Turbulent properties and spectral behaviours of ocean winds observed at an off-shore tower

Journal of Wind Engineering and Industrial Aerodynamics, 28 (1988) 51-60

5l

Elsevier Science Publishers B.V., Amsterdam - - Printed in The Netherlands

TURBULENT PROPERTIESAND SPECTRAL BEHAVIOURSOF OCEAN WINDS OBSERVEDAT AN OFF-SHORE TOWER G. NAITO Hiratsuka Branch, National Research Center f o r Disaster Prevention, HiraL
ABSTRACT Various c h a r a c t e r i s t i c s of the atmospheric turbulence above the open sea were estimated by analysing three-dimensional wind f l u c t u a t i o n s , which were observed at two levels of an off-shore tower under the condition of long l a s t ing strong winds. Gust f a c t o r , turbulent i n t e n s i t i e s of three wind vectors and drag c o e f f i c i e n t were shown to be functions of wind speed. Spectrum of l o n g i t u dinal v e l o c i t y in very wide frequencies was obtained and i t s behaviours were discussed. Dependency of v e r t i c a l c o r r e l a t i o n and eddy coherence to mean wind speed were evaluated f o r large scale eddies in the atmospheric boundary layer. NOTATION drag c o e f f i c i e n t of the sea surface

c D D

observation time or averaging time of wind speed

G

gust f a c t o r

n

frequency

P(n)

power spectrum density

R

vertical correlation coefficient

z

mean wind speed ~,V,W

f l u c t u a t i n g v e l o c i t i e s in the l o n g i t u d i n a l , l a t e r a l and v e r t i c a l directions v e r t i c a l coordinate or height above the sea surface eddy coherence standard deviation of wind f l u c t u a t i o n s

I.

INTRODUCTION The ocean wind, which is never disturbed by configurations, is most favour-

able to make clear turbulent c h a r a c t e r i s t i c s of the atmospheric boundary layer. On the other hand, since the sea surface covered with waves changes with increasing wind speed, the ocean wind has special properties in comparison with the land wind. The fetch of ocean wind can be expected to be i n f i n t e , and the atmospheric disturbance strongly influences the ocean wind. There are many reports about the turbulent structure of the surface layer, 0167-6105/88/$03.50

© 1988 Elsevier Science Publishers B.V.

52

but almost a l l of these are fo r the a i r flow on land. Experimental studies of the ocean wind v e l o c i t y often f a i l ,

because the instrumentation of sensors in

the sea is very d i f f i c u l t . On the spectral structure of the boundary l a y e r , several models have been proposed by Davenport[l], Hino[2], Kaimal et a l . [ 3 ] and other researchers. These experimental formulas can be used to consider the spectral behaviours during about 30 min.

Atmospheric f l u c t u a t i o n s in the boundary layer cannot be divided

i n t o two components, i . e . the turbulence which has smaller eddies and the disturbance which has l a r g e r eddies. Therefore, when we want to estimate the det a i l e d atmospheric structure above the ground surface, the spectrum density in the range of very wide frequency is indispensable. Unfortunately, we can scarcely f i n d a report on long period spectrum of wind v e l o c i t y except f o r that of Van der Hoven[4]. Since D a v e n p o r t ' s [ l ] suggestion regarding the geometric s i m i l a r i t y of the boundary l a y e r , the study on the s p a t i a l c o r r e l a t i o n of turbulent eddies has been developed to a f a i r degree. Shiotani and l w a t a n i [ 5 ] , and Kristensen and Jensen[6] have shown various features of the eddy coherence. Naito[7,8] has represented the d e t a i l e d s p a t i a l structure of the three-dimensional wind vectors observed in the sea. I s h i z a k i [ 9 ] has discussed various features of the atmospheric turbulence from data observed at coasts and islands. The aim of the present study is mainly to c l a r i f y the turbulent characterist i c s and spectral behaviours of large scale eddy and the influence of atmospheric disturbance on the turbulence in the surface layer. 2. INSTRUMENTATION

Strong winds were measured at an observation tower in the bay opening to the P a c i f i c Ocean (see Fig. I ) . The tower whose top is 20m high above the mean sea level is located at a point IKm o f f the shore, and b u i l t on the sea bed 20m deep. The bay is toward the southern d i r e c t i o n , and so the i n f i n i t e fetch can be expected f o r the southerly wind. The wind v e l o c i t y was measured by using a couple of three-dimensional sonic anemometers (Kaijo Denki, Model DAT-300). A f t e r having considered the best way Lo Fig. I . The marine observation

avoid wind f l u c t u a t i o n s induced by tower

tower o f f the shore.

