REPORT Oii J,TL'OSPHERIC TURBULEnCE IliVES1'IGATIOl1S
Thia report covers the results of investications of' atz:toeJiieric turbulence
carried out nt the Guggenheim Airship Iiwtitute duriII( the mwol6l" of 1935.
The U S navy Departcent, the U S eo.ther Euronu, and the C lif'ornia Institute
or Technology cooperntEld in t11e ork. t:r R C Robineo:n of' the eather Bureau
nssieted in taking observatiO?lll nnd in orld.ng up the result8.
i'he observntiontl of wind velocity end temperature lapse rntoe were carried out
at the :ADC radio tower in Tall.melt•. Ohio. A m.gnetotype cup anemcneter.
en EctorlineAJJeUa recorder for recording wind velocity, and a themograJil
were hoisted to various height& up to 85 Detera.
'l'l1is report describes those aspects of the problem Tlhich have been attacked
hitherto and tho main results of' the prosent inveE"tir;ntion. A ffl'fl references
to previous work by other inventic;ators nre included. in order to coordinate
the information availnble. It l!ll>nt be remarked thnt the e~ril:lental cetup
\7'lich hno been deacribed in some detail in ReportD l and 2 (AUo"llSt 18, 1936 and
ovember 16, 1935, respectively) was restricted to meacuromenta ot one cc:mponent
of the wind veloci~j and at only one place duri.n{; n given ti e interval.
In other words, the foll~ paragraphs contain the infom11tion llhlch cen be
cained by tl1e analysic of one en~ correlatod with oorrooponding meo.curemcnto
of temperature lapee rnte, i.e. the degree or stability or the atmosphere.
I. Data
A series or tweJD.tyone observntlana was s:iade, including unemometer records and
tcnperctures nt vnrious heie)lts up to 85 meters • .ond pilot bolloon runs up to
nbout 760 meters. For ten or the obseM'ntions (those me.de after October A, 1935)
the records f"r<l!l o tempornture ditf'erence recorder recording the difference in
t«?tperature bet1•:ecn th() 17 and 91 meter lovele wre avo.ilnblo. The lripae rntes
in tl'1ooe oases wer oaloul11ted f"rom the nean value or the temperature difference
provailinc during t'1c time interval covered by the manometer rocordri.
Table I gives the following datQ for the t;;entyone observntiona:
1) Number of run. The 1"UllL' are arranged according to incroosing lcpae rates.
2) Dote.
3) Time interval over v.hich observation was taken.
4) Durction (in minutes) of reoor:i at eaoh hei(9lt.
5) Height above tho grou:nu, : 1etcra.
6) Tcmpernture lapse rate 't" ~n degrees Centigrade per lee. I:letera.
7) u, the nee.n velocity L. m/aec, corresponding to the ti:JO ,;.,..,tel"ftl end
hoight given.
6)Ju1 X1, the "standard devieti0" 1
, in lo/'eec, of the velocity fluctuations.
The standard deviati® Ju 1 " la defined as tlle square root of the meen
Talue of tl1e square of .. ._ tl.uctuatione (u  u) 3 , where u is the imtftlltaneou...
velooi ty and u tl10 monn velooi ty crttJr the time interval.
.. J7i{u , the "relative atandnrd deviation."
1 '. ~ state of TtCnther. clouds, etc. The desicnntion "scattered cloudc" eir;nifiee
that 0.1 to 0.6 (inclusivo) of tho ek:y vm.t1 covered; 11broken olouds"
cir;nif'iee that 0.6 to 0.9 (inclusive) or tho sky wns covered; 11ovoroast«
ai nif'ies that the clouds caver 'COJ'e than 0.9 of the cky.
