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DT
DI
OF
sUR2 GT HE VO-2';RT2CITYAM
AD D
ZL
FRSE
SURFAE-C IX
-
MThCZ
A DISFHPANi i2RI
IENT
by
John DI. MhLlhaljan
:wK
: jk
SUBleTLED IN PARTIAL FbULFILI:,,'ŽTOF TEE
RRQUIREENTS FOR THE DEGR
2
OF
BAOEELOR OF SCIENCE
at the
Mi'ASSACHIUSETTS
ISTITUIE
fi
OF
rTE'INOLOGY
(1954)
. ** e.-4e
....
.....
44
Siznature of ,uthor....
Certified
by....... .. .
s adSK
.
FTIO
.
.....
.. ..
:
Thesis Supervisor
C
.
a.r *a * tt e
* -* -
**
o
*rde
a
*
*
**o
Chairman, DepartmentOsrnmittee on Underc-raduate Students
:
-
3
.,..@
. . 4 !. j;
*
,
ACIOTiva
iGD zil
NTS
The author wrishesto thank
llan J. Faller
and Professor Victor P. Starr
or their ex-
cellent supervision of the theoretical and
experimental
ork that co.xrise this thesis.
OF C OUtIEIS
TiB3
.icinowvledg ment s
-zbstract
1
TIntroduction
2
The 1otion o a Circular Disk on the Free
9
Experimental
10
o3ries
1
17
Series
2
24
Conclusions
24
Suggestions for ±'uture Work
26
Bibliography
urface
VJork
FIGURS
Page Figure
3
1
Fluid velocities near
the
disk
4
2
Profile o
6
3
Figure
9
4
A sanrle disk
10
5
Coordinate sstem
16
5a
Trajectories o
21
6
Free surface flow lines and lower level
22
7
Free surface vorticity pattern
relative velocities
ch-an-e o
illustra..ting,
variable
relative to the dishpan
disks a and b relative to the dishpan
ronts at to
nd lower level fronts
at to
23
8
Free surface divergence pattern and lower level
fronts
at to
TABL2S
Page
12,13
Series 1 data for disks a and b
19
Data f1rom 4
Page
14,15
r and
diskrs of 3eries
2 at to
versus t. Series 1 data
.i metIhodfor determining the vorticity at tie free
surface of water in a dishp-an experimLent directly
fro. the
rotation of small circular disks is analyzedtheoretically.
In two series of experiments it is folundthat the vorticity
distribution
over the free surface of water closely resembles
the distribution at high levels o the tmospere.
y using
'the silxmlevorticity equation, divergences ae calculated
directly from the vorticity data. The signs of the
calculated divergences are reasonable; themagni-tudes,
-owever,
are often large.
t3yconsidering only the sign o
.!ence, a close resemblance between the divergence
the
ree surface
is demonstrated.
in a dishpan
the
diver-
atterns
at
and at highi lev-.ls in the atmosphere.
-1i
dea
The
model of the
of develo -ing an r-3>-:-err-'.nta'
atm;-oshereihasbeen a
It might be
of the useful
be observed
ortunate one indeed
f.atures
J
o
for
meteorocloy.
to
ist some
~- omnt
.orthwhile at this erly
s oosed
1.
T
CiRODU
CTI ON
an e-r.perimental
nm-odel.
to the atmosthere, dynaiic
rocesses
an
ontinuocusly.
Dynamic processesthat would take week-sto obseilve
in the atmosphere can be observed in a few minutes in an
experimental model.
3.
The three dimensional nature o
the fluid motion is
much clearer than any system of weather maps could possibly
convey.
4L. Conditions in a model cn
theoretical assu=ptions.
often be
For examle,
the
ade to
it
ssmapotionoften
made in theoretical ,-orkthat the density is constant can be
closely a
5.
roximated in a model.
Continuous measurements can be taken over sorme
complete region of the model.
many vi.riables
atmosphere
'at
The consequence of this is that
cannot be measured with accuracy in the
can be easilymeasured rom a model.