proper, each sensor was attached at the

,53 long boom o f the tower. The upper and lower wind sensors were a t the heights o f 23.0m and 6.85m above the sea surface r e s p e c t i v e l y . Output data from sensors were d i g i t a l i z e d

in the t o w e r , and t r a n s m i t t e d to

the l a b o r a t o r y on land by an o n - l i n e computer system. Wind vectors measured were sampled every O.06sec, and a n a l i z e d by s t a t i s t i c a l

techniques f o r a run o f

I0 min, 30 min o r 400 min in d u r a t i o n . 3. RESULTS AND DISCUSSIONS 3.1 Turbulent p r o p e r t i e s o f wind vectors When strong winds l a s t over a long t i m e , the wind v e c t o r a t a c e r t a i n l o c a t i o n is not always s t a t i o n a r y ,

because the atmospheric d i s t u r b a n c e which

genarates the strong winds near the ground g r a d u a l l y moves. Typical strong d i s t u r b a n c e s are the typhoon and the developed e x t r a t r o p i c a l

cyclone.

Gust f a c t o r s at two heights are shown in Fig. 2. The gust f a c t o r was computed under the c o n d i t i o n of a I0 min mean wind speed and a O.24sec averaging time o f peak gust. The group o f the open c i r c l e s enclosed by a broken l i n e is independent of the lower p o i n t s , and i s thought to be caused by the strong d i s t u r b a n c e . Several p o i n t s associated w i t h arrow in the r i g h t p a r t were caused by severe gust storm, and the gust f a c t o r changed w i t h the passage o f time toward the arrow d i r e c t i o n .

In t h i s case of extreme strong g u s t , the maximum instantaneous

wind speed suddenly increased from about 20m/s to 50m/s, and t h a t same maximum speed l a s t e d f o r a p e r i o d o f 50 min. The mean wind speed g r a d u a l l y increased during the same t i m e , as shown in the f i g u r e .

The upper two groups do not obey

3.5 z=6.85m z=23.0m

3.O

\

SEVERE STORM

\ ek~e

2.5

2.0

~o °o oo

",i °~ ° ~ %•

1.5

"~

o~. . . . . . . . .

2-

.

1,o

0

i

I

i

5

i0

r

15

I

i

2o

25

U (re~s) Fig. 2. Gust f a c t o r a g a i n s t mean wind speed a t two h e i g h t s .

3O

B4

the well-known empirical expressions. The lower points were obtained for the ordinally turbulence. We find here that the gust factors at two heights are not so much d i f f e r e n t , and obey the formula already proposed by many researchers. Fig. 3 shows the turbulent intensities, o/u, as a function of the mean wind speed, u, during 30 min. The intensities of the three wind vectors

(u,v,w) are

scattered, because wind velocities are influenced by a strong disturbance which involves large scale turbulences. We find that the intensity at the lower height is larger than that at the upper height, Straight lines in the figure approximate to the values in high winds, and are expressed by the following formulas.

au/u = 0.116,

av/~ = 0.091,

aw/u = 0.050

for

u ~ lOm/s and z = 6.85m,

a /u = 0.090,

Ov/U= 0.071,

Ow/U = 0.036

for

u z 12m/s and z = 23.0m.

U

Ishizaki[9] gives the following expression of gust factor; q = 1 + 0 . 5 (a / U )

(I)

ln(p/s)

u

where D i s t h e a v e r a g i n g t i m e o f t h e mean wind speed, s t h e a v e r a g i n g t i m e o f the peak g u s t .

0.20

Putting

-TF'~---i~

I

t h e v a l u e s o f ~ = I0 min and s = 0.24 sec on ( 1 ) , w e

I 7

Io I T - T ] ~ - I ~ I - - T - - T - -

U

o o

v

o

•o

~I

o

•

:0

l~G

o

0

.

o

% °:o°'~ ' o.,'~

oF

D

-i

OooF~O "",

..

o

o

|,,

oO
o

%'..~.

I~.~.. 0.i0

o

o

o °

•

°°

0.15

have

o

--

,o

o/U

o

O•o

t4

•

~,

o

o o

1 I

,o0

]

o ,

o .°-%:"-:.'._

_-o.o o

• o •

•

t

,t

•

0.05

aF=o. 07

.

.' ...

.