Deni el Guggenheim .Aire hip Inst! tute
• .tiJ::ran, Ohio
{'
2
TABLE I
lio Dnte Tine Duration h u V fu~/u RCIC!Qrka
1 Oct 8 5:00 15 84 0.041 3.6 0 0 Scattered cirrus
5:41 A 2.5 72 * 3.2 0 0
9 55 3.8 0 0
8 40 6.2 0 0
2 23 3.9 0 0
2 Oct 9 8:25 10 60 0.041 8.8 0 0 Dro'!ren nlto
9:00 p 3 40 C: 6.2 0 0 OUl'!llllus nbove
2 22 2.3 0 0 3000 m  A Cu
Oct 0 7:SS 10 83 0.028 3.6 0 0 Sce.tter od Cirnw
7160 A 2 69 3.4 0 0
3 49 1.5 0 0
4 July 12 3:51 10 84 0.028 8.2 .60 .061 Clear
4147 A 6 68 7 .1 .62 .087
10 61 5.6 .28 .050
8 S3 4.3 .63 .012
3 19
5 July 12 6:02 10 85 0.014 7.6 .37 .CX.9 Scattered Cirro
6126 A 2.6 62 6.2 .47 .076 stratus
2 40 5.1 .46 .091
2 20 s.a .48 .126
6 Oot 14 4:26 10 85 0.011 3.S 0 0 Broken Strato
4:39 p 2 68 2.9 0 0 cumulufl and
l 42 2.6 0 0 CUDlllonimbue,
light rain
7 July SO 7 ...  10 85 0.003 8.0 .83 .104 Overcast,
. 5. p 5 61 6.9 .89 .129 .Altocumuluc
4 38 5.9 1.04 .18 ebove 3000 m,
5 20 4.4 .66 .15 thunderatom at
mdnigJit
8 July 30 4:10 10 85 0.003 7 5 1.03 .14 Broken Alto
6132 p 4 67 6.2 1.32 .21 ouraulus above
3 46 7.6 1.18 .16 3000 m, thunder
2 27 6.1 1.05 .17 stor.::i nt rd.d.nicJtt
9 Aug 1 3:02 10 87 0.001 11.6 1.43 .12 Scattered Cirrus,
3:49 p 3 63 9.2 1.68 .17 scattered Cuz:rulua
4 42 8.2 1.68 .19 thunderaton:i at
4 19 8.4 2.08 .25 7:62 p
* The temporature ditferenoe recorder did not register for nn invoraion CTer s° C.
Sinct.1 the ·tical dictanoo botwoon tho elemente '\'l'QS 74 meters, the mininnm
neo.curable r ~8 0.041.
Daniel Guegenheim Airehip Institute
Al:ron, Ohio
·3
no Dato Time Duration h r u r;~ v'J . • ~/u Ecarks
10 Oot 4:, 4:42 10 8:5 .001 6.3 .75 .091 Clear
6:46 A 10 66 1.a . .,., .099
1 66 1.0 .11 .101
4 41 6.6 .56 .083
4 29 5.1 .97 .190
11 Sopt 5:67 10 66 .002 12.6 1.61 .13 Clear
so 6:20 p 2 74 9.2 1.7~ .19
2 59 9 5 1.62 .16
2 3G 8.7 1.11 .13
2 19 6.0 1.66 .28
12 July 9.46 5 84 .003 7.4 .81 .109 Overcast
30 10·02 p s 52 5,3 .98 .18 Al toC.mzulut'.l,
s 35 4.8 l.04 .22 thunderator:i
3 18 3.7 .84 .23 at midnight
13 Aug 1 4:27 6 38 .007 9.4 1.14 .12 Sonttered Cirrua,
6:0~ p 10 87 8.9 1.41 .16 scattered Cumulus.
5 65 8.3 1.22 .15 thunderstorm at
4 30 6.6 1.21 .18 7r52 P
4 16 6.1 .76 .12 •
14 July 7:58 10 87 .010 4.9 .54 .11 Broken Cirro
12 Gz32 A 2 62 4.0 .39 .098 stratus
3 43 4.3 .43 .100
10 21 3.8 .99 .26
2 9 3.2 .fr! .21
15 July 9:38 4 43 .013 6.1 1.26 .20 Broken Cirro
12 10:26 A 10 65 6.5 .as .14 stra.tus
10 56 6.6 l.OG .16
6 22 G.S 1.63 .26
2 14 3.1 .73 .24
16 Oct 10 1133 6 46 .014 8.4 .91 .11 Ovcrenat 
2:08 p 10 85 8.S 1.43 .17 Altoctl":ltun above
4 61 9.4 1.04 .11 3000 I!l, soattered
4 36 8.3 1.33 .16 strnto0Ullll1ue,
3 17 1.2 1.31 .18 thunderstorm at
2:52 p
17 Sopt 3:22 3 11 .014 6.3 1.46 .23 Cloo.r
30 4:14 p 4 31 10.7 2.4 .22
3 58 13.4 1.66 .12
2 78 14.8 1.26 .085
10 86 15.4 1.39 .090
9 48 12.7 1.90 .15
16 Oct 14 3:29 10 81 .017 6.8 .64 .094 Broken ctratol'S:
59 p 3 67 5.6 • 70 .125 cumulua
3 3G 6.2 .63 .102
2 21 4.2 .62 .148
0 Dato Tino DuratiO!l h u
19 Oct 9 3:40 10 86 .017 4.6
4:09 p 2 68 S.7
5 60 S.6
2 3G 3,7
6 12 3.0
20 Oct 10 12:38 10 85 .018 10.6
1:04 p 4 62 9.2
6 46 8.1
2 25 6.S
21 Oct 9 2:16 10 85 .022 4.2
2:44 p 2 67 2.6
6 61 S.9
2 S7 4.6
2 18 3.6
•
~niel Gucgenheil!l Airehip Institute
Akron, Ohio
{ _: { 
./u Rccarka
.80 .18 Scatterod Al to
.86 .24 OUl!IUlUG abO'f'e
.62 .11 :5000 l!1
.65 .2s
1.09 .36
1.29 .12 Broken nlto
1.66 .1a strutus, 12\under
1.37 .17 stoni at 2: 62 P
1.41 .27
1.46 .27 SC:.\ttorod nlto
2.s .92 ou::iulue above
l.02 .26 3000 m
2.3 .61
1.6 .41
•
•
5 
II. Llagilli tude of the \'lind Fluctuations
Daniel GUGeenheim Ainhip Institute
Akron, Ohio
Values of the standard deviation at the top poeition show a correlation ll'ith
the corresponding mean velocities. The averages of the values of the etandard
deviation were obtained for the I"IUlGes in mean wind velocity or 24, 46, 68,
810, eto, m/sec. The results, plotted in Figure 1, conform fairly well with a
straight line t.hrough the origin. In other worde, the mean value of the rel ative
standard deviation, averaged over all lapse rates, is approximately constant,
independent or tho moon wind velocity. This constant is about 0.11 .
