ULAIoW or WitiTicAL
0 W MINAS Of LATENt MAT
7VII
by
OWIN OWU PATRICK
m..* sill Uslwwslty moftmAl
WUIRND IN PAMI IULILLNUT
=am ow wam
OFczz"
A*% t IO
A
*ig6atar
of Matou
a.o0 0**
Dpawsstoil Mt~owle"
Cowtlfl~d by*
w--t
22 MuSt 100
w
pp*-
P*a*S
72hess 3Impervisor
Aooptod by
*
*
****
~&amem Deas~atC Inttm an Grafato Stutdonts
*
SLATON o
WIRTICAL ETIONU 70 1S SRAW OF LAIINT =AT
by
Godwia Olu Patrick
uhitted to the Departaeat of Mteorolgy an
22 AMgust 1900 in partal ftiliment .t the
rquirmeest for the degree of Master of Seinee
ABTACT
An Idealsed model of a stom is coastrueted in Whieh the distribution of latest heat of oodensation is represeted. Stk idealised
stomes me regarded as heat soes
an a lerge
hber of this are
asmed to be rewed in a lie,
suh as Is observed in a squall line.
y appliatiaO of the prialtiv equat ioes of action, the equation of
state, the sentiaity equation, the steady state hypotheats, sad the
first law of theaodyeeies, the pertarbatione in the sm flow pattern due to the heating are detemined. fulh portarbation. indieate
that the latest heat of 0oedensatica nay be Important in triggering
new coentive cells between soy two of the initial heat sources and
that the level at whih the masam release of latent heat nerts,
is that level at Shiet the vertieal 541o produeed by the lateat heat
is greatest.
Thesis Auperrisors Viter ?. Strr
Title; Professor of Meteoroltgy
P. 3. Atta aSd 3. L. 2s for UhAo
I as gostoftl to br.
flisn
naable
Als
tetesssrs V. P. Stew
y appnsatts gest
Phillps ter thol
ter n .p
amalys
Sie this wk
ad sltita.
nsmriq
se ia prqgrsas.
-WN. A.
eds; to lhe wader wather anti.0
sttp to gals nemerS apessAMM with squall line
t
e Sa
4;
to Kiss e
lle sle for th drafliug of
the disgums ad lafly lot maths Iaet to Miss Jams Sialet for
typtag lbs thas.
TANS or comErs
11
1AWU=
Il
IV
O in
POLRN
0YMZING IWATIONS AND ASINMrfON
is
t RATIN NecON AND ITS nowMon.CAL
IM CJcAIOW
ao
A. GErnn1
5. enting tistrbutioan in the nrtinl
lire
1
C.
satig distribstin
a t horiatal
igurns - and 3
25
28
29
30
34
ZWATION
S
V
K)LUOIO
VI
MaONS UIC?
43
VII
CAN Or STARh AMOSPUS
A. Slitta
3. Malys of th total stn
?Igum 4
44
Vill
ix
F IM aZlPBNAL
ltns
47
48
CAN OF AR IMUPVBSNT AI0WMS
A. SoIstmaa
5. Analysis Of the total flehmlne
t 1gwrS6
45
42
so
olso
Or tor= Wan
A. Stable SAaphe-3 4ase
5
S2
5.
Atmspbene with asutral stability
51
55
x
MimsTM
s
xi
acssLov
so
MElOSASET
63
m
Um R wm
1.
ImflDWCTION
The mst vigorous weather phessen that Oer on the earth may
be easderd to be limited to the troposphere.
The sene of
meteerolegy applied to this laepr has .cmeentrated its efforts is
the understadisg of the meehaims end behawisur of such oeurRenes.
sm,
Udmuatedly the most vicious of these phenesm
tornados, squall lines or lastebility lines.
thunderstom activities might
Associated with these
are
anui-
Vigorous
aecmpay any .f these weather patterns.
omveetive activities -
energy treeataMa-
tims.
The types of energy involved isolate potential energy, kinetic
energy,
"r
a
work, heat produced by viscous foroes, eloctrieal energy,
internal energy (inlating the latest heat of ocmdeastion).
energy tratosmations at
BrOes (1958)
budgets in
as**
The
kao bees stadied by
N antleed by Dyrs ant atsham (1949).
Most recently,
in a model given by Lilly (190), he arrived at the coselusion that of
the latent heat of amenaties released in the moist region 42.7 perenut of the total goes into kinetic energy.
The
ounts that go into
horisotal em vertieal kinetic energy respectively are not specifled.
This paper is restricted to the study of ealy ae
tom of the energy,
ilamely the latent heat of codensatios in a line of stoss, with a view
of applying the result to a squall lime situatios.
Therelation of
vertieal mations to latest heat of oeessmmation of istemediate
yste
maob a. eyelas or barrieamss will set be oomeidered in
this study.
Th eftet Of
test flat as large sale atmophric
mattons has boNo diseassed by Aabort (107),
is this study eansors to quOetis such 0e the following are
sought.
etione rsoult foe ella i
1) What type of vertical
O
Of stesS n0e00e as ppsotable amont
stOady state
3)
a line
latet heat under
aenditiems
Are ma mottes sattietent to aiftais the squall lie
mater favourable meteorologieal eenditions?
Apart frm the above two questioes,
it would be usefal to detemis
the positien of mow cells wboe fosmatiom is due to the release of
latent boat.
The apparently
nes foaatic o
now els
of varying
istesity as viewed from ee imstrments as 00"4111-B ruder has boon
most intrig1ig atd challenging to the preset day radar etteorologists.
As an esaple, aben two adjaest cells are observed, is a matter of
slautes, they either remals disteset, disappear or eabine
ateorologits belleve that until mo
Many
smtes diseppearme or reo-
foreemost is fully understood, a thorough baswlete of the sastoeanc,
propegata and dissipaties of the squall limo will sot be easily
explaid.
Sveral studies bave been divested teots teneasting teebiques
sad esaties of squall lines.
Wesier (1900)
amd Abdallah (1965), both have &a es a objeetive of
deriving a
has attempted
Fr iscaple, papers by Beneer and
"ewastin
equatio
aserial
MethoS
or the squall line.
asU"(199)
for the lie, while Netn (1950)
and Teppar (10) heWe attempted to develop modell Pjita (19f)
on the other hMd has given a detailed thre diseseaal analysis of
a squall lin,. All these efforts haen bee made in a attempt to
elueidate our smieretasding Ot the equall lime.
Clearly a therough
understefling of sells' behawiaer is the tin itself suld ban
greatly simplified the questions to *h*
eassers se sught by all
of these isvestigatns.
Reen works a
of the latest heat of
syelemi
seals have Ildieated the importaso
osdnntiea.
Em2aples eve Lilly (1940) in his
paper entitled "On the theory of distnrbasees in a aenditionally unstable atmosphere."
Mother is that preseated by Ptteresen (1960) -at
the Conferees at the University of Chiego.
"Neat soueoss and mebile eyeless."
