TM WRIDIWIAL TRAIMfl
WF KIMTYK INKOW
R051T M. OUI1WO
3.5.. Syrso Univoesty
U.N..
syram" as.Uversity
(1952)
SV~M3D IN PMTIAL-MIILIMOT
cF
MASHl
m
w~
SCWM
at. tw
018I UTIIU
or 11CmxW'
Dwtst
Moepted by
oim mimn
atof melacy.
I1IN"
mto
s- Grdato soheel
0 0
*
Chaizm"n
..
st.t
1900
a 0
TU
alDIONAL T AMIPIR
OFr LI T
C ElMI
RIbert M. Gettuse
on 21 MY 1980
*ubmitted to the L)eprteat of Mtooroleg
in partial ftltillmaet of the rmquirements for the dogree
f Master tof *oiom*
The seridioal transport of largo-.mlo eddy kinotte energy
Asseming
between 17,MN and ".3sN to studied ftr the year MlI.
the S)-mb surftoo to be a repreo*ntative level of the tr posphere,
the Auaitude, direetion ad emvrgemae of the flux of kinetie
she. poleenergy is eaompted from the gw*etrophie wiad,. leolts
with a Maslam yearly moan
ward tramsport eeourring to abhet 7 1,
beteen ST.*NM sad 42.80M.
Upon further analysis of the kinetie energy trusport term,
it is found that, in partiular mrth of U.*No the total flux
peris aeomentod for by the oemtribetie of the not uridiml
smpared
Whem
emergy.
turbatioe transport of perturbed kietle
of emsible boheat
to vales for the advestioe of lats0t heat a
of kinttie eNergy
the
advetieon
thlt
seeo
it
is
in the atmophere,
by large-sealo eddieo
ito oe
oe
twvo
rders of segalitud
loss.
ebge oft mrltfor the tlne rato of
Noover, in the expressie
dional eddy kinotte energy within a latitude bolt the truasport
tern is found to be the som order oft egaitudo as ostiastos of
S.. msasurd over the same rlsem.
L
P. Starr
Tietr
Tbosis Supervisorl
Professer of Oteerelegy
Titles
I m Irateful to Prteoeeor VeItr P, Starr for his helpItl guidamn
I
ge
al
freely
ot this work.
4
throlhsot the writlg
of this
espoelally grateftl to Dr.
enlr. ipt.
B&rry Salitumas
tofhis tim, patlalome ad advie
daring the
oI
mrse
TAX& Or COVI
3.
II.
APWX TO I=U MOON
3.
C.
AvsIUAb)* Dat
Trinaftet of 0&4&
A*
3.
Disssion ef WAvils1 CSnpestlou
Compri... with etbor Stedoo
III.
"V.
V.
vi.
1= Um
CONCL
IL. ?sbulated Dte
S
'S
10
LIST OF TArKD8 AND FlOwn
Table 1,
Table 2.
Table S.
Table 4.
Table S.
Table 8.
Taile 7.
Table 8.s
Table
.
Figre 1
Mea rate ot
rldleaal flax oft iutite emorgy at
00 ab tfor Neveber-Aprl
jl.
Mean rate oft mridio al filam o kistie
emewy at
O0 ab for Mr
inpet
r 1 il.
Moe
rate of total smridlemal flux of kietlte omrgy
at 800 ab for the e"Or
9Il.
Moansmewrgene o
the flum of total kinstie errgy
into " asmal rias
at &0 ab tor 191.
Msea reto of nridimtn
flu of oddy hisetir
e e
gy
aoerdlig to varioues *esre.
Total eddy ketlte emergy w ersm fl
oft kltotle
*umry duo to lawe-seale eddLes.
Moew rat oft mrldlea
portrth
tilm of pertartod kinotte oaewy at SNO b for Mp
etr
11,
Moss et et sridlkenal pertrbat lee tim of porturbed
kiotie oerg at 00 ab fr eeser e-April
Mi.
Nass rote of mrldleml portrbattee fim of perturbed
ktamtle orgy
at S00 ab for the pea 19.
Usm rate of imridleal flum of ktLotle emwgy
Mt pertrbatlti empeset at
Fgure 3
seMm
rato of sridlem
ust psrterbaties
fl
a
x of kistlo
aemp.n
at
ONt ab
f00 Nmbor
ftr
ad Its
Ar-April
emergy msad its
N
0ot obr
1961.
Flige 3
Friue 4
Figure a
tIgure 4
&
Figre 7
Feze
S
Figure 9
Mea rate of total sorldlemal flmu of k
tio ewergy
ad
its ut
portrbatles empsmt at 00m a tor the
year 1941.
Mom rete of total msridlesml tiflm of
tio
*omrg
at S00 ab tor 11 .
ir
raNe of morildlea flu ot eddy tametie erwgy
eaeording to warious see roe.
Ns
rate eof mrldleal
tifm of eddy ioetlO emosagy
Asordln to verwe
ereoo,
UN
seseal
spoetre of 800 mb eddy flu of oddy
klwtle engy
oese 71.l0o
Ue
spemot
o* sn
bteddy tim of eddy
klotie egy
soes
1s3
I..