A definite correlation was found bet,~een the relative standard deviation and the
tomporature lapse rate. To show this correlation the observations were grouped
in tl1e following way: an average value was taken or the obeervations between
10 30 m. 3060 m' 60 90 m. height and for lapse rates l' < 0. 0 <... r < 0.01 ,
0.01 < ~ <. 0.015, 1' > 0.015. 1 ie equal to  d'f/dh , where T is the
temp Nture i.., degreee Centigrade and h is the heicht in meters. It is known
thnt the adiabatic condition corresponds to about r • o.010c/m. The result
of this c;rouping is shown in Figure 2, in which the absoiasae of the plotted
pointe is the mean lapse rate of the runs considered in the interval s given
above. The runs in which there were no perceptible fluctuations were not included
in the averaging. It will be observed that for each layer the second
point lies above and the third belO\'t' the curvoe drawn. Ir more observations were
available, those pointe would probably be brou::;ht closer to the curves drawn.
The fluctuations increase quite rapidly, espeoially in the loirer layer , for
increasing instability. Even for the low lapse rates, the value for 1030 m is
0.15 as against 0.11 for the 6090 m layer. Thia dif:ferenco increases until in
tho most unctable range the values are 0.29 and 0.18 respectively.
III. Statistical Distribution of Gust Inteneitie&
It is an interestin.'.; question how far the distribution (i.e. the relative troquency
of large and smal l wind fluctuationa, or strO?l{; and weak gusts) follows
tl1e pure probability laws. If the deviation in wind velooity would occur in a
purely rand.on fashion, tho time in which the excess wind velocity ia say ~'between
p and p ... p percents of the mean velocity would be proportional to e · P('fl"';.._
\i.1ere Im is the average fluctuation • the relative etandal'd deviation r.entionod
in the forer;oint; eeotion. Let us assume, for instance, that tho mean relative
standard doviation or tho mean relative gul!tinees is 20 o/o, 'Ulen the total tme
in "ihich the excess wind velocity ia between 0 and 5 o/o, 5 and 10 o/o, 10 and
15 o/o and so on, would be represented by the curve in Fic;uro 3. The actual
distributions ...ere ccc:iyuted fr()ll") a number of anemograme. One example is shown
in Fieure 4.
The most convenient method. of comparing the statistical distribution with the
pure probability distribution is by plottinc the data on a speoial coordinate
paper. Tho abscissa represents the relative magnitude of the equo.re of the fluctuati
on in linear scale, t.lte ordinate, the logarithm of the time/total period
ratio. l1ith respect to these axes the error law is represented by a straight
line with the inclination l/2p~ , where p~ • u'2fe2 is the square or the
r el o.tivo standard c!oviation.
Recor.ls ehowing larce values of' nean c;utitinesc appear ac flat, thoee witl1 small
valuec of nean t UEtinesc o.e steep lines. Distributions follO\'ling tho error law
l'lllniel Guggenheim Airehip Inetitut.
