The structure of turbulence during strong winds

Journal o/Wind Engineering and Industrial Aerodynamics, 28 (1988) 41 49

41

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

THE

H.

STRUCTURE

OF TURBULENCE

DURING

STRONG

WINDS

L6sslein

Meteorological D-8000

M~nchen

Institute,

University

of M u n i c h

Theresienstr.37,

2

ABSTRACT Autocorrelation, horizontal and vertical cross correlation as w e l l as p o w e r s p e c t r a a n d c o h e r e n c e s p e c t r a w e r e c o m p u t e d by wind speed m e a s u r e m e n t s d u r i n g h i g h w i n d s in M e p p e n W e s t G e r m a n y . The m e a s u r i n g p e r i o d l a s t e d for 3 y e a r s thus it w a s p o s s i b l e to o b t a i n statistical significant v a l u e s for the i n t e g r a l s c a l e s and the peak of the p o w e r s p e c t r u m . The integral scale increases with h e i g h t a c c o r d i n g to a s i m p l e p o w e r law, w h e r e a s the w a v e n u m b e r of the power spectra's peak decreases with height. Characteristical v a l u e s for the e d d i e 's s i z e c a n be o b t a i n e d f r o m t h e s e data. INTRODUCTION For designing information To

get

ments

concerning

statistical

are n e e d e d

MEASURING

a wind

load

concept,

it is e s s e n t i a l

the s i z e

of

the e d d i e s

information

of

these

on the o c c a s i o n

of s t r o n g

strong

longterm

some

winds.

measure-

winds.

SITE

To

determine

the

size,

windspeed

was

during

N

riod

J

strong of

which

0m

Aachen

I

in

0167-6105/88/$03.50

site

winds

years about a

eddie's measured over

in

Meppen,

flat

and

The measuring

consisted

three

of

a triangle i. T o w e r

of

80 m a n d

A3

were

in M e p p e n

© 1988 Elsevier Science Publishers B.V.

the

48 m

a pe-

200 k m N E

countrysite.

figure

i. M e a s u r i n g

3

lies

formed

Fig.

during

data,

to h a v e

towers as

A1 h a d towers high.

of open site

which

seen

in

a height A2

and

The

cup

42 anemometers

were

the s a m p l i n g

rate was

mounted

on 6 d i f f e r e n t

1 second

heights

from

8 to 80

m,

(ref.7).

AUTOCORRELATION The

autocorrelation

during

which

the mean wind

theory

of f r o z e n

length

with

lation

was

Davenport R(r)

was

computed

speed

turbulence,

the mean wind fitted

with

exceeded

the

speed

based

time

i0

i0 m/s.

minute

converted

The c o m p u t e d

curve

runs,

By a d o p t i n g

shift was

(ref.9).

an e x p o n e n t i a l

on

type

the

to

a

autocorre-

as s u g g e s t e d

by

(ref.2).

= exp(-a

r)

(i)

w i t h R(r)

R(r) 1.0

and shows

an example

define

0.5

scale

a for

i n t e gr a l 0.0

denoting

the c o r r e l a t i o n

r the d i s p l a c e m e n t .

Figure

2

of the fitting.

To

characteristic

length

the a u t o c o r r e l a t i o n , scale Lx

is used

the

(ref.8).

.

1

10

100 1000 r into

Lx =

~

R(r)

dr

=

I/a

(2)

J

0 Fig. speed

The

2. A u t o c o r r e l a t i o n in 8 m h e i g h t

integral

of w i n d

in M e p p e n

scale

varies

with

height

according

to the

empirical

formula.

(3)

Lx (z) = 112.3

z °-2v

This

relation

is v a l i d

the

flat

agreement dispersion (ref.7).

and open with of

country

the the

only

at a range in Meppen.

values integral

given

of 8 to 80 m h e i g h t Nevertheless

by other

scales

it is in

authors

is about half

and for good

(ref.l). of

the

The

scale,

43 VERTICAL CROSSCORRELATION The

vertical

speed

crosscorrelation between

in d i f f e r e n t

h e i g h t s gives

two time

information

about

the

eddyfront.

