JOURNAL
OF GEOPHYSICAL
RESEARCH,
VOL. 88, NO. C10, PAGES 5960-5972, JULY 20, 1983
Near-Inertial Motions Off the Oregon Coast
IAIN ANDERSON
United States Coast Guard, Atlantic Area, GovernorsIsland, New York 10004
ADRIANA HUYER AND ROBERT L. SMITH
Schoolof Oceanography,
OregonState University,Corvallis,Oregon97331
Near-inertial motions were observedat all current metersin an array of five mooringsspanningthe
continentalmarginoff centralOregonduringOctober1977to January1978.All mooringswerebetween
10 and 130 km from shore,in water depthsbetween100 m and 2500 m. Largestnear-inertialamplitudes
(> 30 cm/s)wereobserved
at the uppermost
currentmetersof the offshoremoorings,althoughthesewere
belowthe surfacemixedlayer. The near-inertialenergygenerallydecreased
with increasingdepth,and
therewaslessnear-inertialenergyover the continentalshelfthan at similardepthsoffshore.The energy
levelsobservedover the shelfwereabout the sameas observedthereduringsummer1973,and the energy
levelsobservedoffshorewere comparablewith thoseobservedin the open North Atlantic. Horizontal
coherence
scales
werelarge,exceeding
115km duringthefirsthalfof theobservational
periodandabout60
km duringthe secondhalf;estimates
of thehorizontalwavelength
(50 km duringthefirsthalf and 20 km
duringthe secondhal0 suggest
that thecoherence
scaleis of theorderof threewavelengths.
Althoughwe
did not have current data in the surfacemixed layer nor wind measurements
over each mooring, the
availablemeteorological
data (synopticpressurechartsand hourlywind and pressureat Newport)suggest
that mostof the near-inertialenergywasforcedby the local wind.
INTRODUCTION
Pure inertial motion on the rotating earth is circular,rotating clockwisein the northernhemisphere
with a periodof 2n/f,
wheref is the local Coriolis parameter.Such pure inertial
scalesof about 60 km in the North Atlantic [Pollard, 1980; Fu,
1981].
In this paper,we investigatenear-inertialmotionsin current
observationsmade during late fall and winter at five sites
spanningthe continentalmargin off central Oregon. We demotions are seldom observed in the ocean. There is almost
always someother force acting on the fluid that cannot be scribe the near-inertial motions in terms of their amplitude,
completelyneglected.However,motionsthat are very nearly coherence,and phaseby usingboth spectraland band-passing
inertial in character(called 'near-inertialmotions')with very techniques,and attempt to accountfor their generationby the
nearly circularrotation in the proper senseand with a fre- local wind. Where appropriate,the resultsare comparedwith
quencynearf have been observedat all depthsin the oceans thoseof previousstudies.
and large lakes of the world [Webster, 1968]. The most
common characteristics of near-inertial
motions are well docu-
mented [Kroll, 1975; Kundu, 1976; Fu, 1981; Thomsonand
Huggett,1981].They are highlyintermittentand generallylast
only a few oscillationswith a maximumvelocityof 20-30 cm/s;
the observedfrequency,o•, is generallyslightlygreaterthanf;
vertical coherencescalesare of the order of only a few tens of
meters; and horizontal coherencescalesare of the order of a
few tens of kilometers.
Previousstudiesof inertial currentshave usuallybeen conductedeitherin the open ocean[e.g.,Pollard, 1980;Fu, 1981]
or over the continentalshelf[e.g.,Johnson,1976; Thomsonand
Huggett, 1981]. The few availablestudiesof near-inertialmotions over the Oregon shelf are based exclusivelyon data
collectedin summer.Maximum amplitudesobservedover the
Oregon shelfwere about 15 cm/s during the summerof 1973
[Johnson,1976; Kundu, 1976], considerablylower than the
open-oceansurface-layer
valuesof about 50 cm/sat site D in
the North Atlantic [Pollard, 1980] and 35 cm/s in the Mediterranean[Gonella,1971]. Horizontal coherencescalesoverthe
Oregonshelfwerebetween10 and 35 km duringsummer1972
[Kindle, 1974] and about 15 km duringsummer1973[Johnson,
1976]; theseare smallin comparisonwith horizontalcoherence
Copyright1983by the AmericanGeophysicalUnion.
Paper number3C0480.