The paper is entitled
No indiseted that latent heat of
ecndeasatien is of the same order as sensible heat and it is important
as a soures of esgy for the development of qelese
the North Atlantie OCoea.
partioularly over
The above disuessions therefore show the
neessity ef investigatlng soe esitieally the selation of vertloal
sotions to latent heat of "ONdesnstios in stems.
S.
a differat epprosob Is uandrtakn.
e
thistudy
-
The stems
as heat soares benamse of the latent beat of eoodeuswrgsrdd
I
tics.
The pertarbatio
method is aploped and se shall be interested
in the distributies of the vrtiel
notice that realted.
11.
The proble sth
eal
NAX=N Ow T
MMs
is study Is eomaermd with te
resultant vrti-
notion when latent heat of amnetie is released lk a row of
stoms.
it
ould be thoght Of as te
ains
vertical sotion that
would be gaeated wea such heat t available is te
atmesprs that
sMu
e eessidered.
a result to te
two types of
The primary Itevst 10 to apply
problem .f the squall liNe.
In sloh an applie'-
ties, the 011 eenpemets of a sqall line Could be easidered to be
ooademasig water vapor (and mameematly releasing latent heat) at
the semo time, and theretere eould be treated - heat sources that
are equally spoeed and of the seme dimeasinas.
Though te
problem is essestially a diffiaelt three dimensiomal
on, the emisderatiem of a sapler two dtseiniemal model pemitted
an mnalytie seltiae to he obtained.
IS this first attempt to Investigate the cell behaviour by a
rigorous matbeatoeal met
od,
nay splifying assamptiems hod to be
made se that the problem waett lead itself to staple mathematical
sasipulatios.
It is hoped tat
tatua
work on this subject will re-
quire ftewer assptims.
Physically, the Model sW be theoght of as a large aSber of heat
sources equally spaed a"
eath sUteding istiaitely In the direction
oumal to the seas floe, amd every
etoorologieal parsetar ad its
10l
perturbatious as
aal to the ma
soasidered to be independent of the direftion norflow-
in thre dimeasions, tis
waraliatie pioture
is quickly eliated
Is three diseasins,
e cSaid osmsaider the heat saveus as ver-
tisal eyliader entending tro
whet this is
the greed to the tropapeum.
Clearly,
iewed in two diesias, the pietmre obtained it the
plane would be saller to the se0bt esealistie pietue
tht Was
Just deseribed.
The physleal pittare would Mt be emplete it there were no
desriptie o
eated.
e
see atmophere is Slb the heat surses ae 1-
Wet the poertarbatin method of olutios is mployed in pro-
blms of this astuno it is usal, esamples ae balias ead tun (19i)
and Scorer (1n0), to treat the mareOuniUg atmosphere as hesgenees.
This of nure is ot n
ensung athemeties.
eesey emcept that it helps to siplify the
In this problem, the atmosphere is soasidered to
be flatted by Me trepqanse at Shlb level a lid is assed to be
pined.
This is pleasible sine most of the vigorous eather pheoaena
oar below the tropopsase.
usually the stability of the stratosphere
is suffilent to prevent the ineursim of oavective currents trm the
troposphere.
Oeasiosaily the instability of a soaestinve al
in the
troposphere is etreme enough to pomit the unstable air to "break
through" into the stratosphere,
therefore to a good appromitiosn the
atmosphere is assumed to he hee1gemeos with unites flow throughout
11.
the entire height, a flow Sieh is sabjest to distraees only
through the eftets of heatlg.
Physteal diftubsoes shob as
moutain barriers are disregarded,
In the difterential equations
vertial wind shew tems are aepleeted so that the problem is redueed to that of a bemgeuaes abfesphere.
Also, the etatie stobility throughout the troposphere is
to be eastst.
mmwd
Lilly (190) has gives values .f the stati stability
at various ie ls in the atmosphen and to a good
assumptioe is also plamsible.
Ground frietim,
and tarbalese are assmed to be absent.
lppraintIon
this
ddy wiseesity, stresas,
The only sare. ot vertical
mtion is that attributed to the heat scurees.
Therefore regions there
there are vertleal motions are repiets in whik we might empet the
development of mew cumlus or ammlemabus elaed and it the air is
mist enough or If there is suffieleat eatnisent of moist air, we
could expect that those plans would be preferred reglons for new
precipitation ad bean
leased.
ndensatica would be re-
As scen as thee is ebough oamdensation, moh regions could
be thought ot as
It iS
same latest heat of
w heat snes and s the shalt reaction goes on.
interest
It
to tote that shak a flew pattern was given by Malkus
and gtera (1M8) In the problem of 'table air flw oTer' heated Islaed.
3sssatially the sae mathematics are ampleyd, see ala. Seorer (194),
except that the heating distribution is different and that in their eare
no new heat scares were generated, sine their hoat soure was an
island.
Is.
III* ORINUM 3X1MBN AND AMBPUTIONB
The prialtive oqWatless of netten In the eartesima oordinate
system are gives by
srt yV) +
- 2.a (COS
-C -
(1)
x
dv
C3p - zn(sily-, u
cP1t
6j
-
(
=-
-COSQ
Iz
eSetiuSity equaties is give
The
-
(2)
a
-
+
_x
+
(4)
-ears is
the north and the
eals polating to the smalth,
hesa
towds the eat,
the maxis to
is the earth's asgular velocity of rotation
is the latitud
F
is
te
etioeal tores
is the aCee9eration due to gravity
O(
is the speifle volume
is thepresue
(3)
by
In the above, the
OC2.
-
J- where
is the density
1.
U
is the velocity easpeNat i the Udfrfletion
V
is the veloelty eapeent in the r-dinectian
\W
is the velenity ompnat In the
rdirestieu
is the time.
The essettss of stateMa d the first le
of thesaedrmmits are
also employed
=
f RT
(5)
(6)
) = TCt
C dIt
dITP -d t
Rere H is the umber of malories per gra per seed
the air at a given point, R
the Mat equivalent Of work,
is te
Q-
gas caeat
aupplied to
and Cr are specific heate of dry air
at eestinat vlumes and constant pressure respectively,
tial temperature emd Ti.
Sines the sels
io
for dry airj
0 Is the
poten-
the oeslute tempersature.
.f the motion
e are ensideritg is nmall, e aa-
neglect the eftect of the rotatien ef the erth. Thie eliminates the
presence of the Cerielis pamSeters in equations (1)to (3).
sapliety
n
neglect th. eftect of frictoen.
Also for
This does not affect
the solution Oritieally.
The bast five equations thea redwo to the tollowing in two
dimensions.
m4
CXB
(47)
ex
at.
dw
-
(8)
4
gi
(0
~~jg
az
f'cit
f RT
H
cvdeI
(5)
Tc die
cI+-
+±IPI(t)
cit -
To f.11iase asmata
()
an alm. basroMs
= U0
+
(10)
VI
I
T
(1>
P
+P
H
f9
(11)
H'f
ro
te'
-Yzz
(13)
15.
C)
Nbt at
bt 0
~~lY
at
t
&C-3
6t
(18
WB
=K3il T'()
&t at 6t bt
Equation (10) - (15) divide euta variable Inte two eapomuts, on
npresating the suditios of the undistsrbed flow while the other
(prime qustity) indieates the perturbatios introdued duo to the
beat seu
s.
quatity.