Men 1early (1061) spetrs" of SO eb eddy ftim of eddy
kinetioe esmrgy eSrms 2.20M ad 3.p.
In the
atematieel epse"esi
ef kinotle energy I
for the tie
res of
the atmeehre (Starr, 1961)
that the bortmental kietie
it
is
hag
sbwa
eergy in a fiUed regis am in-
sluediq the wvole semosphere vrte
ae as result ofg
1.
A prodmotiem ot new himete energy within the regis.
2.
A diselpaties of kistte
energy within the regio
threfh ftrist ites.
3.
The perfos
of we
by premssre tersos ad
tal velseoty *mpnm
4.
Advetioe
at the b
of kinatic energy
erise -
dary of the reg ies.
rees the be
ry eof the
gios.
It will be the prpse
mature of the let
regard to the a
of the fla
geoeral,
energy,
the
*spefisolly
the mor-
ittude, direoties and semver-
toer.
other the
Ssooemplished (Iae,
a priori w#
estigte
of bearosrtal kinotic energy in the trepephre -
with partilulr
In
this popr to
et the above toe-
diminl advete
gemse
e
to refeor to
194a Resom
197l
at
already h~s
mta,
1.9),
to determine the dirooties of the f l
as there would be tI
the
es
been
there is
of kLnetie
of total emergy.
O
term have
Assumptions conoerning the magnitude of the adv4tie
been aade, and it
the middle and
generally sesepted that in
is
higher latitudes the rate of meridieml transfer of heat energy
is
of
rder o
i
It his disoeaste
(1951)
of the flux of total enemry
ataosphere negleets the latter term.
aernc
a
due to the adveetes of emisting klne-
symmetrical plar
esp is
tic energy areoe
the bemedary amd thrhm
pressure fores at the bemary.
the work doe
magnitude greater than the first
ecp
m
mtleast
4
by
ooee of the ogm-
the
Threa
the seoond torm beeemes a
tion of state,
n the
t that a
be pointsat
energy of bheriental metie
transfer of kiaotie
Starr
et kinetie Oeergy
magitude thn
>2
since the mieroweepie stleem of the atsipher
C
are
order of
4-)
larger thel
the gross atmospherie maes.
To formulate
the probles Msatmatieally
a geeral
pretsstine
for the time rate of sheoe of bheriletal kinetie omegy is
developed,
Ideally,
dveetioe
and the
term ioolated
A
the troposphere.
represent a
as to stilils
first
for farther analysis.
the oentributioms at many Levelo should be
obtain a muan value for the h riemmtal
lowever,
level where this
voreged
a msa
value.
imsmed to
This onables
geeetrophie data for the year 1951 to eipute,
approximation,
to
flux of kinetie energy in
at this point 500 ab is
flux ha
first
as a
man seasonal and yearly meridionsl kinette
inergy treasport terms for the trepephere.
(i.e.
the 300-mb surface).
found that for Jamnury,
of kimetie energy
vergnleo
the internee mridlemal trasport
o*rred betwoem 100 amd J00 ob with the greatest
and divorgees,
Jet oenter.
140
using geotrphieo winds
(1954)
Ka
of kinetie emergy,
northward flx
strnger wids prevail
ebomea where sme
single level had been
a higLer
than if
the results hereia obtarlMd will be leer
of
The menaitued
Thus it
end its greatest
osearring i
oridienl oeo-
the vieonity of the westerly
eay be anticipated that the lane m*etribe-
tion of the levels above 500 ab to the total kinetio energy will
aee results obtained trem vertloal integratio
of data at amuy
levels to be smewhat greater them thee of this study.
A second objective of this paper is
to ozmime
the ienponnt
terms involved in the meridleal treasport of kinetic energy to
determine thes
which
eatribute mot to the transport.
suits etof this analysis will be show
asumptioms previously mnde by
4
The re-
to differ appreetably free
moe (1N4)*
I I.
A.
Mart
a
a
APPROMI
TO TI
PROWZM
tatmmat -rbLat t-he
For the sakm of oempleteess and for the oenveniaene of the
reader, the matheatieal expression for the time rate of Chaang
of kinatle energy in the ateepbere as develeped by White and
Saltmman (1958)
is
motlon in isobaeri
wre
aster
is th,,
k t
repeated below.
ooordimatos mar
orio,,tal
the uat
The herimental equattem
be writt*a as
mt,,,r,
,,
Co,,is,,
t
t
oter in the vertleal
V
geopotential of an Isobarie serfeam,
in a pressure surfae, and F
i
of
pr,,.,-
is the
the S-D del-eporter
the veeter frietimal ftree per
unit mass,
Upon sealer-aultiplying (1)
by V
.
we havo
(t)
Ixp andin
the total derivat ve Mad letting
we obtaln
)
4
V-
E-
VE
+(2)
6
V4
10.
-her
=
.0
/C
., E
holizontal motion per unit mass,
is the klntie energy
and
t
toi the rate oft fritional
dissipation per unlt mass.
The hydrostatic equation may be written as
S(4)
In isobaric ooordinateo
Using (4)
-
and (8)
the equation of
Equation (3)
' (E +ff) -
eontiniaty is
may be written to the form
(E +
The first two terms on the right side of (4)
are adr.vetve
terms
which vanish if the equation is integrated over the entire atmospbere leaving
J
where
Thus in the
del 4
entire atmospbere
the kinetic energy of the borl-
sontal wind may vary as a result of 1) a produotien tern of the
fore ( 1
,
ano 2) frictional dissipation.