0148-0227/83/003C-0480505.00
5960
OBSERVATIONS
During 1977 and 1978, Oregon State Universityand the
Universityof Washingtonconducteda joint fieldprogram,the
SlopeUndercurrentStudy(SUS),to studythecirculationalong
the continentalslopeoff centralOregon.As part of thisstudy,
an array of currentmeterswasmooredacrossthe continental
marginat 45ø20'NbetweenOctober 1977 and January1978
(Figure1).Occasional
hydrographic
sections
weremadealong
the mooredarray, and coastalwindsweremeasuredcontinuouslyat Newport, Oregon.
The SUS array consisted
of fivemoorings:'Skunk,'overthe
2600m isobathjust seawardof thefoot of thecontinentalslope
with current metersat lea, 600, and 1850 m; 'Leopard,' over
the 1lea m isobathat midslopewith currentmetersat 70 and
820 m; 'Ocelot,'overthe 600 m isobathon the upperslopewith
current meters at 141, 243, and 371 m; 'Puma,' at the 300 m
isobath near the shelfbreak with current meters at 64, 164 and
261m; and'Elephant,'overthe 110m isobathat mid-shelfwith
current metersat 23, 49, and 89 m. Ocelot and Elephant were
maintainedby the Universityof Washington,and Skunk,Leopard,and Pumaweremaintainedby OregonStateUniversity.
All mooringsweredeployedin October,with intendedrecovery
in January,but the originalPuma mooringwas lost and replacedin November,andOcelotwasrecovered
prematurely
in
early December.Althoughthere was only a very brief (390hour) periodwith data from all five moorings,thereare two
A•DEgS08 ET AL.: NEAR=INERTIAL
MOTI08 OFF OgF,OO8
.5961
46 ø N
Elephant
Leopard
ßSkunk
ß
126ø W
ß
Oce lot
125•
124 •
Fig. 1. Locationof themoorings
of theSlopeUndercurrent
Study.Theshaded
areasindicatethelocationof priorstudies
of inertial currents.
periods of about 55 days each with data from four separate
moorings (Figure 2). These two periods are limited by the
durationof Ocelotand Puma,respectively
(Figure2).
All of the mooringsof the SUS array were sub-surface,and
Aanderaa current meters were used throughout. All instruments recorded mean speed and instantaneousdirection at
inervalsof 40 min. Time seriesof speedwere plotted for error
detection,and spuriousvalueswerereplacedby linear interpolation. After removal of obviouserrors,the speedand direction
were used to determine the eastward (u) and northward (v)
componentsof the current.Recordgapsof 120 hoursbeginning
at 0900 October 10 in Ocelot371 m and 136hoursbeginningat
0200 December
N 2 = -g Op/l•Oz(wherep is density,g is theacceleration
due
to gravity,and z is verticallyupward),werecomputedfrom the
hydrographicdata by usinga centeredfinite differenceof 20 m.
These profiles (e.g., Figure 3) show that most of the current
metersin the array werebelowthe surfacemixedlayer,during
both the first (Ocelot) and second(Puma) periods.The mixed
layer wasfairly shallow(lessthan 25 m) duringthe first period.
I"
FIRST
PERIOD '
,I
I
1/85o
I
I
I
Leopora
'l '
, I
Ii
i
Ocelot
, I
I
•l'
I
/oo,,,
I•øø
I
70m
I
8ZO
I,
'
i'
I
I
ß
I
!
Puma I
I
Elephant
•' [I
I
I0
•
II
'1
OCT
SECOND
PERIOD
•
'1
Skunk,
9 in Puma 261 m were were filled with zeroes.
The data were filtered with a half power point of 2.5 hours to
suppress
high frequencysignalsand decimatedto hourly values
to yieldthe processed
data.
Vertical profilesof the squareof the Brunt-V•iis•il•ifrequency,
'
i'
I• '
I
[ 49
iß
20
NOV
I0
20
I.
•6/
II
DEC
.'
I
.
I0
20
JAN
I0
20
Fig. 2. Summary
ofthetimespanofthecurrentmeterdata.Thetwotimeperiods
usedforspectral
analysis
areindicated.