The first order pertwrbation quatities are represented
The rate of beating iU also treated as a portarbatio
by primed spObols tile
the produsta of two sh quantities are re-
garded - ased order pert
letatios entities and an agetd
cempared to the other teas is the ensalg eqatim.
as
Similarly
products of primed quatities and their derivatives are snsed to
be of seoend order.
Equation (16) states that the temperature teses
with height
in the undisturbed eurret and that the lapse rate is
3z
Equatiso
(17) states that the undisturbed current is i
statie equilibrie.
P .
T
aN
hydro-
Equatios (IS) states that the parasters
LA .
is the undisturbed current ae iSdepedest of s.
tile equation (10) states the steady state hypothesis.
1M.
in Uhe denivation
Is ulne ted.
.t the dttremtial eqation
This Implies that the niosty
the teym
ot and
IS the
aftmqher under eesideration is auch larger then the
a that the abakepe
peed
Is enpssithle only with respst
L.
to lifting
ad heating.
e4uatin
mimployl
cit
+(U
')
Az
*X
b
to a simlar any'
3t
+
wL(uo+u')
b6z
-. _L
~l+P)
fC+fos
(19) we have
Uo
4
'Y
-X
'NK
Using (18) ad
+P)
-
SU) + u1(uu+u)
6t
t
=.
dtf=
(7) kees
(10) and (IS) 0aties
eqation (6) beees
L t w&L
-L4
ix
2)
Sploying (is) ad
(20)
-L6X
fLI.P±37-
bz
+8
~0
(19) we bas.
U,0 lL
Since -e have Lose
equation redams to
p
to welt
the tem
dt
(21)
.i the cetinuity
17.
k
+w
x
u
$as
's
0o
z
abe
rod"ms to
+
uJ
bx
The egesti
atat
P
tes sgive
by
=PRT
T
R (T+ T')
RT.+ .T'+ f'T
=
=R P.T
+ RP.T'
Is .m
to be goal .mal
-oee"
()
=0
a
bz
+ P' (P.+ f')
sio.
u. + u'
=
+ fT1]
R f 'To
CRT
Rf.T'+ R f'T.
'-
19.in..<>-
(<)>.ithwh
*agA to dervo the dittesntual
(2)
tis t,3
o tmmess4e .,
~ea9tt
t that Isat intrest to
as la USA pabelm.
IVtk
t (30) ad
t ()
me a
is*
eIJaleate th prosuw O4 *bts
LOI 0
U'a aU, +
au
bz 2)x a-Z bz
IL
4 b
.SLCI
6\
f02- z 2)
OnplQYtsg .*m (19) sON bY
a-& IL
U.
2)z.2-
(SO)
>(3
f~
by
2
+W6
+ L E' f
ax
uo~
the tollouift
+ U
b7w
ftwc the ooutim
f2.
b*V&tlgg (W6)
w 3d 0o
6z
X7
(*6)
fm
+ vq tuo
We hae.
2 Lw
-uo.
; m2.
Y,
wit qtalo
(*U)
(so)
w fied tuat
z 2-
4N~z
Boa"o eq~100 (20) heoaes
u.
,)
++ 2
~
= -- I A
-
ZZ.[
*by,
W
uo
:j f.
+T2 &
(*7)
is*
Nwex equatiou (20) Uas been emplay.4.
31
v2.
=
the Loplaoii
-
We define
-.
Noeas equaion ("?) bone
+ w 32UO
-UOv'iA
b2.
Uo
-
fw
po
FI K
az
La
UDLt z
a P
fo - -XI
)
/
(28)
uo Yi4.]
~z~J
(29)
going
th
affo
6z
eqalon oft *tat* w hve
=f, RT
bz
6-
R
I:z
z
(30)
a^.
simm we
bavo
p
i
-10
N-.
(30)
,+
To
=
Usin ev"4iou
-+
T
-'
R
f
0? To+RTM +KUT/
X
'>o/e
6x
kR p I'
(-I"
meba
1+
RT
R f,-2)x
*ax
Luo-u+v4u>
L
RTOI
fI
2)
ITjj
110
RTOLIU
Using
owtiawity we hav
ua)m +\, U. - I
RTO 2)z
T.U (1
/
ft maim$ (30) "md (31) .qmatie ()
V
boom**
r L-AJ
T+
-
ToR;
,
~L4O
L wT
xZ
-U0
R
V4
+
231.
5olvirn ter
ve
-IIF
wgot]
0
UL3 ZT
±Jto1
RTO
=
b.
3- +T
LUOT
z4
+13W4OT
In
owdew to ellaluzU
thei -
,
U
LtOTO
w bj@t
OWloY tOe
fivet ".g
Of
I" "d the dofinition of the potetial tssp*watnw.
H
FCit
+LWriG
~Tc~kO
=
lAt O,
31500
(38)
0 3z 2-
=
the static stability
Y-YA,
fT
e
T
as em be
twCm the kydroetatie .qvatiefa
Tc{
ax
±~w]
wadily verified
I
Ia3.
by deflattien, the potentl
temperature to gives by
e
Cpr
.. "
F
regarded an a onstaat.
In
"....N...
ft tktg
"em
%o.~ wI
atura&l USgWettuo
ot both sides
= InT + kIn d - kIn P
=a
~1nT
K In~D
-
-L 4_T'
k
To b x
V,
___49
o DTx
U cT'
uT,'
WO r
90ge
pUo
um~cT ~
Fo
u4kTC P
/
-uocKKf
Uc
=
x
u~k
u.CT
4-T
C
p'f
uTLjf
f -Xx
+ uT'c o w
23.
by IAU8
eqeslom (81) v
a
= oc~T
+FwT
--
UoR&F3T'
-
U cT
-o
z
L42TOLU
-w__
RT
To?]
:
u"waU0.
-I
z
W ~vTo C
LLT.x
. FH
a uo
T04C6z
L4.c-
To C z
U04cO 3z
H
T
QOTV
Iest"w.m
2.
C
0
Ito .quatia
z
T1
(as)
t4o2
e haw
UATo ~
-,VI w
U4oq~
4-.9
Toc
TO U02Cr
um
o
weha
Cr
VwA+
3w
b-Z
70/
AH
X
T0QD
LI0
4
-VI
(ft
cZ2-9
24.
or
(22
TOL4O'
If e further asses that thee is as wind sear in the vrtinl
=
i.e.
o a- that c2_ W Is mall
C%is usually Vn
vast of the teams (sse
by Lilly (1940)
a t
.-.
mall as "as eputed
rwepnsts aMplifiestion o the pertur
batios in the vrteal), equatoe (3)
W
epaed 1t the
-H
nodans to the tam
(34)
-
This is a a heqenoaus difftesetial equation with the hefliw
sAting as the teelg tusotiOe.
Me abos equation is a Instase of
the type of equation obtaind by bliUe and Stews (1983),
leeer (1949)
ad more swetetly by Lilly (190) bease essentially the se basic
equations an employed and we ae interested is the perturbations
ealtiq is a stOble Or an isndift nt atboqphene.