If we substitute spherioal coordinates
in (7)
11.
(. )
a'=
lntegratin
Is
o~o-#dx ddP
t0
(7) between
the surfacs
pr. urw,
lItaede olel
we obtain
E
*orl1l4erin
tude circle,
tir
atmopere
),40,
theLrhL of (5),
the first
where
tre
upon
integration around a lati-
vanishes.
vll). oaneo tl
h
Integlration over the en-
third term to be aire,
ls airo at the top and, for all practical purpose,
sine
L
at the bott
of the atamospber.
Integrating the secod
term with rpt
5
that
ooj
n A
_..
0
"
to >) and noting
.--,.,w
obtains
O
-
Ti
12.
Thefre two
(E j)tr
lo
titatig (11)
E/O-
=
jate
(0) we hano
wowo
state
The above eqrat i
that th
ehegq
of the kitati
Im a latltw
emrgy of the herimmtal gewtreMIe wmd with tMi
belt is
boudary et the region,
of U-and
an offset resltia
pOeItle volmo..
thromglmt the
oros
It
tem expresui
at the boar
valeot expresaioe
the
tren the prdiuet
and 3) a frietleml dissilpatie
mes of thme flld.
does met esmtaein an
preareo
2)
aeeM
of kimotie oen~gy
dependent os 1) advestie
reabld be notd that (12)
the perfoems
of the re lem am
derived by Starr.
eof work by
dd thi
The smae to proem r
ordinates has leorporated this osetribttln into t
eqlk
coftohet
13.
saeording to White sud Saltmanm (10lS),
whL o,
snt. a eeeversien
of potential and iternal
aeteully
rpro-
enorl asseelatod
with the rsiq ngof warm air nameo and the siaing of eld air
massees,
bemoefori
this study will eomoerm Itself only with the
mvoestigatin of the first
fashis
the magitutede,
tera, eoplwriqg In
dional flux of heriteatal hlntlo eegy.
LT'rJ 0
titative
and emavegemmse of the marl-
diretim,
ths ten with respeet to
a
q
*
Upeo
lategrmtio
of
we obtain
1 p%-
dP
(1s)
ere we assume that the 500-mb level represonts a laer
typieal of the treppore.
Thas (12)
beemme
where emh trm denotes the kinmote emorgy per unit volume
flwe*
This
that
mros the given seridianm at the oemtant pressmre smrfae.
hen
n is
the expresiont that is evelated in the first
part of
this investigation.
Resembering the oe~ad objetive of this study. let us now
analyse further the maturs of the o
the total kimstle energy fle.
Prm
ment term
that ashe up
the previes sectlon
14.
(1)
2.
where aaln
=
( )dX
J.-f
2jr
The qanetitlee A and 9 sm
(~,
mad a pertlrbate
~)
be
stlem
teId lto
*pr
(AA/,
4)
mea tiem
a
mei tlht
(16)
/t'-=
Thbs (1i)
ay be expressed
AL
I~s~t~ AA,
1.
J
r
A., *AA!
+OAr
fAYATS
1-tr
(17)
Fer gIeetre*e flews ale
amy lttee
eirele (as we have
sen betere)
Fb)
and (IT)
j
~
+L~j
(18)
beeme
r
A 1 4-
.
+w
~~41
(1S)
at trm (10) sm (11)
Evr
~E
y
&' 2
(so)
15.
Therefore (19)
boomes
5
The first
tosm e
the sr
(1)
(0
of (ll1)
exmpeseo
the nt
dional perturbation treasport of portared kn
tle osag7, while
meed tem roprmesets the seridimal trmeaport of kiuetle
the
eoergy asoeiatod with the mosa senal
transport of westerly
n.,
mrl--
Av
arvet
ertheard
and to
amutim.
lale DAta
The data msed in this study were obtamed by Dr. 3. Saltmsan
and Ur. A. Fleisher of M.I.T. as pert of the
es aties
181,
Protjet.
value
rm
w0e
of heght,
latitude sed le-dgwer
,-
and
,'
ftvig
evr
defiaed
polate aleeg oeea
AL
F
2
dtifemes
at e&A poist
the emprooses
*
aver
E
A
teaiques
The peeuet
ameorditg to the geoetropgie wind equatie.
repraet
the are
mtao (and esmqmtly
wid
more obtained by eIag fiste
latitude oirle
ear
remlted In as
This presodar
the knotle emergy trueport vale.) aM
latitude eitrle.
Cir-
re otrmetd for every five-degree
le"itme iltomretes
the poestrephiL
omrs
besilpherie ebatu for the
between latitudoe@ IOM ad 8SPM.
evaluatiion o
.1.1.
of
od arn ad a
i(
14).
16.
Consequently,
365 days of kinetic energy transport values were
obtained across every five degrees of latitude from 17.5oN
to
77. SN.
As has been previously shown,
since
is
E
emputed free
geostropbie wind data, tthis term does set include ay flux of
kinetic energy resulting free mean meridional
ells.
the data are suffieient only to evaluate the flu
to the berisontal eddies.