D o

o z=6.85m • z=23. Om I um3_I I i i I i~_-L~±m±~ 0 5 i0 15

.~kM~_.

2O

o

5

U (~ls) 0.01

~

I

I

I'-7--~q~TT~-T~F

L k_~l.~l

~ L A ~ . ~ t

IO

15

....

20

(~/s) T - U ~ F

~'1

I

o W

o

0/~

o,

/u

t~ o.o5

--o050

o o o o

"

,~o o

o

Fig.3. Turbulent intensities

_

0/U=0.036

, ~" , '. 41%

•

of wind vectors ( u , v , w ) 0

5

I0

-6 (m/s)

15

20

again-

st mean wind speed at two heights.

5,5 G= 1

+

(2)

3.9 (o u /u)

Using the values of the t u r b u l e n t i n t e n s i t y , o u /u, in high winds, we o b t a i n c = 1.45 at z = 6.85,

and G = 1.35 at z = 23.0m.

The above values of the gust f a c t o r agree with the values under the s t a t i o n a r y c o n d i t i o n of turbulence, as shown in Fig. 2. The v e r t i c a l momentum f l u x , ~, is u s u a l l y discussed by the drag c o e f f i c i e n t defined by

% : I~/~I/F ~ = (u./F) =

(3)

where ~ is the a i r density and

u,

= ~

is the f r i c t i o n

v e l o c i t y . The momentum

transported to the ocean generates and develops ocean waves and currents. Fig. 4 shows the drag c o e f f i c i e n t against the mean wind speed at 6.85m high. The momentum f l u x as well as the t u r b u l e n t i n t e n s i t y is considered to be i n f l u enced by the atmospheric disturbance.

I t is noted t h a t the value of c

f o r the D f o r the developed e x t r a t r o p i c a l cyclone.

typhoon is o b v i o u s l y l a r g e r than c D The approximate l i n e f o r the developed cyclone agrees with the formula of Davies and F l a t h e r [ 1 0 ] , who have proposed to derive the surface wind from the geos t r o p h i c wind, as f o l l o w s

(4)

lO3cD = -O.12 + 0.137 ~ i The approximate l i n e f o r the typhoon is expressed by

IO3CD =

0.186UI

Here Ul is in

(5)

m/s

unit.

I f both the l o g a r i t h m i c law and the power law are a p p l i c a b l e to the v e r t i c a l p r o f i l e o f the mean wind speed, the index, m, of the power law can be given by : ( I I K ) c / ~D-

3.0

•

i I

(6)

t

I

[

|

I

I

I

J

F~

o EXTRATROPICAL CYCLONE c~ o

2.0

• T P OON

[

•

I--

~ ,,,.~z o

" "il'

/

/

no o ~,o .,°" o ~ o oog~ Oo / oO~ o °~

1.0 ~q- (5)" Eq. (h)

0 0

T~/;I /

/ .....

J Fig. 4. Drag c o e f f i c i e n t against mean wind speed at the height of 5

i0

Ul(m/s)

15

2O

6.85m.

56 where < = 0.4 is the Karman constant. The above formula implies that ~ varies with the aerodynamic roughness height, Zo. Using the formulas ( 3 ) , ( 4 ) , ( 5 ) and (6), we obtain a t y p i c a l model of strong ocean wind as described by the f o l l o w i n g table~

U1

Case

CD

u,

(cm/s)

Zo

(m/s)

x1000

(cm)

Extratropical cyclone

12.0

1.52

46

0.02

0.097 (: 1/10.2)

Typhoon

12.0

2.23

56

0.13

0.118 (= I / 8 . 5 )

Here the reference height is 6.85m. The sea during a typhoon is very rough in comparison with the sea during other storms. 3.2 Spectral behaviour of long l a s t i n g ocean wind The well-known models of the power spectrum of wind v e l o c i t y are mostly based

on

data obtained during a period of about one hour. In other words, i t

is i m p l i c i t l y assumed that the atmospheric boundary layer is made up of eddies less than the period of about I0 min. Therefore, spectral behaviours of large scale eddies are not s u f f i c i e n t l y expressed by these models. Fig. 5 shows power spectra of l o n g i t u d i n a l wind vector, which was observed more than 400 min under the condition of a s t a t i o n a r y strong wind. In four cases of the f i g u r e , the wind d i r e c t i o n did not l a r g e l y deviate in the observation time. Runs 8402 and 8414-B were obtained at z I = 6.85m. In these runs, the spectra in high frequencies deviate w i t h i n the range between two dotted l i n e s . Run 8414-B was observed in the typhoon. Two spectra of Runs 8606 and 8611 were simultaneously measured at two heights of zI = 6.85m and