This paper and
that of falbus and Stern (193) dal with pertarbtioss eased by heating,
while that of ber
(1940) deals with onillatioss due to mountains
and Lilly (190) easidened the disturbaeses resulting in a conditionally
unstable atoesphen.
Nten the solution of equation (33) is sought, we
shall diseams the distribution of the hating ad its mteorological
ispliestissa
25.
IV.
I
AING PUNCTION AND ITS UUOWIOGICAL IaLICATION
A. Gnoal
The heating tactte
In this seetien.
relevant to a heat Seure will be dieussed
Deees et oe
nature of te
probla, it would be
best if the function are of a tom wkh would be most representas
tiv
ot a atured stom.
tzetles for whiok
Preferoese wold of e.urse be given to a
the lapse rate is moist adiabatie tith turbulenee
distributing the heat under te
Au
amediate pit tall is tat
steady state oendition.
he latest heat of ocndensation
has not lest itself to direst observational measrsaests
a picture oreated by intuition is available in the
literature,
eteorlqieal
lash a picture, however, is supported by evidenee of
eloud strcture
-d
by results of detailed analysis ot the thuader-
storms and squall lines as hae
been prwsented by Newell (190) ,
Anderea (190), Dyers and baehm (1940)
tively.
and snly
d fjita
(1967) respec-
Therefore any analytic fanction that is to be employed in
mpressing such a beating distflhetion both in time and spae Should
be
onsistent with the aork of he shoe
It is
amued investigators.
onmes kaoledge that wherever there is heating, the heat
can be transported either by radiatie,
eonducttn
or onvection or
as in the abosphere by eddy metiens or sitply by turbulese.
In a
aature stowa e probebly bae sells building and dissipating and
age
therefore we have strong localised up and down drafts.
Their over-
all effects could be thought of as distributing the latest heat in
a tows to be described later.
Our main interest would therefore be
centred on this distribution.
An improvement to such a distribution
might be made by taking the efteets of the randam notion into sensideration and by representing the latent best distribution by a different
function.
This would be ideal but it would bring complietions Into
the problem.
Definitely e coaant expect too such frm such a pioneer
study.
It is definite that not all the latent heet of condensation Is
available for the type of perturbation sought.
The heat released is
partitioned for evaporation and fusion, and some part of it is eonverted to energy of other forms, suob as potential and kinetic energy.
Diffusion end turbulence also tahe place and the latter tends to
"spread out," so to speak, the heat to other adjoining layers both in
the horinontal and in the vertical.
Lilly (190), Palsen and Jordan
(1955) and Palmen (1960), have sade same attempts to show how the
latent heat of condensation is partitioned.
While' the actual parti-
tioning is not critically important at least in this study, it would
be of interest to note that it attects the stability of the envirosment.
It is therefore crude to consider that the heating is concentrated only
In the position of the heat saurses, while in the space between adjacent
heat sources the atmospheric charecteristies are the same as those of
27.
the Undisturbed enuiroment.
(CPS
videae fre
radar photographs
er 615-3) has indleat that there is sOmetimes weak pree-
pitaties between two adjaent strong eals is a matured squall lime
and that the
ftetet
meah preelpitation
W Mot be totally diare-
garded in s tar as they oentribute to the heat budget ofthe squall
line regies.
Hoever etude the assumption of
et having precipitation regios
between two adjaeont heat scaees say be, it is noessery so that
the problam will lead itself to simple mathamatloal saipilation.
Undoubtedly the mai
features of the problem ae still represented
aathematioally since the relative
eount of latent heat Of tandem-
satin released in the strong ails
released in the esuireMent.
is larger asepared wth that
The model given i
viewed as representing the distributle
this study eld
be
of a*Ils in a lime at the
initial temation Of the squall line,
In this model as applied to the squall lime the only diserpancy
lies in te
assumption that the region beteen two adjasent aells has
the ae meteorologleal ohainteristies as the ndistarbed regions.
Thus os esaid concive of a uatnom stable or indifferent air sass
extending to a esnsidereble distamme in the horisental wit heat sources
plssed at the position of the alls.
perturbations tat
We are men interested in the
remult between amy tow adjacent heat sores.
me
I.
Keatin
ditriAtion in thm vertical due to
aouloniabus cloud fro
in a typical
atnt heat of
which precipitation is
occurring, It may be expected that a substantial amount of latent heat
On the assumption that there is emnugh moisture,
would be released.
we could think of an air parcel
height
Z+A~Z
ear the condensation level at a
condensing an amount of moisture
Af
some latent heat
A M.
thus releasing
; sme of the heat released goes into the
latent heat of evaporation and am* of it rumains in the stam and
may be partitioned to other fots
In following the pareel
of energy.
from the ground, one could lagine the parcel to have released vero
heat at the grounds and asxism heat at about S.5 Ina (near the eondensation level); then the amount of heat released starts decreasing
until at about the tropOpease it Is only one tenth of the maxiaM value.
In the steady state eendition the upward flow of latent heat is apprealastely equal to and balanced by the turbulest downward transport of
realised heat.
RKoever,
it is unlikely that a parcel originating from
the ground could maintain its identity up to the tropopeuse level.
It sems reasonable that a representation of such a heating distribution in the vertical would be a sort of moothed distribution curve.
A cur.veote
feeoH(z) = z e
k
<*5>
*est representative of the pieture that has been presented.
above foxaula 0
and
k
ak. constants.
would be
In the
While this foaula could have
KMS
10.5
THE
8.75
GRAPH
Z-
H (Z)
ze
k
7.0
5.25
3.5
1.75
0
H (Z)
DISTRIBUTION
OF
LATENT
VERTICAL
HEAT
OF
(IDEALIZED)
FIG. I
CONDENSATION
IN
THE
0.
served the purpose of this problem physically; it creates ame di.ficulty in the integration of the differential equation (04).
A
new distribution that is close to (35) but that presents no dif-
)
ficulty in the solution of (04) is sought, and the town
H(z) =-z e~z
(Zk-(
'
is found to satisfy these requiremets.
C. Barimtal distribution et heatinm in the stamm and in th~e veaiien
If vs consider a stor= or a heat source to be eyllandrical we oupeot
the distribution of heating due to latent heat in the horisontal to be
unif
en d sost intense around the centre and then gradually to
deerease as vs mve away frt
this point.
Amwy tres this cylindrical
structure we might epect asme heating as in the squall line although
this would be auch less than in the cylandrieal region and its effects
could he disregarded.
The heating distribution alg
the horisoetal fram the ground to
about 700 sbs, ight be considerably ditterent, sine. fras coMMon enperieso and observations we find that such a layer or region is always
cooler than the enirement.
The work of
?ujita (1957) supports this.
It is due to this cold layer that s have
the so called "Nwso highVl
the squall line region.
i
D sroand Brahan (1940) and
Nevertheless it
s take a aroes snetiomal slice of the cylinder at a height
Z
such
$1.
that the thiekabss is Az, we might asem that the latest heat
distribution along the
hOle erose seetional surtas of my such
disc that 0ould be out out ot the eyliader is initemn.