Moreever,
of energy duo
sines the wind oeepenents
are averaged over ten-degres intervals of longitude,
flux due to larte-seals herieental eddles is
C
Instead,
only the
represented.
Tra-t-nt fl ~ata
having obtained the data by the methods described in
vious seotion,
the process of tabulation eemeoneed.
the basic data consisted of 36
the pre-
In each analysis
days of transport terms for ee*h
latitude frem 17.6oN to 7tS,WN for five-degroe intervals.
Mneatly
means and sample standard deviations were first obtained for these
thirteem latitudeas
and,
finally,
the
the meathly data embined into soeasoal
yearly mare and standard deviations.
Confidenee limits were
anlealated for bth
seasonal and yearly
averages and have been imoluded with the tabulated results.
These
limits are defined as twies the standard error and indiosat
approxi-
mately the 95 cntidenoe
level.
The formula used is
ZE
:-
17.
is
wher
ts
t.
the standard error of the mean of any qantity
standard deviatie ot the
unmber of independent observatlems (in
days of data).
ople, and
this ea
/
. the
the mmber of
,
III.1
A
i
SULtUr
*f
ofiaa mriant CMlatime
As wans
bor tmtal
n toipated
the winter seam
flux of kintie emrqly
tributio
eketg made
I
Zero total tremmport
the flu
T.P,
eers at about
between ST,
OU.
Timhe
g
ef mimSm
oW to 4TPN, within the regin
with a minm of 10.4 x 10
as for winter (Fig.
2).
m
eagu
ab
displased mrthward abeut t1ie dogree
area for winter.
Max --m
A brmd regien of
MOi
thle
ad
reep
of 3.$ x 10
3.,.
di g1
ov17
slailar to the winter situatie,
Osefedary
o
8 2 x
A rewreal ot direetiom (eq
where the trawport term
tfre
samer traport
to fond at 42.J,
to abet one-
July and AMst are the
mantmm transport polemard is evident between
with a
pel-
reversing diestitm (Fig,
smuths of sin1um kletie energy treapoert.
-1
mb
is
N and 42, W,
third as mob
-1
em
Duritg the .wi-
Maium onergy trnspert ter the smmer msemt
ae
seastt
st individual
of hisetie emerJ
these
e-mry treasport exteade fre
of poleward flx.,
the larl
ember and Jaary.
ter moeths (Novembemr-ril)
ward free 17.7.N screw
evidemoe thMe
0
17
rge see
terward)
Is
-1
- 1
ab
at f.p.
gim evidemt at T,.N
heages *giE,
The yearly mman graph (Fig.
3) elosely svem
tes these of
1).
1.
the iadividual seasewa,
haviq the
ad lati tadee ef pelward
Mnaxim
-1
see ia
nd equatr direeted trampwrt.
ertwrd flux at 48.9 w
-I
generl eemt1guratie
a a Value of
.8,S
The
1017
oerg
.
In all thre
latitude,
of th
Me
tablatlm
imeluslve of the dta
tideme lstes.
This tst
the aure
tor 48.M.
taru
er
* w*
ssed the 08-
bMdimates that a Ir
d@g
et
reliability be gives to thes rellts.
The data ho
v
amu oft the
fiv-dgne
nbee mar~r
mal
3U.PM,
riqe.
data
47* 0M
d
1.71 x 10
17
5? o PN and
ef
Di.rgeao
eot Le x 10
Abem 43,.O5
mmoer
sk
8.,.
o g
,2. DO
Figs.
find i
1 - 3 s
ergo
ewrgem
see
arge. -s
e
-1
ak
-1
is
see
is
tfemd
tor the m
ab
betwuees
eWm,
7T.SN
the rule eMpt for twe
betwoeenom
- vw
.nes, oft
tis
m
year ly data
a
lddies l uto
ito evident Dath of 4,
A amism value tar
The mes rate et mridiaal
data is
ft
the mm em-
sbow a weak belt ot divemem
1.06 x 10 17re
kitetie *emnrgy,
In Ta le 4 to shoe
lux of kiNetie oasy o
with a mium value
ad
d
l rta
betwe
wh Ile a semdear
sews up betwees W. on
perturbetim
mad
flux of perturbed
(At-)
, tor a
Tables 7 -
.o The data Is also plotted
emi mi
and
ar ly
a
that the total eddy Htietie emergy tremport may
be more readily
mpr.d
with this ponrtert
rpst. ie
to smenuet for nroly all oa
rapms shov the pertarbatten te
the total kimtle eongy trenamprt ab
half betw e
47.
N
od W .