Akron, Ohio
5
appear ne atraie}lt lines, point bovo the strair;ht line sh0t1 thnt certain particular
gust intenaitiee ere preforred, points bel0'1'7 the ctrairht line ehO\'f
that the correspondi.n£; intensities appear leas frequently than should be expected
accord.int to the error law. Figure 5 shows the diagrams corresponding to
the f'ollo:dng observatione 1
Date Time h l' u Cm/sec)
a) July 12 4:00  '1110 /Ill 84  .028 8.2
b) July 12 5:05  5115 AU 85 .014 7.5
c) July 12 7:59  8109 /IJl 87 .010 4.9
d) October 4 5 :05  5: 15 .Al.I 83 .001 8.3
In theee curTee tlie ordinate &ives the time/duration of record ~or which
u'/u will be between ~ 2.6 o/o fl'O'!l the value indicated by the abscissa.
Ficure 6 r.;ivoa diagrams corresponding to the
D. ate Time h
a) July 12 9:51  10:01 AU 85
b) October 14 3:38  3148 Rt 81
c) October 9 3:.ta  :5150 PU 85
The points for run a) of July 12th and run b)
the straight line predicted by the error law.
rould E'!:looth out the differ ences.
observations:
O' u (m/sec)
.013 6.5
.017 6.8
.017 4.5
of October 9 deviate moat from
It is possible that longer records
Giblett 1) has plotted curves similar to those shown in Figurea 3 and 4 f or tho
I!lenn accelerations of the wind over five seconds and also for the deviation.a
f'ro::i tho ~on direction at a height of 50 f'eet above the ground. Ile finds that
the distr ibution or those components is approximately according to the error law.
Beat 2) has obtained similar results i'or the velooit'J fluctu'1tione in tho iJDmedie.
te vicinity of the gr ound (up to 4 l'le'ters). The mensur EIT.lenta presented in
thic r eport are the firet similer investigations, to our knowledge, at greater
height.
The general r esult of the annlysis is that especially 'Bhen tho atoosphere is
stable, the distribution of gustintensities conformo approximately lfi.th the
error le.w. Thie means, practically, that the relative frequency or str02Jb and
Treak gusts is about t.he same, independent of mean wind velooi ty ond mean gustiness.
Ther efore, if the rnean sustiness is known, it can be fairly well estimnted
in wl1nt percentage of a total period considered the wind velocity is likel y to
exceed a certain 11Il1. t or be below a certain value. However, it i:uist be emphasized
that as yet nothing can be said regarding "how often" gusts of certain intcneit;
nppenr. This depends not only on the added oum of the time cloments in which a
certain intensity prevails , but on the avonl£>e duration or an individual i;uat.
Thie question has perhapg more practical importance than the statistical distribution
itsolf, and will be discuseed in the next section.
IV. Analls1a ,or Correlatio.n:l  Duration ~ Size of' Gusts
It i~ believed that the time of duration of o certain gu£t at a given place depends
on the aize of more or lose "co..'.ier ent' air na&ses . It la difficult to
7.
Iianiel Guggenheim .lirship Inati tute
Akron, Ohio
obtain reliable information about the averaeo size oi' such masses. The apparatus
available in Akron did not allow taking simultaneous records of the velocity
co:nponente at various etations distributed at distances along and across the
mean !'low. no.. ever, quite valuable information can be obtained by the analyaig
of a sl~le anemogram.at leaet aa far as the size of the perturbations in the
dirootion of the nean wind ie concer:ned. To a first approximation the sequence
of velocities ae they are recorded at n fixed plaoe,oorrespcmd to the velocities
occurring aiJ!lllltaneously upstremn, uo that the velocity deviation, u', 1'hioh
corresponds to the time. .o.t. is of tho em:ie order as the difference between
vcloeities at two points ae.,.rated by a distance o:x. • u At, where u is the
mean velocity. Hence the duration or a certain period of excessive velocity
gives a measure for the linear extension of a coherent air ma.as with exeeaaive
velocity. To be sure, this reasoning not;lects l) the defon!lation of the air
masses considered, and 2) their vertical and lateral motion. Unfortunatel y w
knO\Y v3ry little about the defonuition of suoh 11guots"; howeirer, observations
show that their shape ohangoe relatively slowly. J.a for the influence of the
vertical and lateral notion of tho "guets", it is believed tluit they do not
afi'ect materially the conclusions dra'R?l £ran the analysis of' the anemor;ram. In
tact, if we compare two oases, aae1ming that a r,uet traverses the point of' locntion
or tlie nner:io:neter horizontally or under a alight inclination, the period
in 1,.11ich the anem:w.oter rocor.is shO\v higher or lower velocities will be only
slightly changed. This is de!n~trated in Figure 7. in which tho guet is represented
as elliptical . llhether t:'le mass passes the station along the direction
a or b introduces only a 81Dllll error in its apparent size as judged f'ran the
anemogram.