5962
ANDERSONET AL.' NEAR-INERTIAL MOTION OFF OREGON
I25øL
126 ø W
I I I
0
E
I• I I I
124
ø
I]•
: /o
-- 5OO
-
-•
_
-
ct
1977
13_
-
iooo
_
40 cph
2
i
_
I
--
500
_
_
_
i
15o
I
IOO
S*
126 o w
N•EFROM
SHORE
(km)
50
_
msoL
I
!
'
'
•000
0
P
E
I It '
II ß
•,•o
I)lø
-1-
Dec
I/'.
ß
1977
- ,ooo
(*26Jan1978) -
.
-- 15OO
_
_
•CE
FROM
SHORE
(km)
i
15o
I
I
50
ioo
_
_
I
2000
0
Fig. 3. Profiles
oftheBrunt-V/iisiilii
frequency,
N 2,neareachmooring.
The only currentmeter possiblyin the mixed layer was Elephant23 m; the top currentmeterof eachothermooringwasin
the pycnocline(Figure3). During the secondperiod,the mixed
layer reachedalmost to the bottom over the shelf,placing
Elephant23 m and 49 m in the mixedlayerand Elephant89 m
in the pycnocline;again,the top currentmeter of each other
mooringwasin the pycnocline.
Time seriesof the eastwardcomponentof the currentat all
current meters(Figure 4) show frequentepisodeswith motion
that hasa periodof about two-thirdsof a day (i.e.,roughlythe
localinertialperiodof 17 hours).Someof theseepisodesappear
to beginimpulsively(e.g.,at Leopard 70 m on December13),
but othersshow a gradual increasein amplitude (e.g.,at Leopard 70 beginningabout October25). The amplitudeof these
oscillationsappears to decreasewith depth at all moorings
(Figure4). Althoughonly the uppercurrentmetersat Elephant
are in the surfacemixed layer, all of the currentrecordsfrom
the SUS array contain a substantialamount of near-inertial
motion.
SPECTRAL ANALYSIS
The vector time series from each current meter were used to
calculate rotary spectra,which separate the clockwise-and
counterclockwise-rotatingfrequency components [Mooers,
19731. Pure inertial motion at this latitude would have a
clockwise-rotating
peak at 0.0592cph and no counterclockwise
energy.Sincethe commonrecordlengthfor all five moorings
was too short for meaningfulspectralanalysis,we used two
time periodsof 1280 hours,which both had simultaneousdata
s
Ioo
S 600
S 1850
L 70
L 82.0
0
141
0
24:5
0
371
•tober
1977
November
December
Jenuery 1978
Fig. 4a
P
64
P
164
P
261
•':[
l•J•,.•,,•,,n,i•Al••,
•,,,,.,,,,.,,n,,•.,
,A,..
,,.,An,,,,,
,.,•,,.,.
....
,,,,
,.,,,,_
•,_
•,,•,,,.,._
,,..,
,,,
,••,..,,,,,•,,._
:,....•,
:,,.,.
,.,...,,,.,..
_•,o[I
•r!y"uv"?"•I'p,"'•'•Qlrl•'Vl'lF"'•"nrpV•'llp,:•'•Ir,'¾"
',•",""•,"v•'•'•",,T•,,•"'?l'•
'••'
•':•..,,AI,.,,,,,
_,
•,I,,,,.,,,,,,.,,,A.,,&,•I.LIII,II•b
I•,tlJlil•bll
dlld]A.
,,[11,iAnlllbn,,,J
,,,J
,.t
hi,a,
,I,l.,q
ILb
A,.,,.
_.,,
,•,q.
,.•,,...,
,..,,,
,,.,,t.,,,,•,,,,,,11
.,.,,,_
.u
,t,,,,.,,
•,q
I0
20
October 1977
•0 I
I0
20
I
November
I0
20
December
30 I
I0
January1978
Fig. 4b
Fig. 4. Theeastward
(u)components
of thecurrents
at thecurrentmetersat (a)Skunk,Leopard,andOcelot,and(b)Puma
and Elephant.
20
5964
ANDERSONET AL.' NEAR-INERTIAL MOT•O• OFF OREGO•
Leopard70
Elephant23
Elephant49
clockwise
F•rst
Period
•'
Io
nz
i
01
uJ
I00
o•
I0
i
•
Second
Period
I0
i
0 Iø
0 08
i
0
0 04
0 08
I
0
I
o 04
I
I
I
o 08
cph
Fig. 5. Rotaryspectra
ofselected
current
meterrecords
forboththefirst(Oct.13toDec.5)andsecond
(Nov.20toJan.12)
timeperiods.