.
was negligible for all pre t
that emtfdese
boever,
then the mso
valu
W.N
for *soh
et
he selts
seeth.
of 3 to 4 dW
aly
eetaed
Otheri
iseploths ot esastsmt tlx
Thisoms that, In goemral,
belt ever se
ot kimntle
doeO
It mst be etod,
.OM wre
Isauor
m
ot oddy kblaut
Jmry
wam
mt
flue a-a
it
mert-w
Ls the diLestl
aigstlemt
eanigy
evidest that
pldewMd
Seaeral te
a genel
emvsy o
malts,
far
y
eth
Ori n
of the time
peles
mis,
or equat
re simltamoosely
over a wide
oft latitee.
tee (19)
Mists (lM) l and
January-Febrry and
sJly-mAest,
atliisg
140
th
hme
energy flex vales due to hbarieetmal eddies.
in Table 5 and Fig.
eatribetioe
to a fler
O
to bae
with m appreeiable tilt
diveeted fleu
thee
emputedo.
letitedimally with time,
tatlot
its
al purpese.
ladividmal graphs of the hbortimtl flem
porled
d m
blae 41."
imits north oft
In ua attempt to s
were drmw
These
S.
Meutem's
eslts.
oepr
am data for
ted mom Hust o
These
em
minaed
obtalsed term spetnvl
21.
analysis techniques,
are for the 300-ab level, while Mists's
values are vertically integrated results frem 1010 ab to 300 mb.
In order to mae a valid empariseon of the abeve with the results
only the sres four mouthe wore used.
of this study,
enaten's oaemptatios at the 800-ob
For the winter mnaths
level are an order of magnitude higher then the*
a result not umepeteod,
but still
eof this study,
Althlagh
surprieiagly high.
lategrated values were of the same
larger in general, Mists*
order of ma&gitde aso the present study's.
This feet t
ne esesiders the vwy large sestributlem to the
unusual when
the summer menthe ozoel-
ftr
kinetic eoergy of the higher levels.
groement existed with Mints, while Moatea's reults
lent
about 9-4 time
distributiom
larger.
It
Saltama,
is
flux of perturbed kinette energy.
the year 191
sad t7.5oN) are ealable
sad the author is
wor*
of interest to examine the spetral
of the perturbatio
Results of seepatatieoms tr
(,s.50M
moet
th~mrg
ter two latitude oirole
the iertesy
of Dr.
indebted to him for permission to
inelude this data in the present study.
To provide a brief mathemat iel
(
-ps)
lot Lj()%)
beekreand,
and
represeot the emplex spoetral funeties tfor the
sona 1 and meridiemal eempmets of the geoetr oJhie wid (AL sad 4r
respectively).
Theu the spoetral femetie
tion flux of perturbed kinetie energy,
is
tor
r.
the perturbe-
22.
*Y
A (A)
(2)
o(as)
-r.
F7lally
be
re
entd by ?
nd
-
the seal agd
mwa mrldlml eepoments repectively of this qmantity
-=
K
f+1
(X + Y)
T
Individual plet* of the values of the sp
A (~,
)
ve..r
wa
emr
the seasonal and yearly data for
in Figs.
(throg
wave
(24)
tral
fbtigs
minmer 1s)
3,96N and 73.SoN
,r
-om be femand
7 through 9.
From Fig. 7 St is
soeen that the noet perturbatiem transport
233
aeros T?.*N for both
southward
of perturbed kin tie energy is
Disturbase eft waw nmber two clearly
winter ad samer data.
eeoontributo met to this tranmport for eah
maxim
r
A ee
oft southward tremaport results tra wave mmaber four,
sen
while relatively strel
5.SW (714.
artheard flu
fer by
i eted
is
three and five,
mbr
disturbosoes of wave
At
euasea.
semn asmunts for a large
8) the winter
net southward traaport, partloulasly the metribettles from
despito a lare poloward trmport
wmm amMiere two and ai,
amber tw,
m
ameurrilg at
seethward entribetiea
largely
and six.
mea !data pwmated in Pig.
The yearly
thlt
toward the *qate
- 184,
s -
ad
e learly idates
nber
fde to the disturbemme seemrrig at m
m
fl
twa, the perturtatle
vale
poleward values 9m rrlig at
northward, with mima
ambers thre
wave
the net
energy for the amer
perturbatian flux ot porturbod kintie
euthe is
Snmpt for a
six.
s ef waveamber
resultingq frm dis.trb
t pertrbed
kinetic
Aere*
r r both latitdes.
10687 x 10
x 10 1 erg
polwanrd winter seas
14
se
am
e
a
eotribtiem
evident as the mesa yearly gra
-1
-1
ab
, while
et fle
ted
U.PW the me
eere e T~S,m it
(CImpare with Table
trm wve
to d 1ie
ergy
.)
The large
umber six is
erm* S.W.
is
still
34.
Iv.
COwCIOWS
miphbrlO data t
Utill8ang 500-eb
the yar 191.
marldlomal flux of the kmstle
mrgy of larl
been o
degrees o
to
erme *vwry ft
uted
.OXN.
The maaituds of the
maaxlim of 10.4 x 10
to a
seaser,
17
mlaimmm of 0.4
also duriag the wvtaer.
ergse @*
-1 -1
o
the fu
to
seseale eddles Mho
latitudae trm 1.PN
eraged results vrtod from a
-1
erg
-1
x 10
at 4.PN d4ulr
17
-1 -1
was diseted pel
t TPN
rd to
sourrtin
mm
data.
Die.rg
et aht
me of
ria s oMM
eaded
of S.
took plame
1.? x 10
x 10
ergo
orth of
1?