The larger

the

weeker

the p e a k of the c r o s s c o r r e l a t i o n

figure

is

the d i s t a n c e b e t w e e n

figure

4,

w h i c h can be t r a n s f o r m e d an angle

of the eddy

Figure

intervals

5 shows

height

F r o m this

figure it can be d e d u c e d

top of a b u i l d i n g . of

the

interval.

the d i f f e r e n t

~z and the m e a n h e i g h t

Furthermore,

eddies

The

into a length.

increases with

the eddies

is s m a l l e r

shown

in

at a s p e c i f i c Referring

to

the i n c l i n a t i o n angles

for

that an eddy first r e a c h e s

it can be seen,

of

heights,

the

of the interval. the

that the i n c l i n a -

the d e c r e a s e

curve of the eddy w i t h a t h i c k n e s s

that the i n c l i n a t i o n

wind

slope

as is

is c o n s t r u c t e d w h i c h d e s c r i b e s

(ref.6).

different

when

the

of

the two

3. The m a x i m u m of the c r o s s c o r r e l a t i o n o c c u r s

time shift,

tion

series

in larger heights.

of

the

height

of 16 m

shows,

It grows

larger

are closer to the ground.

Z

R

__

a:

8/IS m

X

Fig.4

Constructing

angle of i n c l i n a t i o n i

-20

I T

-i0

Fig.3. of

i

0

Vertical

wind

speed

combinations

1

I

I

I0 20 tins

cross

correlation

for

different

of h e i g h t

the

44

z

into

A z= 1 6 m

60_

40_

20. i

0

i

I

I

~__~t___

I

30

0

~L

I

60

90

deg

in Fig.5.

Angle

front

mean

HORIZONTAL The

speed

decrease

virtual

connecting

=

A1

A1

A1 A 2

the

Figure

two was

the

and

of

to

the

obvious

with

the

decrease line

of

horizontal to a

length

figure

the distance

the w i n d d i r e c t i o n

series at

the

converted

According from

time but

connecting

examples

constructed

from

more

towers

again

two

towers

becomes

and the

speed.

by

relative

8

a

of

the

to

the

a n d A2.

*

maximum

9

shift wind

was

and

sin a

is a l w a y s

distance,

computed

at d i f f e r e n t

between

7 show

time

A1 A2'

a n d A2

A2'

combining virtual ted.

A1

was

winddirection

the m e a n

distance

line

Line

and

the c o r r e l a t i o n

6 and

The

using

towers

measured

the d i s t a n c e

Figures

two

A1 A2'

of

a between

crosscorrelation. by

were

peak

of

towers.

shift

eddy-

intervalls

crosscorrelation

which

The

the a n g l e

the

an

CROSSCORRELATION

height.

the of

height

of

heights

horizontal

wind

same

inclination

for d i f f e r e n t

different

of

of

perpendicular of

the

a horizontal shows

(4)

to

correlation

the

winddirection.

with

the

crosscorrelation

correlation

versus

width

corresponding

can be of

By

construc-

the e d d y

at

a

45 height

of

8

The

m.

crosscorrelation

autocorrelation

corresponding

for

from

travelling

tower

to A1

the

to

is time

the

normalized shift

virtual

R(r)

R(r)

1.0

1.0

with

which

is

tower

the

needed

A2'

0.51 -400

-200

0

200

Fig.6.

Horizontal

lation

with

of

60 m a n d

-400 -200

crosscorre-

a tower an

o.o J,

400 rinm

angle

distance of

4°

Fig.7.

Horizontal

lation

with

of

Similar

60 m a n d

to

the

exponential

Ai/ /

integral

characteristic about

63 m, leads

in

//

in

4.6

in

in

the

Fig.8. virtual

Constructing distance

the

of

is

44 °

for

fitted the of

width

an

of

48 m it

ratio

of

order

is

8 m,

is the

eddy

about

an

is

72 m.

3.2

an

chacteristic to

These as

and

of

and

(ref.ll).

an

width

a height

8 m height

same

distance

autocorrelation,

48 m h e i g h t .

by T e u n i s s e n

400 ri~m

crosscorre-

angle

to a v a l u e

length/width eddy

an

scale At

200

a tower

function

calculated.