This type of
pieture iamdiately suggests a restangular pulse, of possibly unit
aplitude.
pulses
W might therefore think of the rws of heat surees as
ouch that between eacb of the ouser
the heating is se
and
in the region ot the heat souree the amplitude ineases Sarply to
unity.
The question of the spaing -betwem these heat sources is
also important, beoese ouch spacings deteumine regiess whee we Might
expect preaipitaties.
Siana we think ot eact heat sure as a generator
Of new beat sources, it might be Smful to ash tether after ese tine
the whole regis would not be UniteSly keated and
ISequtly there
would be no distinct regions where the heating appmniably exceeds
that of others,
It is ageted here that tw
heated region exists, the moel breaks doe
such a unifosly
empletely and this might
be one of the factors centributing to the dissipation o the squall
line after it has been ative for as
ppreoible length of time
(usually 3 - S hr). lowever, the problem in this paper is concerned
only with the ftt.
ot the well spaeod heat sourees having the distri-
bution that has been deertbed in previous paregraphs A. mh beating
is assued to be independent of time.
The spacing between thes heat
sources is asined to be twie the dieater of seA heat source. This
assumption is not asoesosary nor is it aseesosry that all th heat
32,
sotuces be eqally spmeed and of the amse dimensions.
aasptione I
iavatge In asking moh
The only
the siaplielty ot the mathe-
atimal eputatlos Involved.
heating distributios In the horimsatl Is agreed upon,
If mwh a
the ?ourIer mile. suggests itself as a asoae of breaking dow the
pulse Into the s-o
el
aui=eidal was and empreing the Spesings
between the heat surmes.
man be represented
The heating distribution In the horlesetal
ouwrier theorem, applied to a weetaugular pulse as
by employlng the
00
HMx
~
+
Q
LL
cvCos
nT)( +6,ssnrx]
(37)
L
L
eh.re
c
1
=Lf
H(x) c,,s nn
x
(,)
-
H(x) sin nFr
ax
(3.)
-L
k=
LIL2L
ci 0 -L L
H(=
1
= 0
for
oxr -f/
4
2d
i
elsewhere.
no
Here
Qo is ehose
to be sa"
steady state hypothesi.
sources Ibile
~
In order to be omeisteat with the
2. L
.mo.s the dIstamms. .e.w..s*t.
deates the dim.ter of a heat sou
beat
.,
L
H(x) sin
1EXY,
d
LL
= si
x
u
4
-00
/a
L
f~
=
Jx
+ o s a dx + o'.Ssin n1Tx
L
o
Gimilarly
L
H(x) Cos
-L
:os nI
rxxx
L
L
Ax
-'liz
4.
-
L
nTr
nT
H-
Hx>
fl7
2~Ls~r-n/.
L-
2L
2L
L.
H (X)
-2.5
0 2.
I__'7
7.5
12.5
x
K MS
RECTANGULAR
PULSES
OF UNIT
A MP LITUDE
IN
DIME N S 1ON S
FIG. 2
DISTRISUTION
OF
LATENT
HEAT
TWO
70
3.;-
1.75..'..//////////////////////...
-
2.5
2.5
--
X
DISTRI3UTIO N
OF
LATENT
LINE
OF
KMS
HEAT
OF
STORMS
FIG. 3
CONDENSATION
IN
A
35.
V. SOLUTION OF T
NTIAI, ,WATION
DIm
Fram the discussion of the distribution at the heating tuetion
and beam we are interested In a tastIon
that would be oepavable
we cam write
H '
we.
H
i.
=
H H(z) H )
a .eeptaat.
HI
=
It follows thef that
sin nf.
H.z e
nT
y onsiderig the all hemoen
L
2L
alone, the equation
2.
-u
beeames
2 Ze
VW,
(z-3)
T.L.e V)Tr
+h
ks in
h]i-. c.-s rmx
2.L
L
TO Q&
Y1
I
If we further assums that
4
fhere kestuand
= Aiz)ke
e Le.
for ""eal part ot" the
equation (43) beos
(42)
s.
n, -
*-ZT
(43)
This equatia Is of the ton
A
=
e
44)-
L a .'>'
0,i- n.r
The *mplmNtaWy
while
s*utiO
h patilar
to (4)
Is given by
Cie.
=C,e
X ±An
+ C2.
solution Is given by
jd,
_-_
=
, x)
_
C2
(x)
The general Soue
+ C(x) efTn
e
=
C1(x) =
C
2L
Is given by
x (rA +
2________
)4,+__-.F
-
A2,, ex
n
xj
(
L
7~
$7.
=
9
+j
i0e.
+'
I
A
4-C
+ Cr4x
Cie
FA
TAlX
(45)
Applying this result to (48) we oat write
-/
e F,,+
z
(4)
+2e
+C,e
(KZVA-,-
whore
Z ZA-
+4An'k
The subeript
t
deAote that the quatity la
ftanstio
of n.
Nw the bswaawy eSndItions ae
that
\4=
W=O
0
at
Z=O
at
Z
:
(growd)
(tropopa)
Applying the bemUdary endition (47) to equation (48) we have
(47)
(48)
38.
O0
Fn + C I+ C.
=
.
C,
+ C2.
()
By applylng ts condition (48) we have
HeMoe
T...
C
+
e
+,
.. V t.
the
C,
.
.....
I
+
a
C
ad
c
YTh1T1
when
n~i
(50)
and w have
L~AQ
f/k ( +*
+
Ren
2I
d *
UO
e
the solution of equation
(34) Is gives by
A,(.Z)
-ei~ f4 tJAZ]+
a
IFp
AV~
fp k4
39.
es/k
eg
zsink ZAi L
the came *.a
NMv amelf
= ' 4-A
(z)
LpzL
C,
n
e
&z]+ (c,+c) cos z
+
-
+ C.
(c,-c4 siz
Applying the bad-netsa 00aition (47) we have
o
.
-'P
C +
=+
C, + C2.
=
Applying the ocnditios (4)
o
-
=
-e64
[f
C2
(1)
we be
+(c,+c2 )Cosp
+j
COSR I
X
-
Sin
solmang for C,
and
LLIC~
Ca ers (51) and (83)
we hw
+c,-cstg
(52)
40.
-e
C,
-
C
[fp ln2)
+ FcS
c
(f Im+l) +
_I]
Fitc(O AM
Smn~
C,
10nse
ad C2aWe
OaMples umbe, one of them being the retloo-
tieo Ot the othwr Ia the Real amiso that Is C is the ea0plea O"mJw-
gate of
kz
-
C2.
e~
cos
+±Si-p-z
rn
k)
j
The genral slutto
to equaties (34) is them given by
z
=00O
Sined
2L
T U.*
(
QD
k)
n1Trl~~g7
.
u0r
I.
k
gjLK
LE
uLQk
Ll
'
tk
s
-
)z7
Cos nTrx
L
41.
i-T0
U2-0
2LT
2
n'TrZ-
11
std,
U-1
Stnk
sin4
-~-
___.
It'
(
,A=n
2- 2CLo
+
. 22
Q2
a +
Ya L 2Tuo2- n-Tr
ZL
+;-
)zJCos
Y4 42 a Sin ~E
ni7T
L4~
2,L
441
h1Tr
I
l2
l+
~tZ
L~
Cos4B~§-n~
C>-, +j
~~-_
fX
n16 2* /-k
X
(k+±
(Au
702-To-
Cois hTFX
+
Loz
+
n"Tr' -7
sb-I
LU
Lc -u 02.