-1
eagl
o
ab
ear SOsN sad OPW.
ao* (184) stated tat
smild be oppnwstd k
the mirldlemal flux of histo oergy
the piedet. o.
eur'at and the rate
omentm (O
ssumptlis
the regiso
flux is
thease.f
degrees m
CoeMrgMsOW
at W.
40m, with a yearly assamimm
Doul
.8 x 1017
eoeIed at 48.PN
up to 400N with a MinsMm yearly mm diwgeomm
existing
at 7TS.Pn,
The yearly mm mlam of
or both yearly and soesseml
ab
g thewlater
go ow Imb
hborsmtal hkintie osergy eat of fie
ase
the
squat eon l1).
to be g
t
erbar
the seem
tre
This iavestP atte
mllly mild seuth
studied, and Ia partlelar
lety
o o
it
t
hi
t 42.PN.
t he
strly
tof
fe
his
sewhwen
Nerth of U.PU,
ever
the total
a oonted for by the emstribtim oft the sot Mrldtisal
-11
25.
perturbatiem trasport eof prterbed kLmtle emergy.
Ivestigatien by satSm
Junotion with the above fiadig, as
em
sieem
etbheard for
toe
of the perterbtim flu
into the spectral distribstieo
b shwn
In o0-
yerly treaspot to be dlwroed
e.1i
dmimtoed by diest rbaiSe of
S. 3,
3.PW Md 7
wave ember two.
emery in the
it
is
Soeu tot
oddles is
em
Thoe
the
to tw
sm
tiesl
diseipatlem smde by
tremsprt oe
the JanarPeb-
I e
see
art (1641)9
M1
s
-,
eddy MkIetie semrg
ary mme
a
-1
naresm
tru
port of eddy kiet
r
with OtlmasM
of frio-
e
s
well as with a value
h
rato of Merthard
P
so obtatied frm
data of this setdy.
mgligible In the ese of total emW
emgy
pettial
Their valu e f S.6TS ergo
1M.
no o der of megaited
me
j stitted.
otLt mted the eddy omtrt-
of melable
Mbumsary,
late kimtie emergy fr
nd of mnible
tm r I
by
semptem ma
the ladividual
tm
heat
e adyretim of latet
betiem to the rate of eenversie
itely
les
orders of omtita~d
orisiml
agre
e m~y by lag-e-omlo
of kimeti
dvemttoie
Saltms and Fletaier (1W) be
oft aprI
(14).
mspere as obtaimed by White md Stst
eeatriibtiem frm
beet.
the ftm of total
a fr
a
Table
t
to
o the vlee
epar"
WheW
Thme althe
tremport, the miertd
o emrgy tIo Sortant to the
awse oft klmette emergy within a liated regise.
al
t rate et
In additte
24.
If contributtons to the transport ternm arising frm
S.expressions
as thoe of the
oluded fro
are nglgible or in th
/
torm ovalsted hereina
Table 4 that the effeot reslting
integral of Rquatlef
s
(11)
is
peeltive
A-
and
dim
r t
it
frt
emth of 4.9,
n
ay be *inthe
)o
MiniZm A
Table
1
2.
Lt
itmos
(isgi...)
m Yte ft nerdle.l flmo kitetle esap
S00 ab ter lNemberwAprt1 191.
-1
O1
Ya Wate
1 14 oogese
ab
oaa.3.
mo N = 181
nu
uII
as.8
110
ma
4,74
"010
oem
ST.
as.
10. 457
.tlth
OMASS
p171
186
14000
14.604
t142A
6110
±t us
71,.
egf. 8
0Ib1--
-- 4
±
611
4111
at
Taal& 2.
Mesa rat. of sridion l fle of kinetie er7
at 100 ab for Ma-otober 1901.
.-1 -1
14
ab
a
10 eig
Wlte
Letitvd.
IW
0U5N.
184
N
(dgrees)
I6
32.6
*
m
46l.!
-0
.t- IISI
027.6
8.1
900
. .
3000
S.
78.6
97.*#
-14 1t
***o
o1
±
1S
14P0
4m17
4151
OM
874
n sr
,able
3.
Latltu4e
( agr*ea)
Mean rate of total serldioal flUx of kinete
esery at $O() r for the year 1981.
-1
14
orne ab se0
Unite: I
Mean
8.L.
1( 4.
N a 3"
178
8l11
S
3674
17.6
fit
23.8
1I69
27.8
23894
32.5
604
±148
13,744
37.
on
t 1142
10,010
41.6
66
t1100
11,284
47.5
6 34
1111
11,M88
a.$
"4
44
"7
t11o8
11,00.
62.5
14M3
± 13l
7.S
400
47
440
M11
T.6
-46
±
266
8490
17.5
-73
±
8T
11
'e
4.
oan cove'repnce of the flox of total ikiatlc eIruiy
.nt Ibc &nal rtngs at K)0 b fo 1051.
+ ue4
co@ ergewlle
-. £~men
divergfenoe
Uuites
10
14
-1
r*e ab -
oo
-1
Zoaal Itar
lkttsmmer
Y"er
(de re)
1w1
17.3 - 12.
S3.f
- 2?.
t27.1
31.8
8.6T.
t8es
0S1
4
-
-
-1s8
- 23
-1?3?
-43.0
-5181
-3
- 410
- 50
- 497
3
' .