This

0

those

for

a value ratios

the

of are

obtained

46

R(r) 1.0

0.0

I 10

i

POWER

Fig.

rinm

versus

9. H o r i z o n t a l distance

correlation

in 8 m h e i g h t

SEPECTRUM

For m s -~ ,

every

10-min.

the p o w e r

number.

obvious

with that

different an

run

was

10 all

some the

curve

to the p e a k

of

was

a height

published

spectrum

of

the

3

• • ...

2

'

•

This

: : : : : :

versus

-

leads

to e q u a t i o n

LSsslein Davenport (1961) ESDU ( 1 9 7 4 ) Harris (1971) Kaimal (1972) Simiu (1974)

:/..'/:.~'i ":!:'; ~ . ~.~:'~. \ :./ ..~."~"~:~.'-"~ ~.~ L

'..' • 5 .~...l~ .~;~ ~:.

":'4::"

0

""

• :~.~:'~4.,:?, 3. ...-~,

".',

. . . . . . . . . . . . .

10 -s

~.,.~-.'~.~k-.',

/: ~ ,:: '.~.~

~'_7".:÷: / ~ .:/ .

1 0 -4

""

• ..............

1 0 -s

""

'.

,'-

":-.":'= ..~..

10 ~z

1 0 -I

Wavenurnber k in I/rn

Fig.lO.

Comparison

of d i f f e r e n t

measured

the

numbers

./

-:..&-~.. • ...;. ~

to

power

spectra

is

computed

wave

" 4:/\ \ . 6 .< h - ~

• ,...; ~. :./.,

shown It

leads was

i0

the w a v e

are

authors.

o 0Q

exceeded

80 m

height

to the

1 2 3 4 5 6

of

spectra

every

spectra.

4

speed

by other

for

fitted

the

wind

and plotted

for

scattering

A mean

exponential

the m e a n

computed

spectra

fittings wide

curves.

corresponded

of w h i c h

spectrum

In f i g u r e

together

and

100

which 5.

47

kmax

= 0.0027

SPECTRUM

OF

The the

example the

COHERENCE

spectrum

wind

wave

which

coherence

length,

vertical with

means

of

a wavelength

extension, heights.

The

exponential

of

the

in

is

of An

ii. The

The

the

wavelength

the

have

also

of be

than

than

whereas

distance can

length cut-off

shorter

extent

cut-off

shorter

wave

a wavelength vertical

coherence

series

location.

called

heights,

to

time

figure

measuring

exactly the

same

the

eddies

a vertical

the

measuring

fitted

by

an

function

n Az - exp

-C

(6)

v

v

Here

n denotes

speed

in

the

frequency, specific

considered

constant.

versus

mean

the

dependence length

wind

derived

specific

layer extent

layer.

is

The

figure

speed

and

the

Az h e i g h t

In

on windspeed.

is

vertical

of

From

12

the the

decay the

decay

characteristic

It

of

1 shows

shows

the the the

v C

factor

factors, with

ratio

Table

and

factor

decay

layer.

in c o n j u n c t i o n

computed.

difference

the

a

mean

wind

is

usually

is

plotted

remarkable

cut-off

wave-

thickness

of

the

horizontal

to

the

results.

1

Characteristic rent

to

two

the

0.5

a smaller

two

with

coherence.

with

eddies

have

amounts

n Az R

TABLE

the

that

the

decrease

shown

of

equal

which

is

at

a coherence

wavelength

distance

is

smaller

to

This

heights

spectrum

the

corresponds

cut-off

is c o m p u t e d

in d i f f e r e n t

a coherence

wavelength. the

of

speed

of

(5)

Z -0.27

thicknesses

Thickness Ratio

in m: :

ratio of 8 6.8

of

the

vertical

to h o r i z o n t a l

extent

for

eddy

16 5.1

24 4.0

32 3.4

40 2.7

48 2.4

56 2.0

64 2.0

72 1.7

diffe-

48

R(r) 1.0

°ii

O.

!

"$ ,.,.

.:.[..

,~.~::.:,~,>~. -.[,~.4

lO 5

! __!

Fig.ll.

