

1.0E+01

1.0E+00

1

1.0E+00
1.0E-03

UdH s/νw

UdH s/νw

Fig. 3

1.0E-2Keｗ

u* [m/s]

1.0E-05 1.0E-04 1.0E-03 1.0E-02 1.0E-01 1.0E+00 1.0E+01 1.0E+02

1.0E+02

Kew

Fig. 5The above process may show the typicalaspects of the wind-driven water surface
observed in laboratory experiments. In thisstudy, the wind speed condition under which
the micro wave breaking occurs, becomesapproximately U10=5m/s.
In addition, thecondition for definite wave-breaking may be
below approximately U10 ＝8m/s. The friction
velocity on airside for this value of U10 agrees
approximately with 0.2 m/s, whose value is thecriticalfriction
velocity
proposedby
Mitsuyasu5). Large-scale wave breaking withthe generation of bubbles may occur
approximately at U10 ＝ 15m/s, which agrees
with the windsea Reynolds number RB of
1.7×103.
This value corresponds to the

1.0E-01 1.0E+00 1.0E+01 1.0E+02 1.0E+03

RBｗ

Relation between UdHs/w and Kew(e) Ur = 8.31 m/s（U10 = 15.9 m/s, u* = 0.598m/s ） ： the wave breaking with bubbles
occurs [BB]．
(f) Ur = 9.44 m/s（U10 = 27.6 m/s, u* = 1.401m/s）：the water spray produced due to thewave breaking is observed.

1.0E-02

Fig. 6

Relation between UdHs/w and RBw

critical windsea Reynolds number of the orderof 103, proposed by Koga and Toba3).
Therefore, the validity of the transition of thewind-driven water surface in the present
experiments may be supported by the resultsof previous studies. It should be noted that
under high wind speed conditions, theaccuracies of u* and U10 decrease in thecomparison with lower wind speed conditions
because of the difficulty of the wind speed
measurements close to the water surface andthe influence of the water spray in air.
3.2

Relationship between Transition Process
and Drift Current Velocity

Figure 3 shows the relation between the flowrate of the drift current Q and the friction
velocity on airside u*. Here, the two solidlines are drawn in the figure, and they denote
the regression lines for the ranges before andbehind approximately u*=0.1m/s. It is seenfrom the figure that the gradients of the twolines vary definitely before and behind this

九州大学大学院総合理工学報告

point. The value of u*=0.1m/s corresponds
approximately to the condition that the micro
wave breaking occurs on the water surface, as
pointed out in the previous section.
Thewind stress acting on the water surface drives
the wind waves and the drift current in water.
In the range of relatively low wind speeds, themomentum of wind is considered to betransferred mainly to the waterside via thefriction on the water surface. Thus, it isnatural to consider that under such conditions,the momentum may be injected to drive thedrift current in water, not to develop wind
waves. After the generation of the wave
breaking, the momentum transferred fromwind may increase the momentum in the flow
direction through the wave breaking process.
In addition, eddy motions induced by the wave
breaking should diffuse the turbulent energy
near the water surface. The increase of theeddy viscosity via such a process promotes
the air-water exchange process. Thus, thedecrease of the gradient of Q due to the micro
wave breaking may be understood that the
momentum transferred from wind is used todevelop the wave motions. The finding thatthe drift current varies at a certain criticalcondition relating to the wave breaking is very
interesting from viewpoint of fluid dynamics.
The mean drift current velocity Ud was
calculated by averaging the value of Q over the
cross-section area of water flow. In Fig. 4, thevalues of Ud normalized by the friction velocity
on waterside u*w are plotted for the Keulegan
number defined by
3

Kew 

u*w
g w

(2)

where g and w are the gravitational
acceleration and the kinematic viscosity ofwater, respectively. The two solid lines are
the regression lines before and behind theoccurrence of the micro wave breaking. The
critical Keulegan number for the micro wave
breaking becomes approximately Kew=2.0×10-3.
This figure shows that before the criticalnumber, the dimensionless drift current
velocity increases slightly with Kew, whereas it
decreases definitely with increase of Kew
behind the critical value. Such a behavior ofthe drift current velocity supports the
hypothesis that when generating the wave
breaking, the momentum transfer to the wave
development becomes larger compared to thattransferred to the shear flow.
Figure 5 indicates the relation between
UdHs/w and Kew, where the parameter UdHs/w
can be interpreted as a certain Reynolds