- 4S.
-
42.
- 47.
+ 740
+
+S
+ 401
47.6 - 02.5
+3!0
- 138
+113
- OT.0
+6Q
+ 736
+140
+940M
+
e62. 6 - 97.
+05
+1140
+108S
87.5 - 72.8
+
+
++14+
+ 13it
+ 34
+ 180
$.
7.1 - 63.6
72.$ -
7.8
-
43
+190
TaaLe 5.
Mean rate of moriolonal
ftlux of edd
kinette enwrgy
aeording to various sourem.
14
-1 -1
Unitot
LG erga sec ob
(Minus sign Indieate eqes6orwsard adveetton)
J'a-mbhrUMUt2, ta
Lati tude
(ncgrees N)
1intz
(10oic-
Benton
(300 Sb)
.p-tEmI t
_
Oett*uo
(S00 Sb)
L-t.
Mints
et Dta
Benton
Gottuso
200 ab)
77.5
75.*0
73.5
70.C
67.5
69.0
62.6
60.0
~ 108
- 3.0
40
700
1548
s0
2600
O4
7400
16749
57.5
515.0
52.5
6(.0
47.5
45.0
42.6
40.0
7,9
37.5
35.0
32.5
30.0
27.5
28.0
22.5
20.0
17.5
37 74
10 00
7 10
10400
2726
125 37
0700
135 01
11700
35634
43
*a
03t
77. 5
75.0
71.6
70.0
07.8
88.0
62.8
00.0
567.8
66,0
St.
50.0
47.5
46.0
41.8
40.0
-
-64
- 400
-2061
N3
700
1147
1800
4304
810
1100
1200
S4
142
1800
1916
1800
4904
37.5
15S00
520
1407
1500
45
1"600
68866
0o14
38
300
10469
1400
30.0
27.5
S1.0
2S.8
10.0
17.5
800
I17
135
483
100
IN
Table 0.
Total\e"dy kiutte. ergyr
ue to i
nert
Units$
i
fl,x
re
M
t kif
tle
-1sl
10 14"1 ow
After Starr and WVL
&
h)
(dafet
(19O0)
L
laest
Gottum
(1091)
ram at klJ
Imw
-. 0.00
70.0
3.8
0.8
4.1
0.01
0.00
01106i
66.0
S.a
a.
a.1
0.11
6.
3.t
.8
0.16
0.14
31.0
'a..
3. 1
$.0
g ll t thm
di Whto
Notos I~atU by Stair
do to
unrgy
adv0tie ofr ktaetle
large-seale oddtes.
ti
Table 7.
rate of oridloal prtrbMties figs Of perMeaN
turbed kinetto oegrgy at 00 ab for Map-Oettber 19O1.
Units
LatUtse
10 1r, as
a-Ib
+Tno
Maea
.D.
(s a
17.5
gS
±
WV
14o4
a,
04•
d m815
1460
014
4190
CI
41Ye
4.5
4
4).S
3W
57.s
asso
v.s
3W
73.6
-131
77.6
-
±
±e
: 483
S l 901
M
± s1
1I
Table
wt-u rwtvt oI ks trtlt~rmal prturbation
tuw-t4ed !:inoteC entrgy at W, job forT
V rtIto:
Lat Atode
10 4rge sea I bI
boonCJdr.D
m 151
-34
± 1
212540
±130
09"
am
±1771
lisle
117.
tis
11018
17.5
oil
37.9
1419
1±10
45.5
SI.
of perf4comacir..Aprpi
fluxx
62.5
323
tital
VkZ
67.8
405
± "4
4M3
3181
75
-184
±473
77.6
-104
± 3
1b1.
Taule 9.
Meam rate of meridisal
perturbtiom flux et
perturbed kinetic emrlgy at
00 ai for the
Yar 191.
Unitst
tetlttue
(droeM )
10
14
-1 -1
m e
ergse
M
*m
oa
5.0.
Ir*
19. 6
13
, tae
1901
83..5
lr4
03
±. 11W1
841
W 18o
af
3Ci
± e3o
oo
rM1
1431
± s944
47.sI 4
02.6
a
07.s
381
72.8
-si3
.
7T.S
-6
±
sem
oo
1r
1sT
*IinM
3t
n
IE
IO-
u
('
",-
L
')
0
I/
I
5
22 5
_
I
27.5
,/
32.5
I
I*.
I
37,5
_ _
42.5
47.5
LATITUDE
52.5
5Z.5
62.5
67.5
I
I
72.5
77.5
(DEGREES)
Fig. I. Mean Rate of Meridional Flux of Kinetic Energy
(solid curve),
and it s Net Perturbation Component (dashed curve), at 500mb
for November - April , 1951
Qa
U
I.
T
&;
o)
I
'4
I
17WII
I
I
.
.
22.5
Fig. 2.
27.5
I
.
32.5
.
I
37.5
I
.
I
42.5 47.5
LATITU Ut.
I
I
57.5
62.5
.
..
52.5
U(t
.RS)
m
A~
675
A
72,5
7.5
72 N7.5
I
Mean Rate of Meridional Flux of Kinetic Energy (solid curve).
and its Net Perturbation Component (dashed curve ), at 500 mb
for
May - October, 1951.