Thelocalinertialfrequency
f, andthesemidiurnal
frequency
M 2areindicated.
from four of the moorings(Figure 2). The first time period,with
data from Skunk, Leopard, Ocelot, and Elephant, began at
0400 UT October 13 and ended at 1200 UT December 5; this
period includedan episodeof strongnear-inertialmotion at the
end of October.The secondperiod startedat 0400 UT November 20, ended 1200 UT January 12, and included data from
Skunk, Leopard, Puma, and Elephant. We allowed the two
periodsto overlap by 15 days to useas much of the available
data as possible.Spectrawereobtainedfor eachtime periodby
ensemble-averagingfive periodogramscalculated from 256hour recordsegments.
The resultingspectrahave 10 degreesof
freedomand a spectralbandwidthof 0.0039cph,about 6% off.
The rotaryautospectra
for the firsttimeperiod(e.g.,Figure
5) all showa prominentclockwise-rotating
peaknearthe local
inertialfrequencyand very little counterclockwise
energyin
that frequencyband.In all cases,the near-inertialenergyis
equalto or greaterthan the semi-diurnalenergy.The peak
frequency
of thenear-inertialmotionvariesslightlyamongthe
differentcurrentmeters;in mostcases,
it is somewhatgreater
thanf. Similarfrequencyshiftshavebeenobservedelsewhere
in
the ocean[e.g.,Fu, 1981; Gonella,1971; Kundu,1976]. The
peak energydecreases
with increasingdepth at eachlocation
exceptoverthe continentalshelf(Table1, Figure6). The ratio
betweenthe majorand minoraxescomputedfromthe rotary
TABLE 1. Characteristics
of theClockwiseNear-InertialPeakin theRotarySpectrumfor EachCurrentMeter DuringBothTime Periods
SecondPeriod (Nov. 20 to Jan. 12)
First Period (Oct. 13 to Dec. 5)
Peak
Peak
Peak
Peak
Current
Energy,
Frequency,
Width
Major Axis/
Energy,
Frequency,
Width
Meter
cTn
2/S2
cph
cph
MinorAxis
cTn
2/S2
cph
cph
26.9
5.1
1.9
0.0625
0.0625
0.0625
0.0098
0.0085
0.0066
1.01
1.01
1.02
19.9
11.3
2.7
0.0586
0.0586
0.0625
0.0106
0.0097
0.0101
1.01
L 70 m
L 820 m
147.0
3.4
0.0586
0.0625
0.0060
0.0062
1.01
1.02
56.1
3.1
0.0625
0.0586
0.0054
0.0054
1.00
1.01
O 141 m
O 243 m
40.1
18.6
0.0586
0.0625
0.0084
0.0082
1.03
1.02
O 371 m
16.5
0.0586
0.0097
1.03
S 100 m
S 600 m
S 1850 m
P 64 m
P 164 m
P 261 m
-•
E 23 m
25.8
0.0664
0.0122
1.10
E 49 m
E 89 m
9.9
13.2
0.0625
0.0625
0.0107
0.0069
1.18
1.03
-•
-•
Major Axis/
Minor
Axis
1.02
1.02
•
•
13.7
0.0625
0.0100
2.3
0.0508
0.0108
8.8
2.2
0.0625
0.0625
0.0074
0.0097
1.06
1.51
1.03
1.20
4.4
3.4
1.4
5.7
0.0625
0.0508
0.0547
0.0586
0.0099
0.0118
0.0156
0.0069
1.46
7.02
1.41
1.22
ANDERSONET AL.: NEAR-INERTIALMOT•O•4OFF OREC,
O•4
SPECTRAL
ENERGY
at 0.0625cph (cm2/sec
z)
I0
I0
I00
E //
I000
//
ioo
////
///
// / • ,/I/
, I
I
SPECTRAL
ENERGY
ot 0.062.5cph (cm2/sec
•)
I.O
•
ioo
IO
IOO
IOOO
, , //, '//'•
.//.•E
///'//
,// /,/•L ///
/
p
/
w
/
//
/S •//
//
SECOND
PERIOD
(20Nov-12
Jan)
/
/
I0,000 /
/
/
/ , ,4
•
,
Fig. 6. Log-logplot of the clockwisespectralenergyversusdepth
for both time periods.Along the solidline energywould vary inversely
with depth.The separationbetweenthe dashedlinesindicatesthe 95%
confidenceintervalfor eachspectralestimate.