第 40 巻第1号

5

1.0E+04

1.0E+03

UdH s/νw

平成 30 年度

1.0E+02

1.0E+01

1.0E+00
1.0E-01

1.0E+00

1.0E+01

1.0E+02

1.0E+03

1.0E+04

RHｗ

Fig. 7 Relation between UdHs/w and RHw

number based on the drift current and thewave height. Across the critical value of theKeulegan number for the micro wave breaking,the gradient of UdHs/w against Kew varies
obviously. However, the other types of the
wave breaking such as B and BB cannot be
observed in this figure.
According to Koga and Toba3) and Toba et al.
4), we consider the windsea Reynolds number
RBw, defined by the friction velocity and thekinematic viscosity on waterside as follows:
2

RBw 

u* w

 p w(3)

The relation of UdHs/w with RBw is displayedin Fig. 6. We should note that the values of
p in the cases of 1 to 3 have been estimatedconveniently from the values of Hs via Toba’s
3/2-power law. The behavior of theexperimental data on the space of these
dimensionless parameters is found to bequantitatively similar to those in Fig. 5. We
also should note that the critical value of RBw
appears around approximately the order of 0.1.
This suggests that it is suitable for the scaling
to use the physical quantities on waterside.
That may be because the phenomenon of the
wave breaking appears on the surface of thewater waves.
Figure 7 indicates the relation between
UdHs/w and RHw, where RHw is a windsea
Reynolds number defined by
RHw 

u* w H S

w(4)

This figure shows the gradient change aroundthe micro wave breaking becomes quite
smaller in comparison with Kew and RBw.
The behavior can be expressed approximately

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Laboratory Experiments on the Transition of Wind-Driven Water Surface

by a certain one regression curve. Therefore,
the dimensionless parameter RHw may beinsensitive to identify the critical condition of
the micro wave breaking. Conversely, there isa possibility that RHw is a universal wind-wave
parameter independent of the transition
process such as the wave breaking.

4.

Summary and Conclusion

In this study, the transition process of thewind-driven water surface was investigatedthrough the wind-water tunnel experiments.
The visual observation of the water surface
was made, and the wind speed, the wind wave
and the drift current in water were measured
under various wind speed conditions. We
treated with the relationship between thetransition process and some wind-wave
parameters. The behavior of the drift current
velocity in water was found to be varied by theoccurrence of the micro wave breaking on thewater surface. It was concluded that the drift
current velocity gives an important aspect ofthe momentum transfer across the water
surface, so that it becomes a significant index
to describe the transition process ofwind-driven
water
surface.
We
alsodemonstrated that the wind-wave parameterssuch as the Keulegan number and the windsea
Reynolds number can express the criticalcondition of the micro wave breaking.

Acknowledgments
This work was partially supported by
Grant-in-Aid for Scientific Research (C)(Coordinator: Y. Sugihara, Grant Number:
16K06514) from JSPS. The authors would
like to thank Prof. N. Matsunaga at Kyushu
University and Prof. K. Toda at Kyoto
University for their encouragement.
References
1) Toba, Y., Local balance in the air-sea boundary
processes I. On the growth Processes of wind waves, J.
Oceanogr., 28, pp. 109–121, (1972).
2) Masuda, A., and T. Kusaba, On the local equilibriumof winds and wind-waves in relation to surface drag, J.
Oceanogr. Soc. Japan, 43, pp. 28–36, (1987).
3) Toba, Y. and M. Koga, A parameter describing overall
conditions of wave breaking, whitecapping, sea-spray
production and wind stress, Oceanic Whitecaps,
edited by E. C. Monahan and G. Mac Niocaoll, D.
Reidel, pp. 37–46, (1986).
4) Toba, Y, S. Komori, Y. Suzuki and D. Zhao, Similarityand dissimilarity in air-sea momentum and CO2transfers: the nondimensional transfer coefficients inlight of windsea Rynolds number, Atomosphere-Ocean
Interaction Volume 2, Ed. W. Perrie, WTT Press, pp.
53-82., (2006).
5) Mitsuyasu, H., A note on a critical wind speed for
air-sea boundary process, J. Oceanogr, 73, pp.
169–180, (2017).