*A
/
AIt
U
0
"T
I'
o0)
/u
\
/
fdAa
s
0C
17.5
22.5
52.5
47.5
37.5 42.5
(DEGREES)
LATITUDE
57.5
62.5
67.
Fig. 3. Mean Rate of Total Meridional Flux of Kinetic Energy (solid curve),
and its Net Perturbation Component (dashed curve) , at 500mb for
the Year 1951.
-
- -- - 1- 1 P m
0
o
0
Winter
~ ~r
0
I
)
/
Year
"T
U)
)
0
0%
SSummer
I
.
/
17.5
22.5
275
4
Summe
32.5
37.5
52.5
475
42.5
LATITUDE (DEGREES)
Fig. 4. Mean Rate of Total Meridional
at 500mb for 1951
575
Flux of
62.5
67 5
Kinetic
72.5
Energy
--------- --~"~i~~~
-
6%-Mintz (1010 -200mb)
--- Gottuso (500mb)
-- Benton (300mb)
5-
4-
7 3
CO
o 2
17.5
22.5
Fig. 5.
27.5
32.5
Mean
Rate
37.5
42.5
475
52.5
LATITUDE (DEGREES)
of
Meridional
According to Various
Flux
of
57.5
Eddy
Sources.
January -February
,January - February
Data
Data
62.5
Kinetic
67 5
72.5
Energy
4. 5r
/
\
---
Mintz (1010-200)
-
Gottuso (500 mb)
(300mb)
-Benton
-
II
'
/
I
U
Q)
(n
/
I
/
I
0
oC
I
/
/
,y'
/.1
-.1
,.
-
"9I-I
" /
*
I
I
I
t,_I
I
5
22.5
27.5
32.5
37.5
57.5
52.5
47.5
42.5
LATITUDE ( DEGREES)
62.5
.-
%
675\ 72.5
I
77.5
'
Fig, 6. Mean Rate of Meridional Flux of Eddy Kinetic Energy
According to Various Sources
July - August Data
"-'
150
100
4/ = 72.50 N
I
I
50[
1<
11
/
I
__
I
__
ao
t"
501-
*'%
-
\
I\
I
I
2E
o,
1,
I!
\
I'
I
-100
Summ er
I
-150
I
I I
II
I.iI
-200 -250
I
2
Winter
SI
3
4
a
I
6
5
WAVE
Fig. 7. Mean Seasonal Spectra
Across 72,5 0 N ,
7
I
I
I
I
II
8
9
I0
11
I
I
12
13
NUMBER
of 500mb
Eddy
Flux of Eddy
Kinetic
Energy
14
15
= 22.5 0 N
150
-o
100
E
Summer
/
/
50
0
\
/
/
.
'.4-
-50
100
C
:2
Winter
-201
I
Fig. 8.
2
3
4
5
WAVE
Mean Seasonal Spectra
Across 22.50 N
6
7
NUMBER
of
8
9
500mb Eddy
10
Flux of
II
Eddy
12
Kinetic
13
14
Energy
15
150
100
22,50 N
//
50
E
N
'N
0
.0
-50
Q)
C
IL
cQ)
-I00
72.50 N
0
-150
C
0
-200
-250
I
2
3
4
5
6
WAVE
8
7
NUMBER
Spectra of
Fig, 9. Mean Yearly (1951)
0
Across 22.5 N and 72.5 0 N
9
500mb Eddy
12
10
II
Flux
of Eddy
13
14
Kinetic Energy
15
'15.
A eamp.,e
3.s 3l.1We
1butme QOeg too OW Arthur B
at 300 mb
pw*se
e
i
ftehlatim ofetswp
1.
stpklas U
31*1swr"Ns. Jes
Userltr,
4.
Wtwelty
t.e~
~e~
w~.1**Din~
19411
0,
k1
Lma&I
m I Do 9 1041 s
LemdIe Camawid"
soa.
Uw Taft*
** see$ Shib'Oms. =1Sg TU merliluum
.f~
mu
ownw In h a
.~
&I
Nesu
m
go at lows
lesso
tismu' of ksese
ui
of1 *
I~~e
si
Orw(
l
00
3.. *t "S. MSIs( fth UWr1Ato~ *Lvesl&tiM
sAd r less. ot k~sue Os.V5 is the tispis *AItw
ftUMa
15e 371-1770
9.
Seitems
,5.
larger sesl..
Be.
the mawV"S O
msia of
the
SUNOMLO tevwiusI au
*m 130
of
ai As FViuhe
10.
Sltamen
III
start. To pot ma.n
Al, swm
ma3tle
gsy=WAMS
100t
WhItom 194
aCbwlaiesar
the aeon
t vr e
Waamr usiuwes
D
at
MISr*
4C) .
ft&r
12.
Iti
T. Pee*
AMIMU
of awroy PWINGIP1..
~tmob.1 see.
13.
*wow es Me amol
_______
*Lmiattee
of the *&rule aftwohm.me45
1
theav
e4o
meal*edtilo
I& b8o
,
Ishlti
d
eWeS$S.*a6
owdirae
me~ 2Is~
me 5, 4W4of
89
wv..
f
"ewbt~
aw