TTro mtJthotls lYere used in order to obtain infoniation on the avera~e size of rrusts.
a) The first method coneirts or averaging the excess or defect or velocity u'
(i.e. the actual velocity  mean velocity) over a civen til:le, A t and e&.l culating
the standard deviation for such averaged velocity fluctuations.
In order to explain the physical meaning or this !?lOthod, let us t.ake an
example. AssW!lill(j the mean velocity .. 10 m/sec, then a time interval of
6.t • 15 sec correaponde to a length of 150 m in the wind direction. Ifence,
.1.... t e average vnlue of u' for the 15 sec period is found to be equal to
1.6 m/seo, thie means that over the m ole 150 m length the wind velocity
was on t.he average 15 o/o higher than the mean velocity. Computing now t.he
standard deviation for suoh "150 m segi;ients" , vm obtain the "mean gustiness"
experienced by a body of 150 m linoar dimension. The rate of decrease of
t he standar d deviation ../u~.2 with tho length of the segments considered ia
a rolative measuro, whether more or leas gusts of considerable extension
are present in the wind.
Some or tho characteriGtic curves are represented in Figure 8. These repret:
ent the .four rune of July 12th and are derived from the curves given in
the preceding report. For the first three runs. representing a wide range
in stability, the curves fall very near to each other. These dirterenees
might be smoothed out if records longer than 10 minutes were considered.
If we con~ider a body 300 meters lonJ. the curves show that in the stable
atmosphere the standard deviation over thia range is around 50GO o/o of the
valuo calculated from instantaneous values of tho velocities. On the other
hand, it the atl!tosphore is unstable, the value rises to around 80 o/o.
8
Daniel G\\ggenheira Airahip Imt itutie
Akl"an, Ohio
b) The aocond Jlletbod uaed for tho aruilysis is tho co:nputation of 0 oor1elat1on
oocfficientsu between i:irc o. ~ velocity valuoo following each other in a
certain constant tie.e interva1 Ai.. or, nooordint; to cur h~thesia, ooourring
ai.J:lultnneously at two poi.J..~ s . too. by the distnnot' Ar • u At in the
"Id.nu irection. The cla:_elntion ~oettlclent le de1" .ne<. by the proiuct
~tu.\ • .,,t /iJ.." or ,._.; u.'~1"4.,. ~ • Ii' 6 x ic so sri.all that the two points
and '.J x are praotloall!;r Hlways in the Gam.o gust and have the same velooi
ty, t e correlation ooei'i!.oient will be neuly l. If the velooltios u.'.,.
o.nd u'.•+o.,. are independent, tho correlation coetticient will be zero. The
ooou'!"!'en~A of negative correlation coefticientc ic a sign tor n vy" or definitely
periodical charnotor of tho gust distribution. Figure 9 shows the
correlation coe.fflcientc o~puted for the foll0';14_ne runs:
Date Time h r u (c/seo)
a) July 12 4s00  4sl0 AM 84  .028 8.2
b) Oot 4 6:06  6116 All 83 .001 8.3
:~ July 12 9161  10101 .AU 85 .013 6.1
Oct 14 3138  3s48 PU 81 .017 6.8
The curves are repented in Figure 10 with A ·1 a. 4 "or abscissa.
The eo:ipstrison or the corrolntion curvee of 'iguro3 9 and 10 shows strikingly
the increace of cunt ei:tea with .l.noreas1Dg inatability. Another f'oo.ture or
e~o of the correlation curves ie shown in Figure 11, mere the cO'"'rpu '\tlon of
tho oorrolation coefi :ini s ia carried out to a tine intern.l of At "' 120
eeo., oorreapoDdiDg 1 o 0 1 • 1000 •· Tho correspondine tcperature la»Se
rnte it: r .. 0.001, 11. ting a Dedium degree of otability. The correlation
ourvo £.i0'.'18 tio nerative ninir.!n and two positive xi.ma with an avel"llge halt
11wnvo length" or about 200  260 m.
Tho oorrole.tion curves undoubtedly give a proper ccasure for the relative
size or the gusts or coherent air ?DaSses. All far as tho absoluta measure of
their extension ia oonoerned, s<Dt indication.a c.m be given by caloulatian
of the correlation CUJ'TO for SCJ::le idealized conditionss
1) Let us assume tbnt plus and :::i me velocity fluctuationa of equal mgnitude
occur in equal time interval 't' corresoondint to equal alternatinc gusta
or the length £. Tl1e C01'l"086 0 • ... .,on;;., tion curve is shmm in Figure
12. The correlation io zero fo.,. c..x • I/2, ond tho length l is given b:y
the distance between the Oriti to "h t' e looe.tion of the first nego.tive
ri1ni1111m. The canputation for a pure sine l'la"'9 loada to ca similar result,
except that the train of strnicht lines ic replaced b:y e sine curve.