In connection with the last feature above, most continuous
measurements have been taken
rom the dishpan experiments.
:-easurements of the u and v cormonents of the fluid motion
ave
been madev.ith some accuracy. In theory, at least, r.1anyother
variables can be calculated from!these velocity measurements.
In particular te vorticitr
at the ree surface might be
w~tn1elal<;ed^ ol
a1t
'-{8'tL
C
ay
au
?Fuchcomputations are both laborious
and not very a.curate.
-in 1%22t oW ihaft has
the
eer sa-.d abut
v '-,aslrementsit mistt be tLouht tht
values
o
shlould be
ossible.
o,"-,rfth. u and
r
re:,oably
accurate
The reason 'for le innaccuracy
arises -frollthe definitiono fLte vorticity itself. T'0
calculate
fro te definition te .derivatives.must be
approiL.matedby finite
differences:
UA
the
Nowthough the percentage error in u and v is small, the
absolute value o th1e error is of the same order of -:mgnitude
asAU ndAV .Thus
the error in
is of the sde order of
magnitude as
itself.
In a uantative analysis of f'luid motions,
r
accurate
estn Ues of the vorticity
ared'esirable.
ince the calcula-
tions of +he vorticity ffo,:h the velocity co:.,monents
u,v are
tunsatisf.acory
found.
some oa. er meeansof determininq
This pae ex
ll
1
must be
~zine a newr -nd more. direct
of deterraining the vorticit-y in
method
dish pan eeriment.
'TEREM:_4OTIOOF A ClRCTUl:L? TDISK1M
N
'jT
F='
3U':'OT J'
Ifa luid in a plane is in solid otation than the
vorticity is eual to2Af, ,.e
eef is h'e angular velocity
of -the fluid. it is possible, then, to hink of t vorticity
in trms
the
o aofrotatiio-n.
The followin
derivation
hysical connection bet::een vorticity
era bly clearer.
w^ill mnke
and rotution co.nsid-
-3Imasfne a cylindrical disk of radius R, tickness
.
uniform density
oup ose
h,
next that the disk is immersed
in a fluid contained in a rotating dishpan such that the
axis of the disk is
fluid.
erpandicular to the free surface of the
Erect an x-y axis system fixed relative to the dishpan
and tangent to the free surface.
(0,R).
Imagine the disk to be at
Figure 1 illustrates the orientation of tne axis system.
The fluid velocity in the immediate vicinity of the disk will
be given by
U: Uo.,-
(1) V=o
The term
ttimediate
vicinity of the disk" will be clarified
after the derivation has been coraDleted.
4~~~~~
Figure 1.
luidveloceities near the disk
r=a
The fluid vorticity in this region is
Supiposelastly that the
W
relative to the
isk is rotating with
ngular velocity
ishpan.
To determine the motion of the disk the law Of interaction
between the fluid and the CAiskmust be kncwn.
I shall suppose
that the law of interaction between the fl uid and the disk
is as follows:
The force exerted on a unit area of the disk
is proportional to the velocity of the fluid relative to the
disk.
he velocity
by the
resence o the disk.
of the fluid will be assumed undisturbed
If
the
(2)
roDcrtionality constant is b
then the shear is
(2)
'~b%/teLX
Vye1 Vces
(C= ut .v+
One way to interpret this shearing force is to think of the
fluid as being undisturbed at some uniform depth do .
reLis then the velocity gradient betwveenthe undisturbed
do
fluid and the disk.
The shearing force
to the veloc.ity radient.
becomes proportional
Tle assumption of a viscous shear
proportional to the velocity gradient is often made in
theoretical analyses of the viscosity of fluids.
In this
light the assumption of (2) seems reasonable.
The motion of the disk can be separated into two kinds:
translation and rotation.
Each type of motion vrill now be ex-
amined separately.
I claim the velocity of translation of the disk is
U.= Uo +o.R
V=o
To prove this from the dynamic assumption (2)VieL of translation must be knon.