z2

= 23.0m. The smooth

curve of Run 8402 f i t t e d to observed spectrum is described by nP (n) u _ 2

71 n

(7) (I + 93 n )S13

u

where ~

U

= 188 cm/s is the mean value of the 30 min standard deviations of the

l o n g i t u d i n a l wind vector. We f i n d out t h a t the spectral features, e s p e c i a l l y in lower frequencies, d i f f e r from each other, and that each spectrum has a peak and a trough except f o r Run 8606. The trough is considered to be the lower l i m i t of frequencies f o r the atmospheric turbulence of the surface boundary layer. A d d i t i o n a l l y , as seen in Runs 8606 and 8611, the spectrum density at the upper height is l a r g e r than that at the lower height in lower frequencies, but t h i s feature becomes contrary

57 105

I

I

I

I

I

I

I

I

I

I

I

RUN 8402 104

D=40Omin

103

Eq.(7)

"'~

Ul=l,239cm/s

10 4 RUN 8414-B

D=720min

c~ ~Q

ci

103

~

10 4

,Q "~ b~ tJ~ D=820

u~=l,087cm/s

i

~' ~'~

10 3 RUN 8611 10 4

2

=1,29 c

//~

U/--I, 330cm/s

10 3 U2=I, 613cm/s ¢~'~. ]_0 2

10-5

J

I

10 -4

I

I

10-3

I

I

10 -2

i

t_

i0 -I

l

I

i00

__

J

101

(,~) Fig. 5. Power spectra of the l o n g i t u d i n a l wind vector under the condition of a s t a t i o n a r y strong wind. u l and % are the mean wind speed during the observat i o n at two heights of 6.85m and 23.0m respectively. in higher frequencies. I t s behaviour indicates that the strong f l u c t u a t i o n s by the atmospheric disturbance is e x c e l l e n t in the range below the cross frequency, which may be close to the spectral trough. The peak frequency in Fig. 5 is considerably smaller than the expression proposed by many researchers. As previous noted, large scale turbulence dominate the atmospheric boundary layer above the ocean.

58 3.3 Vertical correlation of turbulent eddy Vertical correlation of the three-dimensional wind vectors (u,v,w) has been discussed in the previous papers[7,8]. But when the vertical separation distance is very large, the well-known expression of the correlation coefficient and the eddy coherence is not applicable. Under the present condition of the distance of 16.15m, the vertical correlation of the vertical wind vector was scarcely recognized. Fig. 6 shows correlation coefficients, Rz, of horizontal wind vectors for the duration of D = 200 min and 20 min against the wind speed, ~, which is given by the geometric average of the wind speeds at two heights. The corresponding height of z = ]2.5m is also given by the same technique. Values plotted are obtained at the peak of the cross correlogram. Panofsky and S i n g e r [ I l l express R as follows z

R

= e2Cp {

-

a

z

i

( z I/3 2

zl/3)}, 1

i

Here the decay coefficient, ai ,

:

u

,

v

(8)

is assumed to be constant. But as shown in Fig.

6, i t is reasonable to assume that ai is a function of D and u. We can obtain the expression of a. from the approximate curves in the figure as follows 1

au = 0.076 ( u -

7.0),

for D = 200 min and u > 8 m/s,

(9)

a

5.0),

for D = 20 min and u > 5 m/s,

(10)

U

= 0.122 ( u -

where u in m/s unit. The correlation of the v component is s l i g h t l y stronger than that of the u component. Eddy coherence, ~, for the large vertical distance has complex behaviours in the short duration of about 30 min. Therefore, we can expect the exponential

I.O

.. o\O O

~o.5

•

u;

D-=-20min

oo e .

~o ~.A O

V; D=20min • u; D=200min • v; D=200min I

]

I

[

]

5

I

A

0

"~-.~.~

°°~-'~" ~ bO~ ' -°O ~ :O °t^~ a

~

o

~--" Eq.(9)

~ o O ~ ~ Eq. (ii)

I

[

[

i

]

I

t

t

lo

I

15

I

t

i

I

i

20

I

i

i

i

25

(m/s) Fig. 6. Correlation coefficients of the horizontal wind vectors during 200 min and 20 min agair~st mean wind speed.