spectra[Mooers,1973] showsthat the near-inertialmotion is
very nearly circular offshore,with slight ellipticity over the
continentalshelf(Table 1). The bandwidthof the near-inertial
peak, definedas the differencebetweenfrequencieswhere the
energyfalls to one-half of the peak value [Fu, 1981], is about
0.008 cph (twice the spectralbandwidth)offshore,and somewhat greater over the continental shelf (Table 1). The bandwidth of the peak is inverselyproportionalto the persistence
of
near-inertial motions [Munk and Phillips, 1968]; the persistence seems to be about 120 hours offshore and 100 hours over
the shelf.
5965
period; elsewherethe mean flow was much weaker.During the
first period,meancurrentswereweak everywhere.
During both time periods,the near-inertialenergydecreases
monotonicallywith depth at each of the offshoremoorings
(Table 1). A log-logplot of the energyversusdepth at the most
commonpeak frequency(Figure 6) showsthat the pointsfrom
Skunk, Leopard, and Ocelot lie roughly along a straight line
correspondingto an inverserelationshipbetweenenergyand
depth.During both time periodsthe currentmetersat Elephant
(i.e., over the shelf) have much lessnear-inertial energy than
offshore current meters at the same depth (Figure 6). The
current meters at Puma, at the edge of the continental shelf,
have lessnear-inertialenergythan thosein the deep water but
more than thoseover the shelf(Figure 6). Data from previous
studiesshow a similar variation of near-inertial energy with
depth. The energylevelsobservedin the open North Atlantic
[Pollard, 1980; Fu, 1981] seemto be comparableto those at
Skunk, Leopard, and Ocelot (i.e., thesedata seemroughly to
obey the sameinverserelationshipbetweenenergyand depth).
The near-inertial energy observedover the Oregon shelf in
summer 1973 [Kundu, 1976] are similar to thoseat Elephant,
and energy levels from the vicinity of the 200-m isobath in
Queen Charlotte Sound [Thomson and Huggett, 1981] are
comparableto thoseat Puma. Thus, it may be generallytrue
that there is lessnear-inertial energy over the continental shelf
than at similardepthsin the openocean.
Coherenceand phasespectrawere computedfor all current
meter pairs and both time periods.With 10 degreesof freedom,
coherencesquaredvaluesof 0.53,0.58,and 0.68 are significantly
different from zero at the 95, 97, and 99% levels,respectively
[Thompson,1979]. There was significantcoherenceat the 95%
level at a clockwise-rotatingfrequency between 0.0508 and
0.0664cph between23 out of 55 currentmeterpairsduring the
first period and between 19 pairs during the secondperiod.
During both periods, there was generally higher coherence
betweenhorizontally or diagonally separatedcurrent meters
than betweenverticallyseparatedcurrentmeters(Figure 7).
The horizontal
coherence scale exceeded the extent of the
array (115 km) during the first period and was at leasthalf the
extent of the array during the secondperiod (Figure 8). The
large horizontal coherencescale of the first period exceeds
thoseobservedin the open oceanat comparabledepths [Fu,
1981] and is comparableto the coherencescalesobservedin
the surfacemixedlayer at siteD in the North Atlantic [Pollard,
1980] and in the relativelyshallowwatersof Queen Charlotte
Soundoff BritishColumbia [ThomsonandHuggett, 1981].