VY
t. =0
Uve L
(3)
U 0 Cali vsiR
UtyeL = Uo+boan - l
,,- RI
R
AsL is plotted below in unbroken line.
Y.
Figure 2. Profile of relative velocities
-5-
From this relation
and -'iure
it can be seen that the
relative velocities of translation are siraetrical with
respect to the center of the disk.
In other words, for every
force element acting from y eual
to y eual
equal and oppositely
y equal
Eacting
force element in the region from
to y equal R.
Hence, with respect to translation
the disk is in equilibrium.
of translation
;
Uoa
for
o
2R there is an
the disk
UO-O-R
It is convenient that the velocity
(in equilibrium,
whilichI assume)
is
is from (1) exactly equal to the
unrdisturbed.velocity of the fluid below the center of the disk.
Jince the disk is oftoonstant density, any rotation will occur
about the center of the disk s axis.
result that te
his leads to the useful
center of the disk w-,ill remain atop the +water
particle directly beneathit.
There might be a uestion
rotation
as to v.teher
an arbitrary
could upset the translational equilibrium.
2 illustrates to
igure
purely rotational relative velocities (in
broken line) at points s=netrical
w.ith
respect to the
enter.
.ince the vectors are equal and opposite (and it is always
possible given one point to find a smmetrical
no net translational force.
translational
point) there is
Thus rotation does not afect
o quilibrium.
<lthough equilibrium with respect to translation has been
established it is by no means true that euilibrium
to rotationis
concurrent.
with respect
This is especially true i
an
arbitrary counter-clockwise rotation WA is imposed on the disk.
It will be seen that there is a particular value oC
-which
euilibrium
occurs.
at
The relative velocities arising from pure translation
are rom (3)
U-teL=a('SR
o
Nyel_-\t.e
It is convenient to resolve U*eL into components along
the radius vector from the center of the disl,and pernandicular
y
iJotethat
to this vector.
Ž9ce
(U.I
l
-
-
J
_
·
V
-
R+Tsih1S
_
I
0
Figure
3
The result of this change of variable is that
= oYsinecos
U/TeLr
(4)
C/yeL=
4/ eL8
0
$f
U/eL 0 due to rotation
(5)
O
is
=--C
ButUjrwill not give a torque about the center of the disk so
that the net torque per unit area is due to the relative
velocity
eL + /reL6,
UU
-
(6)
then
(7)
d
(
2
an
Y'(asi
)
aoi
O (asiA
T"=
(9)
which fron (4) and (5) becomes
4
A
6*-JA
W+A) CIYJ
S I-bY(asht9w)dr4
'4'+
rYcJe
c
wfich interates
Irb R.+4)
to
-7The mo:.en
..thien
-
o
of 'the diskc
inertia
dw
-I
(10)
R
is
leads to th-^edifLerential euation
(
-
The solution of this differential e-uation is
(11) W(
)e
W.-
f
+
j w. =w
t
The interpretation of this e:uation is that i a dis is
reeased
an.glar
in the
luid at
the
the fluid beneath the disk.
In equation (7)
there is the tacit
fluid acts only on one
on both
, then its
approaches one-half
velocity eonentially
vorticity o
W
ngular velocity
ac? of the disk.
aces the torcue must b
ssumrtion that the
If
the fluid acts
doubled and eouation (10)
becomes
(0a)
(ll)becomes
=)and
-
U.~. i =-t
(1la) WW.=
Up to now no mention has been made of the torque acting
on the side area of the disk. Vether the :neglect of this
n the sid.e area of the
tortue is reasonable or not depe-ds -c
on
disk or directly
smaller torque on the side
and h.
can be mzadeby making the side a.rea smaller.