2) Let ua assuoe n01r thnt pln." ~ntt mi:tIW> velool ty .fluotuations of' equnl magnitude
occur, but the durnt: .... the custs ie variable, the ?!lean vnluo of'
the duration being equal to "t" • In this oa.ee there is no periodicity in
tl10 distribution of ti1e gi ~ .. and we ucumo that their distribution ie
of a pi.rely atatistice.l chnractor. Tho correlation coefficient can nlco
be calcul ted in thin cace, nnd the recult ie ehown in Figure l~. 1'he
..., t \al 1iant';ent to t1I e intersectll the abacieea at tho diemnoe
A\. , J~ ~ ~ , uhor l...._ iD tho equaro root of the mean Talue ot the
• • ·e o." the lenethr o , · ·o gusts. The "width of ~,., ..... orrelation ourvo"
corresponding to 60 o/o correlation is equal to .60 !...._
9
Dentel G~enheb:l Airship Institute
Akron, Ohio
These idealized oases DllY give sor.ie idea of the aotual size of tho gusts.
For the stable oases given in Fir;ure 10 the value of ~ x, tor vmioh t.li.e oorrelation
eoof.t'ioient is 0.6, is 30 r.otere. This r;ivee 60 meters tore.'IU.. For
the unstable eaees the vnlues nrA l.._ = 250 and 270 neters respectively.
This ceems to indicate that the •,Jredo:iinent nve lengths for the unstable
cases is four or five tir:les that 1'or the stable oasee. If' we estimate the
'mlve lentth by r:ieans of the ?:1ethod (a). (see Firure 12), from the ourve of
Figure 11 the indicated lencth of the gusts is around 250 meters. For the
unstnblo eases the wave lengths indicated in the correlation CUM'•• are much
loncer, and it was not oonsidored. safe to carry out the oorrelationa in the
ten minute records to the tioo intervals necessary to show up tho wavy character.
nether the waves indicated in Figure 11 are of thermoe.erodynam1 c origin or
are due to tho topoi:;raphy or tho country aurroundinc Akron cannot be deoided
.fra::i the recor:is available.
Giblett 1) carried out aor.ie oorrelations along and across the mean wind. The
investigation involved the simultaneous recording of Wind speod and direction at
four stations, three of which were arranged in an equilateral triancle, tho tOUJ'th
biseotine the aide of the trian<;le in the direction of the prevailing wind. The
instruments were tif'ty feet above the ground. Re finds correlation raotora ot
0.8 and 0.6 at distances ot :550 and 700 teet respectively. in the dir1'0tion of
the mean wind, for a tir.le difference botween the records equal to A :ir/ii , lllhere
u '!El the mean velocity at1rl tl x "' 350 and 700 feet respectively. The records
vroro mde under T.iult l'l'Ore ooneidered approximately adiabatic oomitiona. The
croseYind correlation factor 'tWlS about 0.5. the distance between stations being
about 600 teet. Since this correlation factor has a high negative value, it
was co.1cluded that the breadth of the gusts wae of the order of 600 feet. A
caloulc.tion of the correlation factors .fron the records ot one station showed
that a minioum factor wu.a reo.ched at Ax "' u At • 2000 feet. It 'WllS therefore
concluded that under adiabatio conditione a olaaG of guste exists l'lhoae downwind
and crosswind dimensions are or the order ot 4000 by 600 feet respectively.
Giblett also carried out a te':f correlations in the vertical direction (between
50 .feet and 40 feet and botwQen 60 feet and 30 :feet above the ground) • He finds
correlation factors up to 0.94 bei;m)en tho simultaneous velocity fluctuations at
50 feet and 30 feet for the stable atmosphere.
Some measurements or crosswind and vertical correlation factors in tho lower six
meters over flat tleadow land were earried out by 'i7 Schrlidt 3). Tho apparatus consisted
of a frame 6 x 10 meters. with pressure plates arranged at vertical and
horizontal distances ot one moter. The deflection of the plates wae recorded
photographioally as a function of the time. Analysis ot the photographs gave a
picture ot tho wind velocity as a .functiOll of the til!lo at each of tho t1.nemometer
positioll3. Ho finds that, even at six 1:10ters heic;ht, the eroaswind oorrelntion
factors drop to 0.6 at a distance of 5 :meters. The vertical correlation faotora
dropped to 0.5 aver a distanco of 2.5 rietera (betrMen 3.6 ~rs and 6 Deters above
the ground). If the lilllftlysis vlhich led to 1''iGure 13 is appliod to tho vertical
and cross· 1.nd dimensions of tho gusts, it would indicate that at a height of eix
netera the crosswind extent of tho gusts is about twice the vertical extent.