10 3

Example

of

a

coherence

I0 1 spectrum,

)k i n m

measured

in M e p p e n

at

a

h e i g h t of 16 and 32 m

C

20L IB/32 m

,_

0

I0

,

2

20 v in m/s

Fig.12. wind

Decay

factor C

versus

mean

s p e e d from 16 to 32 m h e i g h t

CONCLUSION For ratios of

the flat and o p e n c o u n t r y s i t e of v e r t i c a l

to h o r i z o n t a l

in M e p p e n

dimensions

l e n g t h to w i d t h of an e d d y w e r e c o m p u t e d

winds.

These

computations

they are c l o s e r grows

with

show,

to the ground.

height

the

characteristic

as well

as the

ratios

in the case of s t r o n g

that the e d d i e s

are s m a l l e r w h e n

The r a t i o b e t w e e n

l e n g t h and w i d t h

and the eddy front

is less

inclined

with

in-

c r e a s i n g height.

REFERENCIES

1 Counihan,J. Adiabatic a t m o s p h e r i c b o u n d a r y layers: A r e v i e w and a n a l y s i s of data f r o m the p e r i o d 1880-1972. - Atmosp. E n v i r . , 9 , 8 7 1 905,1975 2 D a v e n p o r t , A.G. The s p e c t r u m of h o r i z o n t a l g u s t i n e s s near the g r o u n d in high winds. - Q u a r t . J,RMet. S o c . , 8 7 , 1 9 4 - 2 2 1 , 1 9 6 2

49 3 ESDU 7 4 0 3 0 / 3 1 Characteristics of atmospheric turbulence near the ground, Part I: D e f i n i t i o n s and g e n e r a l i n f o r m a t i o n , Part II: Single p o i n t data for s t r o n g winds, - E n g i n e e r i n g S c i e n c e s Data Unit, London, 1974 4 Harris,R.J. The n a t u r e of the wind. In: The m o d e r n d e s i g n of w i n d s e n s i t i ve s t r u c t u r e s . P r o c e e d i n g s of a s e m i n a r h e l d on 18. june 1970 at London, - C o n s t r u c t i o n and I n d u s t r y R e s e a r c h and Information A s s o c i a t i o n , London, 1971 5 K a i m a l , J . C . , W y n g a a r d , J . C . , Izumi,Y., Cote,O.R. S p e c t r a l c h a r a c t e r i s t i c s of s u r f a c e - l a y e r t u r b u l e n c e , Quart. J.R.Met.Soc.,98,563-589,1972 6 L 6 s s l e i n H. Das b o d e n n a h e W i n d f e l d bei S t a r k w i n d und Sturm im H i n b l i c k auf Bauwerksbelastungen. - Diplomarbeit f.Meteorologie, M~nchen 1979 7 S c h r o e r s , H . , L 6 s s l e i n H. und Zilch,K. M e s s u n g e n der S t a r k w i n d s t r u k t u r und d e r e n A u s w i r k u n g e n auf das Windlastkonzept yon B a u w e r k e n . - A b s c h l u ~ b e r i c h t eines Fors c h u n g s v o r h a b e n s des M e t e o r o l o g i s c h e n I n s t i t u t e s der U n i v e r s i t~t M~nchen, gef6rdert d u r c h das Institut f~r Bautechnik Berlin, M ~ n c h e n 1983 8 Shiotani,M. T u r b u l e n c e m e a s u r e m e n t s at the sea coast d u r i n g h i g h winds. Jour.Met. S o c . J a p a n , 5 3 , 3 4 0 - 3 5 4 , 1 9 7 5 9 Shiotani,M. and Iwatani,Y. H o r i z o n t a l space c o r r e l a t i o n s of v e l o c i t y f l u c t u a t i o n s during s t r o n g winds. - Jour. Met. S o c . J a p a n , 5 4 , 5 9 - 6 6 , 1 9 7 6 I0 Simiu,E. W i n d s p e c t r a and d y n a m i c a l o n g w i n d response, Am. Soc.Civ. Eng. Str. D i v . , 9 , 1 8 9 7 - 1 9 1 0 , 1 9 7 4 ii T e u n i s s e n , E . . Structure of mean winds and turbulence in the planetary b o u n d a r y layer over rural terrain. - B o u n d a r y Layer Meteorology,19,187-221,1980