The purpose o
the preceding analysis was to ga-her
physical facts for investigating the
circular disks o
-,easure
ossibility of using small
the vorticity in
directly from t e rotation of the disks.
be calculated
(12)
some
ishpan eri -iments
The vorticity
would
rom the relation
3=
where
W is the
rotatin dish-oan.
dishan.
angular velocity ofthe disk relative to te
U~~~z:
-'C)-
-ill
tt
aissu3 iOn
f
-aeziona,.bLe
first
I'.2e
b
e-(1ined
he
is tuhatof the assuijmedluidvelocity distribution.
w-as originally ostulated as eistvi1g in the
4iimmediatevicinity of te disk.' But in the derivation the
distribution
distribution
as mathematically used only in the area covered
b'y the disk.
Hence, the area o
by the
the disk is trhat
innmediatevicinity of the disk."
s meant
This aea
can be
made arbitrarily small by merely making the disk arbitrarily
small.
Thus, other things bein
eual
better values of
can be deterrLinedwith smaller disks., If the disk is small
enough'the assumed velocity distribution will be closely
ap-proximatedw-ithin the area of'the disk.
The meaning and validity
of the postulated lar of inter-
action between fluid and disk was discussed when the law was
proposed.
although at a point in the traiectory
o
the vor-
as
ticity of the fluid may; qual twice the angular velocity of
the disk, at some succeeding nearby T-ointin
he tr.aiectory
,?here the vorticity
not L.ave austed
to te
is differe
the
nt disk ;-ay
new voraticity. According to (ll)
place exponentially
ib)diminish
.,
b, the visosity
-
~rom (11) there are three .r.ays
to hasten
(a) dilinish h, tihe thickness of the disk,
the adjust-ent:
irinshi~n-h
the adjustment takes
the density of the disk, 'and (a)inc'rease
of the fluid.
perform
-ofi:'nd
-reduces
L
~
~
~ the
..
It can be observed tlat
t.:ro
funtctions: it
..
-3terLsthe
on the
side
--~:..e
1r~ue
r-ca+
U.
h
z e
'"~o
adjutment
-oeat k eikdisk.
',C.:
;;.:.{..
...
o
IZ; w^u.J.
7J~~~~~~~~S
-se Sof-r ::,
To rin.:i
_
,
sll -'::izitude
he ima
o
...e i st
term in euation (!i), the disk was ut firom.a 2lin sheet of
?,::,:er,
the
series
of data
the disk
Disks
ensity
",as 3i
of radius
of W...icl
we;:re:etaken.
2-,v5s
uch less
%?an one.
In the first series the radius of
znd the radius of the dishpan
10man wer-e used with
in the second series.
Dwo
was 150u.
a dishpan radius of 300mm
The velocity gradient
does not vry
as rao idly over te freesurf'ace
in a lar)ge dish-an so t-hat
1ar ger disk radlii ay be used.
The data in both series -was recorded by camera.
camera mounted three feet above the
ree sur-,e
and rot at ing
withLthe dishpan vWas connected to a tiaing mechanism
every second a .otoraph
A
so that
was t.,:en of the d shlan with be
disks floating on the ree surfiace of thew-ater.
By projecting
the pictures on a grid in olar coordinates data was obtainable directly
rom the neg:ative
Thne disks were numbered
LramCs.
or identification
as illustrated
in figure 4.
Figure 4. A sample disk
The position of the disk is considered in
relative to the dishpan.
Thllecoordinate sstem
olar coordinates
is shov
in
-10
eunit,
, r i,- been L-trs
ad C
unit
o i G.-,
n.
£aor
ct0r 1Lstbelie d to
.rinsforr: r to cr. Thle convers ion factor s M±ffrent for
bot, series o lata.
,
:ie ,,,easured in dec-.-ees.
=',1:ura5~e
e
wad...Q.dJL
Kd
af tter
2re valTues oJIte
var
i&2e
z sc on ds hv e ea r se .
~a~
c
. avee been
by using, central differences.
_s
X
;esti.'mated
from.t-e discrete
data
For e:-:mcule,
O+A
4°-.