t series of measurements of tho orossseotlonal structure of the wind at high
velocities was mde by R H Sl1orlook 4). The apparatus consisted of one 250t'oot
•
•
10
Don1ol G~enhe:bn Airship Inatitute
IJr:roc. Ohi 0
~ror with an«:io::iotero nt 60 toot intorvnl.s o.nd covon 60fo:>t to;;oro with lllletlOooters
t tho top. i'ho to'liorc ro ~ed in a northcout.'1 direction nt intezovnl
or GO 1."oot. Tho BnO'l~Otoro re or l!I. apooinl pronaure plnto typo, and all
wind volocitios re roaordod sir:ultcncouoly by r.oans of' a 12olt"OOnt oscill~ph.
'l'J o otnioturo of tho wind ie roproeonted by iooivelooi ty linos ns f'unotion ot
tl1 tino and vertiool or hor1zcmtnl dietcnoe.
V. Velocity Profiles
Tho voloolty profiles correspondin to t."'i.e observaticma (!;iven in Table I and tho
corroepondine balloon rurui re ehcmn in FiguNJ 14. The circles represent tho nonn
volocitios deten:dned fran tho one:t?o:neter record8, and the pointe represent pilot
balloon oboervationa. Dnlloon runs "Here either aill61o or double theodolite.
Thoy ore decignated by (S) eicni1'Yinb sin;;le, or (D}, aignifyin,; double theo
dolite runs. Balloon nm is nbbrevinted B.R. oh intflrval on tho abaciee
ropr aente 10 ~sec; the orieino for tl':o various runs are also indicated long
tho nbcoieca.
Tho wind diroction profilea are given in Figure 15 Each division on the ftbccicca
represents so0 , tho origin being displaced for the veriou~ profiles.
Tho roeorde are not l1Ur.l6rouo enough to allow a detailed study of the effect of'
tomperaturo lnpse rate on tho velocity profile. Runs 1 1 2, 3, and 6 allowed soro
guatinos'" nnd the prorilec sho;v no eyrle:?mtic dopondonoe on lapee rate. nuna 4,
6 1 10, end 13 show n tendoncy toward linear profiles fr0C1 about 30 meter~ to
160 to 200 notero, folloivod by approx h:::ately conctont voloci ty at higher al ti tudec.
Another method for claccif'yi~ tho velocity profilos ic ncoording t~ the paror.
ieter
fl, •
<druz) a
.C. d e
e dz
'Where du/dz is tho velocity crudient, e is the aocolcrntion 0. ~ra"'l.:: . '\Jll: 6
is tho potentio.l tempen t ire ~., the atmosphere ia stable ~e / lr. '> 0
and en it i~ unsta">le de/dz ( , The adiab tic nt;nospher .i.c f"'"Mf''":ted by
T. 0.010 or de I. z • 0 "e /dr. is derived frO!!l r by tho for.:W.a
~ e 1dr. • 0.010 
In tboso cases Tlhere du/dz io indefinite near tho ground, we can uee the pora~
ter
11 ...
A de
e rz
U.,So
where u.n>o signifies the TT1nd velocity o.t '760 Deters.
Under adiabntio oo!ld t: • o. under ctable conditions M / 0. nnd under
un:itnblc conditions . ( · . 11 Juls the dimension of (meters) · '!'hie para.meter
te.koo into account bo · · lapse rate and the wind volooit'<J.
11
Daniel Guggenheim Airship Institute
Akron , Ohio
'i'nble II r,i vee values of fl and M ror the various runs. For runs l, 2, 3 • 6,
9, 11, o.nd 14 throu£}l 21, the scatter of the points did not allow the detennina
tion of a reliable value for du/dz, and hence f:> , near t.lie ground. In those
co.sos tihere the observntions did not reach 750 moters, u750 wae obtained by
extrapolatiDG the velocity proi'ile to t.1lnt height.
In the report on frontal investigations it 'as stated that the ratio of the
surface wind to the geostrophic wind (Ua/Ug} has an average value near 1/3 over
la:n.i surfaces. This value ms tnken i'rcn lecture notes of Dr SVerre Petteresen.
As an approximation to (Ua/Ug} the valuoe of U30/U750 were oaloulatod for the
various runs. These are included in Table II. The values show considerable
variation, tho ovorall avers.go boing 0.10. If we neglect the oxtrotioly atable
and the Ull2tcblo values. the average for tho runs 4 through l'k is 0.42. llany
more observation3 a~ necessnrJ• be.fore s.11 l:lvcrage value for nll conditions can
be determined..