9
Cos nX
t
E
__
-I
43.
The solution (58) is eebersen
that itw
had aisned a
the towa ot the
enough.
-ntant wind hw
.seltloa would he the aem,
tios
msted her
sm* that
esgept that
that amob a toa Would nt
sad. Is the problea,
-
*
bz
()
lapwoe the asamp-
ad that In the *am of the
phere muoh a tSa would only atteet the peta* t
istigatIon It
_3I _
+p.2Thee
c-
+ 0C--
It Is
it is of Intewst to sate
affles to ematda
table atmo-
mm..
For this
the *amof so vad dsar.
43.
Vn
A
iwcT
=MORA
ganes at te soluton (83) flows
ta all the tans estain
atasterILI
n2Tr
9 o-
ot the faster
it follows that whenever
, the soliition
__-.
Also the dastaelt wan amber is the
would "blow up".
to this reasae pota
e eloest
W d. not han mAsh bloieups IA the atuo-
phere probebly beooua the banes of haling such a regular atuatiou
as In this eadel, and the asset relatis fer nressMe,
ane slim.
Anoter possibility IS that if the abephewe started to blew up* oter
taters whict han bee@ sglected would prbably beans
Lastly - bae the possibility tat
the wavelength.
tw
ASprtant.
-m preferred valuea for
2. L.
This is libsly to be important sine in a squall line
the spawtg of the atems Sasld be iaportant in detesising the new
region. in hit
it
is intesting to note that hew the abqPhee
stability
sAch a
there an appreciable vertieal actions.
[c
nesm
=
o r it it is unstable
efteet is eliiata d sd wee umnr
destat in this model
has neutral
a
negative
one is always
thew
VII * CAM OP PO8TItB STATIC STAMLITY AWD ITS ANATYIS
a8 te geneal 00lation at te
quateIO (583)
AS It stands C.. to peItivel . To get
tion (34).
distribution ot WA in gpage, we need to evalwat
and then
apste W .
In ash
Vsputatos
dIttewsatial e
of the
ame Ide
all the esatana
the follewbig valvo
aew
employed
a
TO
S00e
**ea./*
..
'do
3x'
-1
TO
U0
k
L
a
10kts::
*
5.0 has
S*me
a 5.0 kne
3
3
3.5
hes
8.5 lae
a 10.5 lase
The athw has cM puted the latest heat ot eondesation tres stoe
Jn a autall life tras quantItatIve weder data tahm
Sueh eenputed values were in reough
at M.I.T., Cambridge.
Ieement with thes given by
45.
1
H
0. the tollo
<To d* e0-
- 6-
Br-hm
0ate ofeleae
isa -o
w
et letast heat et omdesnsation frm
s muse.
"A
ot the
atoms is given b
7.
x 10 I
aS6ta
The dienster ot the st*e is 6 ma..
eglindrwial thee the
It the stems wae igarid e
ross seetiaoa
area is givem by
-E x 25x I0~ m2
13
Beat is
'7"~.55
{7 0
o
xCfcs.
4
x
10
0
=
....
mA
c
z-P
-kHze
H.
m
~5 5 x 10'Se
x
2L 4
kj
sec
see
- z-a
+ Hok
c4k.
xI50
z
VrT3
e-
sec-
Is appAlition Ot the anodI to a essall lint, UL een be
thoaght ot as the relative veloeity Ot the eaniwonsset and the stoes.
Thisseene thft
the evwonU
O =
Ue - Us
hvse Ue isthe velo ity ef
t is the veleeity ot the stoms.
that the hat sme
The pertation
are stationses
Nee the assmption
woid he valid hae.
ftyemliwns ean b enpuated by mplo"Ne the Owe-
tiuity equatein
1Xu
()x
- bzw
bz
=o
46.
.-
ots" n r ear
IN
' (Xi z)
nle
r.A
p,.
U"
bx
I
2a z
IN'
=,
lstgntl
fSx
2Tr±ECosnpiIzr
r*
YW/
4-
Ce
L)
by. hto= wo hole
L (F+ E)sin nr
d.". C, t. th.
.... at r
+ CI
4-)
++
I<%=s1
nYj
L
F
ttoa.
ad
F
-r easly eeamsn two the ealsa (BR>.
It is ale. pei.ib)e to oaspete the tota streamia
up the alme aa t
a6tna
s.n. tz)
.sastaot. h
in
naoS 4a
=-uz + C2 wtotal etasll en
. s.
i
.aa
slam
at tb petur-
rntnrwn stroenua. ad th
. Themabsswbwsta se mu l
by
, 15 gt e hr -
u dz
c2. .awsrwy
a
eampetea amipeI as am
47,
lagprn 41 ftraaliaes or trasOtoriss are indiosted by the
solid line.
They
epreOt the -
the uadisturbed wtnalite.
oft the pertrbatte and
Th. first ftlo
(or beat maros)
upstrem is a..n by dadt line enlosig the regien -L.B
2.6 to. Sine we asses that
to
Sm
nrd
2L
ianse4aSOn (al)
sen" for all af
hanso
it is
W
. are usad in the cptatis.
H
sigatiosty.
a 3.x
21
1r 8
. the taster
Sm nDI
amsees
vales of n,
tead that wsay the tirt
d=L
?-
0
ad
.
aly the odd
From the emputatioss,
odd hsios
4als
a
cotribute
0c
*1 and the
valUe of the heatiag at the tropOpaUss is asumIed to be 1/10
ot its awno
valUe.
.
Clouds ae skethed In the plae hene they say be eapetted to toa
it
as
auttietet astute Is available.
A
I
.15
I
.5
I
5
1
1
1.5
5
12
25
55
45
35
X ---
KMS
FIG 4
,
65
75
85
95
105
115
49.
TIII*
CAR
O
INDFERNT OR
For this *ase
= 0
b_
bz
4ition
Lmr
0-
KVRAL.
NTABILITY AND ITS ANALYS1S
or
-T
n 1T
N =0
. i*
>
-A.
L
for all valius of yj .
fl = I
from
the following
n=)
c
Therefoe the suwation in ("$)
ill
be
n = co . Making this subetitution we have
to
emalt
l- Sin
02
W =
this eem-
To U nm
-
+
n2Le
ZL
z-.
(fl-fr)
L
ZI
C(.S nTX
+4
L
L
k
eL
4H,
st
Sinh {n
L
sin
-F
-I Z
sink nT -Z
T)
I
nrr +
n2.
'L-.
+
f
Tr
L
L
k
L
In this *ase the waNS nasber -n doinates.
Cos nT X
L
00.