Ahrln
Figure 5 Coordinae stst..
sstm e rrati i
'
o te
dishpan
Series 1
In seriesone the rdius
o te
thie radius of tiie disks was 3.
to te
the
dishpan v'as 150m
Te fluid otions relative
dishpan were induced by heating the lateral
an w-ith
amipns. lThean,:-ular velocity
was 20.8 degrees sec'-(3.47
r.p.r,
and
-
of te
0.363 rdians
ameaof
dishpan,
sec-l.)
,
-1 -
Table I contains
data
-from series
one
or t=,o ais';.s,
a and b. Here 4.81 units equal 1 cm.
Graph I is a plot o
disk a.
Grah
versus t
r versus t and
II is a similar plot for disk b.
or
In addition
Li-ure 5a depicts the position relative to the dishpran
two
disks
lotted at three
by points
econd intervals.
Graph I indicates that over the one minute
a 'l1aspredominantly negative vorticity.
that
there
are
large sc.le changes o
scale changes superimposed.
of the
eriod disk
It can be observed
vorticity with small
Such a attern
disk is moving in a meridional path.
is cos-ion when the
(A meridional
trajectory
is indicated by an approximately constant value of r.)
Graph II is much more interesting.
I, there is a -eriodio variation
is almost eactly
of r being
values
o
r.
As op-posed to Graph
The variation
o
in the same sense as r: increasing values
conjoined with increasing values of
; decreasing
of r conjoinedwith ecreasingvalues Off
relationshipbetween r and
had a significant
eriodic variation o
Since the gradient o
apro.-imately
was observed
for
every
This
dis-kwhich
r.
the vertical velocities is
zero at the free surfacethe vorticityeuation
below can be assu.ed.
But
is constant in so far as e-perimentally
possible
so that
(13)
Qualitatively, this
are
sociated
eans that increasing values of
1with convergence and decreasing values of
-12-
I
I
I
I
b
I
I.
l
I
Table I. Series 1 data or disk a.
4.81 units equal 1 cm. R
.A_ 20.8 degreessec.1
I
I
150 mm.
I
I
I
I
I
i
I
Al
Table I. Series 1 data for disk b.
4.81 units equal 1 cm. R_J-= 20.8 degrees sec.-1
is
I1
150 minm.
-
i
-
T(uclits
seC)
*o
-/t Oro
60
to
*'0
--0
so
c0
- /0
GraphI.
r and
ve(rsust.
Series 1 data for disk a.
-r
d
;
T(-nits'
-5(J
st'SC-/I
f /00
to
0
w4
II. r and-versus t.
Grapbh
Series
datafor dis b.
-
Figure
5a. Trajectories
L6 -
o diskl- a and b relative
the dishan.
Deries 1 dta.
sec. intervals.
to
Points at 3
-17with divergence.
Since graph II is typical
or a
eriodic variation in
r, it can be concluded that there is convergence to te
of a troughaand divergence to the east of a trough a
free surface o
the water.
the
This conclusion is eactly
to the divergence pattern observed at hit
500mb)
wiest
levels (say
analogous
above
in the atmosDhere.
Following this result a more extensive picture of the
vorticity and divergence fields wEs sougat in
Series
eries 2.
2
In series 2 a dishpan of radius 300mm was used with
disks of radii lOnmm. Heat was supplied to the higher radii
by electric light bulbs mounted directly below the outer
region of the dishpan.
Sixty disks were placed on the free
surface of the wlater with an initial attempt at uniform
spacing.
using a technique developed by Alan F. Faller, potassium permanganate crystals were scattered over
of the dishpan with the heaviest
radii.
the floor
oncentration at the inner
These crystals dissolved to form a dye which remained
at the lower levels of the water.
After several minutes
elapsed the dye was observed to be concentrated at the inner
radii with a very sharp boundary between darker and lighter
dye.
Temperature measurements have shown that the darker
dyed water is about 5
cooler than the ligvhterdyed water.
Analogously to the atmosphere distinct outbreaks of cold
water move to higher radii.