TABLE II
No .L. ll r U3{)"u750
1 0.52 .041 3.6
2 0.015 .041 .52
3 0.44 .028
4 3.3 0.013 .028 .45
5 4.0 0.0086 .014 .46
6 0.012 .011 .27
7 6.2 0.0019 .003 .34
9 0.0023 +.001 .77
10 6.1 0.0014 +.001 .41
11 0.0006 +.002 .29
12 12.l 0.0001 .003 .24
13 16.8 0.0009 .007 .65
14 0 .010 .28
15 .0023 .013 .83
16 .0009 .014 .so
18 .0047 .017 .63
19 .021 .017 1.os
20 .0033 .018 .65
21 .011 .022 .69
The value11 of Pi for the four runs 4, 5, 7, 10 vary from 3. 3 to 5 .2. Runs 12
a~d 13 give higher values, but in those cases de/dz isl~ and a mnall error
in l can make a largo difference in the value of & • It is interesting to
observ"' that G I Taylor found thnt £or a value or f.:> equal to 4, a linear profile
beoomea \m.StAble.
lf ·re group the profiles according to values of H, vie find some indication of
the differ ence between the profiles under adiabatic conditions and those under
unstable conditions. Fi~uro 16 shows U/U750 plotted nee.inst hei(;ht for the
profiles for wl1ioh 0.009 < l.l < 0.006 and those for U ) 0.009.
For those profiles undor nearly adiabatic conditions (o.009 ( i· <. 0.006) the vdnd
velocity increases rapidly near the ground, followed by a moro bro.dual inOt"eese.
12
Daniel Cuggenheim Airship Inst itute
Akron. Obi 0
For tho proi'iles under unotablo condition.e, the wind velocity increases rapidly
ncnr tho ground and then ra::aains prectically constant up to 750 1:1etera •
• tmospherio turbulence and the velocity change with heie;ht as functions of the
temperature lapse rate, ore studiod. The results ere baaed on anemometer and
thormograph reoor::le taken at various nltitudes up to 8!5 meters, alOJlG with the
reoorde of pilot balloon obeervations. The records from a temperature dU'terenoe
recorder, recording the ditforence in temperature between the 17 and 91 meter
levels, nre also used for deten:dning the lapse rate.
A detinito correlation wac found betReen the relative standard deviation ot the
fluctuations in the threo layoro , 030 meters, 30GO meters . 60 90 meters, and
the temperature lapee rate.
The distribution of the velocity fluctuations nocordi?I[; to tho probability law
wan investigated. In tho stnble careo the distribution followed the probability
curve, but for scne unstable cases considerable deviation wae found.
:vercgoo of the fluctuatio1e '79' 1r li,.'ferent time intervals A t for downwind
cpnce intervals, defined c13 A • .. u A" were u is the ~"18.?' veloci~y •• ero
enrriod out. The valuos 01 1 e r ... "ive standard deviation plotted against ~for
'Vnri01 s runs show the relative degree of guatinoss c.tteeting bodies of linear
din0J1sion:.. e:.. A. under stable and nnstable conditions.
In nn attempt to find a measure of tho "r,,ust sizes" under various oonditiona,
corrolation coefficients bot"Yoen velooity fluctuations separated by various time
intorvals woro calculated. These oorrelRtion coefficients are pl otted against
D..i; tho oorrolntion interval, and Ai • u At for va.rious stable nnd Ull8table
rurc ~o r,othode or interprotin,•· tre curves in te:nns of gust eizes are given.
The results indicate that in tho unste.ble e.iznosphere tho domnrl.nd gust sizes are
on tho average around five timoo thoir size in tlto stable stnospiere.
Tho velocity and direction profiles derived from the nnemomett>r and balloon run
records nre civen. Soce methods ot correlatinc; tho pro.files aro tried. Uore
observations e.r e necessary boforo de.finite conclusions with regard to the corr
elation between lo.pee rate, wind velocity, and velocity profile can be drawn.
R FERET.CES
1. Giblctt: Structure of tho ind ovor Level Country, Goornysioal llemoir
10 54 (1932).
2. A C Beati Transf'er of Rent and 'caenturn in tho Lo~st Layers oi' the
tmospiere, Geo~ys icol anoir o 65 {1935).
3. Schcldt: Turbulence near tho Gro..md. Jour Roy ero Soc Vol 39, p 355 (1936).
4:. R H Sherlook: Picturint3 tlte ind, Civil Engineorine (1932).
8 136
Dr A Kuetlie
lf
For Fi ures 1  13 <
see
Third l'roe;res !' Report on the ... eteorolo< icu 1 .. cti vi ties
at the
Guggenheim .irship Institute
February 18, 1936
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Fi ure 15. •ind dir ection nrofiles correspondin1 to
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