Figure 5s
As la figure 4. the solid lines do
streaullnes.
the total
The positien af the first heat sour". uptwee
is shin by the dashed straght lines.
sources a"e samed domette.
All the other heat
Clouds ae sketoehd i
the
ploes where they may be expected to to= it sufftelent sole-
ture Is avallable.
a 2.4 x 10
*als a
see
.
This value is one itnth of the value used in the caputation
for the case of the stable atmosphere.
to avoid excessive amplitudes.
This is dose in order
As in figure 4 only the first
few odd ham"entes ootribute sigaiticantly.
~'
>1
25I
555
II
175L
-
S
15
25
35
45
55
X
-
FIG S'
65
KMS
75
85
95
5
15
125
Os3.
IWSION or 1=
Ix.
A
Case of the~ stab1
SLTS
ataane
the undisturbsd str
at the leves
linS
v 4S'As
%
$' -/s
rs vespetively.
and
point was eloest
Sine in this particular anlysis the reamms
to
3.50 5.25.
rereesented by the total
7.00 ad 8.75 Ims Sea porturbed -
stralinea labelled
1.7.
ae nuber three, we apct that all the streeslines wuld defplet
acme ohareteristica of this we
departure tre this pattern.
Clearly T, aces a
ambr.
Th waelength ot this strealiss is
*qual to the upecing btween the two beat uOor"e.
It is the
longest wavelengt.
It is
toad that
44
is 10w out ot phase wit
,
W,
This phase ditteence night be attributed to the tact that
varies sisuiCIdally with Z. .
W
Sad the btta of the
applied to he sautiof t the diftteetial eipatiea.
such out ot phase patterns alled siges ta tloas
in vibrating qstms
sore ces
Ts*
is type Ot variatiSn Was introdweed
Sn the boundary oaeditions at the tropopus
atoaphere en
and
suh as sed
mas
e smally obtaiaad
in a spherial amity. or
y the vibrating string.
It is interesting to not tat
the weae
are esastly in phase and the mplitade et the 1
andp m,
wae is greatest.
Near the regi.n wre this eplitde is m.a.s, the vertical velecity
S3.
is of the order of 4.
s/a.
should be remebered tat
This result i
It
very remarkable.
it is at ths level that we have the a=I-
This result therefore indiates that the relative
me heating.
heating intensity or heating distribution p1ays a anjor role in
detewmining the levels and msgsitudms of the vertiaal motions that
are obtaned.
bosus of the above correlation between the region
Where we have maimsA
relas of latent heat and the vertical motions
that occur in that level, it would be interesting in the Osall lime
studies to investigate the wind direction at the level 3 bas or 3 hs
and to -W it
level.
-m ells toem in the dEtion of the wind in
ouch a
It this were so, then the result of the present analysis
between 2 Ins and @Jos could be interpreted as the behaviour of the
atmosphere Ahen all the assAptions made in this problem are takes
into consideration.
wve
TIe large amplitude in the
caused by the sisoidal variation of
W
with
7-
might be
and possibly
related to the artificial eOnstraint placed at the tropopase level.
In general therefore, the total strealine pattern between 2 bus
and 0 No indicates that the most tavourable positions for vertical
motion Which aight initiate precipitation are regions close to the
trost edge of the first heat seure and the rear edge ot the seat
heat soure
*Obteen
these regions are two other smaller regions
that are also farourable.
The region halt way between the two heat
sources is the most unfavourable region for the develoent of cloads.
4f
Around Minh a region we have generally dessesding Sation,
It is
possible that it the speings of the heat soues were ditterent
and the diaenoe Of the heat soe
s
have obtained a ditterent distributim of
presipitatto.
re not the se., we sight
regi"M tleurtde to
This is the resin W it was mentioned earlier that
the denims and speags of the heat eares crit ally attest
the results et the problem.
It would be desirable to selider a
am where the spacings an arbitry adthe dimensions of the heat
seurns -e ditterent.
Utah a eas would definitely be aoathatieally
campliated hut
*hatever
reult is obtained, it ebould rednes to the
result
band in this study,
be identieal, and
wen the h8at sates are assued to
en the spacag between two
is assed to be twine
idaeOent heat sumes
the diaeter of a beat ewarns.
Mh solution
obtaiet here is therefore a speoial sass ot a as gevel soluttn.
there ta.
doubt that sh
a general solution if obtaed
pesmit a better applieticm to the sall
Would
line.
Aother sigatitnst point to note is that the trejeetery ot a per-
eel originating at point A wald be the streaoline
*
The Stres-
line
the se
ti made.
On the assumption that the parel Is kept almas moist and
as the trajestaries siase a teady state hypothess
that the level 5 is the a-neatiMn level fe
asch a parn, we find
that ep$t i the regims between A and 3, C and D, S ad 7, 0 ad N
I and J. sAck a pansel mild onon. throughout its path. The inteneity
o,
of the presipitatios Wmiud defiaitely be a htiOn of the posities
of the parel.
This result thereftoe indicates that ten tour or
five ideatital stoms heo arnaed themselves in a line sua that
the whole system a- be regarded as a smgall line, and that it
initially there vere no weak regions of precipitation between sack
eqaIly spaed and idential astems, then the latet hat of cotdenatiow released by these stones to eagh to trigger weak precipitatics regions between ay of the two stomas, aS Is amnly
oserved by a suttaintly sensitive rekder uh a the MVCML
the resalt also indicates that the original stem wold tend to
break itself into two, so that a stem treoahr or a adar eteorelogiat
who originally regnedd the origin as the entre ot gravity of the
first heat sore (or atom), wald after a tme find that in the
region of the first stom, he c0ld dietinguhO
twe difterent Oe-
tres of grarity of new cellsa
,
Cas t
lm
otabnlt
e with ntma
The total atamaines in this ease are labelled a4
Nten 44
nd ',
.
lbe ae the acterpafla of
reqwetively.
4j.
lj. E .
'4.
The strealies is the neutral Stmsnphere are
all i phase ad the waelengths are leer thaw W4.
thorn oof
'14 and
wes.
This rselt is to be espe!ted aince in the case of the neutral
go.
atmosphere, wae number OnW daiates. The mWelngths ot the
N4
Warl
,g
(4d are the sMe ad they
are twice the diameter of the heat soure.
and
of
are tond to be greatest;
at
The amplitudes .t
14
Waa thns. are in the region
heating.
As in the ease of the stable atmophere, the analysis here
indicate that regions at the trout edg. of the first heat souree
and region at the rer Of the mst heat soeroe (desnstas a) Would
be most taounsble for the initiation of -
conective c0116.
analysis alm indieates that the general region halt ewi
two favourable regios would be most untavosrable.
The
bnetmen those
Twe umaSa
ver-
tieSl sotiom Is the region of rising attien is fOund to be about 14.4
e/000. for the same aount of heating used in the case of a stable
atmosphere.
3m the *covective streamline plotted,
in order to rede the very large amplitudes tat
The amplitudes are proportional to H,
-L [.
is used
10
ight hare resulted.
.