The ensuing fronts appear as
dark bands progressing southward (toward higher radii) and/or
-1
-
higer vales of e
eastwara(toward
.
for series 2 was held at 7.56degrees sec
-.IL
(1.26 r.p.m., 0.132 radians see-1 .)
A series of data ten
formed is contained in
meaning
as in
5.36
l
units equal 1 cm.
hen a strong cold front had
r and 9
able II.
¢¢ , however,
Iable I.
-
have the same
is not directly
entered into Table II.
The vorticity and divergence pattern
to .
as required at
t_3, t,
tl
Data were compiled fort
and t+S
, where
the subscripts refer to the relative time in seconds.
Estimates of CW_ and W.+1 were calculated by central
differences and are designated -40
and A+4
·
A¢~4J-3
A mean value of Kh and A1J
(15)
taken as W 0 .
s°+.. i-
E7=
The vorticity ~
E-7 is
,
is given approxinately by
(16) 3 ZA§°
The absolute vorticity is f plus2.(Vwere f ecualsZAL
An estimate o
fIt ororalternativebL~
atraiei,9
-
is calculated by
central differences and is labele.:
(17)
~afte
~~(
~~~)
_
'_¢-_
_
Lastly, the divergence from (13) is approximated as follows:
1
out the constant factor two.
canceling
-19-
A3
-,.
Z'"
.
1±o2
/ Asz
.o/. f.=
1.C
//yZG*04.3./
~~~..
a.im
/d
-.,.
I-.-s='
,
_IS
_~uv~itS
V
- * .|- _Zd4L
*1;-~
/>1*:
t- _ifd-.
ZZ•11~~*.
~~3~~Z
,,iwl.
,
_
I,'t
,--
_
3±A
4
Jmk
- d.
--
0-I-
+-.
-°.60
-
-.-/~ . 2z
/
dI
-*' /.
,4.0-.,
- +.1
- L~
.../i .ii
A&,
, r-..t / 3/$.
.-- ._aP Z
-
~-~o,
:
_d,_
-$/-
ZQ0,
- .
-a
.
e.±
-
,f±
/
Z
"_
. ./3L+/'
,
_4Jo.I
-... z'-.
--- 6/-
_
--
2e.
.s"
-
./ r. . .0 -.
I
-re.
7
.
f
- of
-,-,Q
/.4
'- + -31
.I -2.o
-4-."
'--~,
x.3z
'.-S..'
J.
.1z-.'-.~
9P
-33/
azL-.I
JI..
/.,¢'
-.,"
--
-d.,
-7./-~_4"i~
--. ,dme
,,a.L -Z,,,
A.--,,/
ed,
--3, 2. +
JJ.a6 +.:Z37 -.. 2
. -- _+'Z
3*-d' ZV.-.- d
/~.
/L
k
-,/a.Z.e
''.~F
..4 2:232 _/-J,
,
.a.
3.
-3.
/
_
~
j2_ . z.
Z'/2. ~~J.A .I /
~~z2
307 -~~
/./ .
-. ZJLR
-..
,
_2
.,,;a,
z
,J7
--D.
'-/.
~
f/.
,~
31,
';
J9~~.~
*0
7J- -,d. /
~
--.
Zap -. .
-- £a/,fz -:../.--./f
_~~~ ~' -'--,t
-- '/2Z_.E -~. 9
/Le
.~~/
.A. A
y-/ ~
-IL.
a
- 7
+'3.#1
~-&d
*4
..
4
72..
1
*3/
-.
.4.0~
,..,,d%.7 *4L
- -i3
9
0./.Z_/.
&
¥.t_7
z
1,;
P~
/--
~_;
- '
'f',f.gq4. +la+3.3
J
0-2
~f 7-- -/z -/.0
-!
z _ '/
z3a- . N
Z . --7 --4-
am.
fg ---o&
.f,
Table II.
-
f
, 4,7.d
,.
2/f
-
.7A
a-
o. / +/,/3 a.2. +/7-/ 4A~,
o -13,P a.77
F
+,/,
, /1,
A,
/.l *:;
Data from 40 disks of 'eries 2 at t.