59 decay of the coherence only f o r the long observation time. Fig. 7 shows some examples of the v e r t i c a l coherence of the u and v components during 200 min. Smooth curves f i t

an exponential function to observed values of the u component

in frequencies of n < 0.05 Hz. We can therefore state that the coherences do not approach the value of zero fo r higher frequencies and have e f f e c t i v e small values. As a r e s u l t of the present observation, many coherences cannot be approximated to an exponential decay function of the frequency, e s p e c i a l l y in high winds, and the dependence of the v e r t i c a l coherence to the mean wind speed is not clear f or the horizontal wind vectors. But the coherence of the l a t e r a l wind is a l i t t l e

larger than that of the l o n g i t u d i n a l wind.

4. CONCLUSIONS Long l a s t i n g strong winds were observed at the off-shore tower. Remarkable results were shown and they are as: (I ) The gust f a c t o r of the ocean wind is usually small, but has very large values f o r extreme 9usts caused by the strong atmospheric disturbance. The turbulent i n t e n s i t i e s of the three wind vectors were obtained at two heights,

i.o, ~

r

i - - ~ - - T

I

i

~,i

o

°°\o "

u=l,llOcm/s

'<{, o.5

o.~.~

1 u

i

• v

..

o •o • o i ~ o

•

• •

•O + o

• .

o

o

~

• .

...

o.~o OOo~

1.0

-~

U=1,265cm/s

>- 0.5 ol Oo\ • o • oe.~

•

• •

o• " ~ 1.0 ~ + - - F - "°~o

i

•

•

~oO I

~o.o,o0

I

I

-

~=i, 514cm/s

r+, o o.5

i °° ° ~ o o•

.

o° I b •

o oo ~

o°

..... o~.o

L - - L _ L _ . _

I .....

~

•

00

~^..o L_

0.05

l

~

•

I

O.o. ] / o.io

n (~z)

Fig. 7. Vertical coherences of the horizontal wind vectors during 200 min.

60 and those were r e l a t i v e l y small in high winds. The drag coefficient of the sea surface differs depending on the kind of the atmospheric disturbance. (2) The power spectrum of the longitudinal wind was obtained in very wide frequencies. The spectral peak deviates toward the much lower frequency in comparison with the well-known expressions of other reseachers. The vertical correlation coefficient for large distance decreases with increasing wind speed. The dependence of the corresponding vertical eddy coherence to the mean wind speed is not clear and may be influenced by the atmospheric disturbance. REFERENCES l 2 3 4 5 6 7 8 9 lO

II

A. G. Davenport, The spectrum of longitudinal gustiness near the ground in high winds. Quart. J. Roy. Meteorol. Soc., 87(1961) 194-221. M. Hino, Spectrum of gusty wind. Proc. 3rd Int. Conf. on Wind Effects on Bldgs. and Structures, Tokyo, 1971, 69-71. J. C. Kaimal, J. C. Wyngaard, Y. Izumi and O. R. Cote, Spectral characteri s t i c s of surface layer turbulence. Quart. J. Roy. Meteorol. Soc., 98 (1972) 563-589. I. Van der Hoven, Power spectrum of horizontal wind speed in the frequency range from 0,0007 to 900 cycles per hour. J. Meteorol., 14(1957) 160-164. M. Shiotani and Y. lwatani, Horizontal space correlations of velocity fluctuations during strong winds. J. Meteorol. Soc. Japan, 54(1976) 59-67. L. Kristensen and N. O. Jensen, Lateral coherence in isotropic turbulence and in the neutral wind. Boundary-Layer Meteorol., 17(1979) 353-373. G. Naito, Three-dimensional space structure of turbulent eddy in the atmospheric boundary layer above the ocean. J. Meteorol. Soc. Japan, 60 (1982) 1299-1315. G. Naito, Spatial structure of surface wind over the ocean. J. Wind Eng. and Indo Aerodynamics, 13(1983) 67-76. H. Ishizaki, Wind profiles, turbulent intensities and gust factors for design in typhoon-prone regions. J. Wind Eng. and Ind. Aerodynamics, 13 (1983) 55-66. A. M. Davies and R. A. Flather, Application of numerical models of the Northwest European continental shelf and the North Sea to the computation of the storm surges of November-December 1973. Dtsch. Hydrogr. Z. Eng.-H. A. 14(1978) 1-72. H. A. Panofsky and I. A. Singer, Vertical structure of turbulence. Quart. J. Roy. Meteorol. Soc., 91(1965) 339-344.