Th. remlt ot this analysis clearly supports our eapeetation that
whetn an indifferent ate
e is subjected to the same disturbance
as a stable atmsphere, the tosmer atmosphere wmit react more
asaitively than the latter,
Nor tis reas.
the resulting region of
vigorous vertical actions is more eatensive than that for a stable
atmosphere.
Squal l
uually ocur is relatively ustable regoe, th
.7,
ep epet that the nasult of fhe ustna
cloest
to wbat Sald be obtained is s"al
a..hure
1i
ld be
air masses.
The
result e1 the motral atoephere indietes that there woald be lawge
Vertleal settee
is a fairly large regies.
It to pessible tha
the
squall Its iseiepeontes the properties of the results @ both the
stable eat natral atespheres.
".0
x.
It
EGSgTIONS IDR
aUR
WORK
mold be interesting to s-e it a model for a single stoea or
Mat mee
miald be dran.
ftch a nodel would be aere advetageaus
than ne with eany regularly
paed and identieal heat searos as
was inestigated in this problem,
ease of several
It
said be need to study the
regularly spaced Stomss; also it emid be used to
verify the ease presented in this paper
study cannot be used to study the es
The technique used in this
t a e
staom model,
author has tried to apply this technique to a -m flet
has obtained a trivial reslt.
The
ease and he
It therefore seems that a new approack
to the Aore general problem must be sought.
It is possible that we
sight Mt seesarily employ the type of the ditterential equation (34)o.
If a method Chould be found weby the stieas fneties for enly -ne
disturbance is obtained, wn
sight then £ind the useessary *auditions
for reinfoement and sncellations ot strem functiens generated by
adjacent stms.
Such a meadl
ight threw seame light in te
growth
or dissipation ot squall lines.
The pieture would be more camplate it the medal were to take te
following into oesideratie:s
I
vertical motions is the steam iscluding the horizontal
shear of the vertical wind
ii
etaisemt
s.
111
uwd sham
1v groud
v
trictlos and viscosity
elea" of lateNt heat
a vi turbulsane
WheA all thes
be
spread
of n b beet.
tactors are taken int.
ossidertia
the model would
son realistic than the eane prsented In this study.
It Is
possible that sMoc a picture would be siilar to the proble of
heating frm
belos tee to radiaties Ow saw
other astre
For siaplicity sWt a 8otel could be teatd
first la t
(a-S)
plan.
of heat.
dimesias
U.
COLURN0
A general and strict rule about te
squall line
here.
behaviour of sells in a
annot be sad an the basis of the studies vsdertalmn
This is beaes the assumpttoss nplay" in the Omputation
have reduocd the results to a special ass of a sore general solution.
Therefore any deduetens made should not be gennissd.
Resever, on general conelasien
that the latest heat ef
d
sni
ti
the results do
at tst
aotions beteses any two in a line of stoes.
adiest. Is
appreciably the vertical
Awbert (19M)
in his
study of the efftet of latent beat C" large scale atmospherie notion
of the eyeldoe
type arrived at the emlussion that he beat released
during the sademOtisa preess has a Immediate signifisa
t offset
on the lango Male vertical aetin field in the vicinity of the
Oedenatiae.
Re ase oeSladed that he greatest inIrease La te
vertical
motion due to the latest beating Occurs at or Oear the level of seetsm
rate Ot eenana0ti.
The results .t the current study are in egreeset
ith this latter senelusion.
It is reaonal
to eonlude also that if in a squall line the
stesa arrange themselves in such a way that the assnptioas mad
in
this study are Justified, then the steespherte behavieur in the squall
line region would be inserporated in the results obtained in this study.
It Should be emphasised that the heat sources are supposed to be
#1,
iidepeest of tie.
Rim9e the lifetme Qf sters iS a squall line
is about t0 alss, to ns hour, we culd eonsider that assimptims
ande tor the heat smures are Osit should be obtained within the
interval of about 10 sa, to 4$ mias. wimthin te
lite of the sato=.
The
steady state hypothesis.
This should the be emistent with te
results of this study couid then be istevpueted as what shald be
obtained at the interval of 10 mins, to 45 mis, after the first sets
of cells
have toned on the amaptics that they ae all in a lime.
r
The results for the stable abopre in1ate that it the
is
Moideasatioa
tins made in this study an valid, the latest heat of
secenry for the generatiOn of the general wide spread region of preipitation between ny two stoe
spread precipitation
This
in a squali line.
gion is observed
This type of wide
dar.
n th AICM4s
aodel has its ams detects, When aplied to the squall line.
The air between any two stosas in a squall line does not is general
ohansteristies as the atmsphere far tro
haen the me
stems
any of the
The vertical wind shear ad its variatios has been neglected
is this model.
Sba
(1908) has
sen that for the thirteen eass of
pretrostal squall lines he studied all aSwed that a definite wind Sear
existed between the areos gestrphis wind and the 700 ab wind.
wind shears
owes foud ahead of the sqWall lines
Anderson (190) has
tabulated the wind field in the maulsm cleads he studied.
Sees the effeet of horisontal Sea
Suh
of the vertical wind.
is table
It is
n .
possibl, that large eonvetive system like canulaaflus clouds would
how some eftots of both borisoutal sad vertieal wind Shear.
3itally, it must be amntioeed that radar study of asesoeale systems
is cenparatively young and that it might be helpftl it instreentattion
for quatitative meama
euuld be improved to give a better idea
of the level at thich maias
oadesaatie
is released In a stem.
The winds In this level sight be the key to the preditiss of the
that would be triggrd, and suSM
a result
would clearly be a step forward In the ameiling of ae
of the
position ot sew cel
mysteries of the behavieur of celle in a sgall
line.
63.
DBILIOSAUY
Abdullah, A. J., 194t
The aeridionl growth of squall lines.
J.Mtkar., Vol. II,No. 4.
Mtdersa, C. 3., 190; A atad of the malatinK
P.D. Thints, M.I.T.
gaaMl
uurItnh 'tf
Aubert, lo J, 1947: On the release of latest heat as a fa*tor in
Vol, 14, No. 6.
large sgale aftospheric ation. 4.J Met.
oucher, R. J., and Wealer, R., 1990s The otion and predittability
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No.
Ar
19(04)-5204.
tract
Braesh,
R* R., Jr., 9Si The water and energy budgets of the
thunderstom ad their relation to thuanderstom developamet.
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No. 1, pp. 1.
p
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Byers, N. R., and Brakes, R. 3. Jr, 1949s
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TheTud
m.
U.S.
Churchill, R. V., 1941: !purier eries .andRoaadarn aU PrObleas.
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DifferUatial 3Mn
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19531 Matheatia
n. E., 1960S
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Phystem.
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I1", 9N.Y.
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a vertiaa
radonaiviy dta
tranae0t
frWm wethr
radar and
5e.D. Thesis, M.I.T.
Newton, C. W., &ad Newton, R. R., 19:
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Vertical irelatie and release of kIntic energy
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, Vol. 7, No. t.
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Pettersse,
n More
&la..
S., and Dradbury, D. L., 10is
cyclanes.
AAt
.
Vl.
I and II.
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a WeahrP
a
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iatar.,
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