-L 7.56 degrees sec.
5.36 units= 1cm.
R = 300
',
mm.
-20Table II
~
original sixty
contains the information
,diav,
for forty disks.
' X K
-I 'W ,+
Tenty
of tlhe
diskCs were either in collision or rubbing
against the outside rim of the dishpan at to and hence were
not used in the calculations.
igure 6 is a map of the free surface flow lines and lower
level fronts at to o.
igures 7 and 8 are maps at to of the
vorticity and divergence patterns respectively.
The prominent features of figure 6 are first the four
approximately symmetrically placed high pressure regions;
second, the two fronts in the second and third quadrants;
third, the three sharp troug.s; and last the strong polar
vortex.
At this point, one serious disadvantage of the experimental procedure is apparent.
interesting
This is the absence of disks at
ositions in the dishpan.
Tor example, it would
have been desirable to have disks in the upper level trough
in quadrant three.
In figure 7,
VLonewere there, unfortunately.
the vorticity pattern resembles strikingly
that of the atmosphere:
Over the four high pressure regions
there are maximum negative vorticities.
:&aximum positive
vorticities occur in the major troughs.
In figure 7,
atched
areas represent negative vorticities.
The divergence pattern
interesting.
s depicted in figure 8 is
However, the magnitudes of some of the divergences
are much too large.
This must be due to the fact that the
)0
Figure 6. Free surface flow lines and lower level
fronts at to.
Figure 7.
Free surface vorticity pattern and lower
level fironts-at to. lhe two broken lines
are characteristic flow lines at the free
surface.
'?
C}
Figure 8. Free surface divergence pattern and lower
he two broken lines
level fronts at to.
are characteristic flow lines at the free
surface.
-24-
err-or in V is of the sme order of mriagnitude(or greater)
as 9. This can readily be understood when values of f
are examined in Table II. Values of S9of one, two, three
degrees cor.espod approximtely to the error in V so that
the magnitudes of the divergences must be considered
to large error.
Nevertheless, the sign o
probably reliable.
in
igure
subject
the divergence is
To emphasize the sign of the divergence
, regions of convergence have been hatched in.
Again, as far as the signs are concerned the resemblance to
the atmosphere is strong.
The eastern sides of troughs are
regions of divergence while the western sides of troughs are
areas of convergence.
In the atmosphere this condition
exists at upper levels (above 500mb).
C ONCLUSIO NS
The vorticity and the sign of the divergence patterns
on the free surface in a rotating dishpan as calculated
from rotating circular disks closely resemble patterns at a
high level in the atmosphere.
The divergences are much too
large, although, due apparently to small errors in measuring
the rotation angle of the disks.
SUGGSTIOSl FOR FUTLE WORK
It is
ossible that by a proper choice of disks, vorticity
and divergence patterns at other levels in the dishpan could
be measured.
Experiments to det;:rminesuch patterns by
using liquid layers of
been successful.
slightly different density have not
If the magnitudes
of the divergence
are to be calculated
wiith accuracy a much better method of determining the disk
rotation angle must be used.
Insufficient time prohibited
experimentation to determine the best feasible method of
taking data.
6ome means of locating disks at interesting positions
would be desirable.
It often happens that an interesting
situation occurs with no
isks near enough to give data.
An increased number of disks would give an increased
amount of useful data if the number of collisions did not
increase directly with the number o
collision, its data are useless.
disks.
I
a disk is in
One third of the original
data had to be discarded because of collisions.
-26-
BIBLIOGRAPEY
1.
A4lan 3. Faller, "A cuantitative Study of Eperimental
Models of the Atros
here, "
S.M. Thesis,
. I. T.
January 19, 1953.
2.
Dave Fultz,
On the Possibility of Experimental Nodels
of the Polar-Front Wave, t
9, 1952, p. 379-r,
Society.
34,
Journal of ieteorology, Volume
The American Meteorological