Phasespectrawerealsocomputedfor both time periods,and
confidencelimits for phasewere determinedby the procedure
describedby Koopmans[1974, p. 284-285]. This method of
computingconfidence
intervalsis conservative,
sinceit assumes
During the secondperiod,therewereprominentnear-inertial
peaks at all current meters of the three offshore moorings
(Skunk, Leopard,and Puma),similar to thoseobservedduring
the first time period,exceptthat the energywasgenerallylower
and the bandwidth was generallygreater (Table 1). Over the
continentalshelf,the inertial energywas much smallerduring that the time seriesdata have a Gaussian distribution; if one
insteadthat the data consistsof a coherentsignalplus
the secondtime periodthan duringthe first(Table 1, Figure5). assumes
The spectrumof the top current meter at Elephant (Figure 5) incoherentnoise,the phaseestimateswould be exact [Schott
hastwo near-inertialpeaks,centeredat 0.0625cph (very nearf)
and Diiing, 1976].The phasedifferencesbetweencurrentmeter
and 0.0508 cph (about 14% belowf), respectively.A similar pairscan be usedto determinethe directionof phasepropagasplit was observedat Puma 64, near the shelfedge(Table 1). tion and the wavelengthof the motion, if the separationbeElephant 49 m has a relatively broad, flat peak centeredat tween current meters(horizontally or vertically) is small com0.0547 cph, about 7% belowf All other currentmetershave a pared with the wavelengthof the near-inertial motions. For
singlepeakfrequencythat is very nearlyequaltofor somewhat example,Kundu [1976] useddata from 11 current meterssepgreaterthanf (Table 1).The downwardfrequencyshiftsmay be aratedverticallyby 4-20 m to estimateupwardphasepropagaa result of Doppler shiftingof the near-inertialmotion in the tionof 0.1-0.4cms- • andverticalwavelengths
of 55-225m. In
are diagonal,
presenceof a mean flow [Thomsonand Huggett, 1981]' There our case,mostof the currentmeterseparations
was strongmean alongshoreflow, about 20-30 cm/s, at Ele- making it difficult to estimateeither the vertical or horizontal
phant 23 m, Elephant 49 m, and Puma 64 during the second propagationspeeds.To add to the difficulty,most of the sepa-
5966
ANDERSONET AL.' NEAR-INERTIAL MOTION OFF OREGON
S
126 ø W
1•5oL
0
i
ioo
200
300
5OO
I000
_
ß
FIRST
.
PERIOD
--
_
(13 Oct-5
Dec)
_
-- 1500
_
_
-
ß
DISTANCE FROM SHORE (krn)
i
150
I
ioo
2000
50
,•5oL
126' W
_
I
0
P
E 124*o
ioo
200
300
5OO
IOOO
ß..
SECONDPERIOD
ß
ß
(20 Nov-12 Jan)
ß
ß
ß
1500
ß .
150
DISTANCE
I00
FROM
SHORE (km)
I
50
I
0
200O
Fig. 7. Distribution
ofcurrent
meterpairscoherent
in theclockwise
rotatinginertialfrequency
bandof0.0508-0.0664
cph.
Pairsconnected
bysolidlineshavea squared
coherence
ofat least0.58,the97%significance
level.
rations(both verticaland horizontal)arc largerthan the expectedverticaland horizontalwavelengths.
Nevertheless,
wc
used the phase spectrato estimatethe horizontal east-west
(cross-shelf)
wavelength
by makingthefollowingassumptions:
dcnccinterval of 36-56 km. Similarly,the phasedifferenceof
380ø(20ø + 360ø)betweenPuma and Elephant(19.7km apart)
yieldsa wavelengthof 19 km (the 80% confidenceinterval is
18-20 km). By addingintegral numbersof 360ø to the phase
(1)phasepropagation
wasfromeastto west(i.e.,energypropa- differencesbetweenthe other pairs, wc were able to obtain
gatedonshore);
(2) the verticalseparation
(maximumof 71 m) consistentestimatesof the cross-shelf
wavelengthfor eachtime
between
Elephant89m, Puma64 m, Ocelot141m, Leopard70 period(Table 2). The averagewavelengthobtainedwas 50 km
m, and Skunk100m wasinsignificant
whencomparedwith the for the first periodand 20 km for the secondperiod.The 50-km
horizontalseparation;
(3)duringthefirstperiod,thehorizontal wavelengthfor the first period is consistentwith the large
wavelength
waslargerthanthesmallest
horizontalseparation; coherencescaleobservedthen: Only three wavelengthsspan
and (4) duringthe secondperiod,the horizontalwavelength the entire array. During the secondperiod,both the estimated
was sligtitlysmallerthan the smallestseparation.With these wavelength and the coherence scale arc shorter. In both
assumptions,
the phasedifference
of 115ø betweenLeopard70 periods,there is significantcoherencebetweencurrent meters
m and Ocelot 141 m (13.9 km apart)duringthe first period separatedby two horizontalwavelengths
or less.
yieldsan cast-westwavelengthof 44 km with an 80% confi:
Wc also consideredestimatingthe verticalwavelength,but
ANDERSON ET AL..' NEAR-INERTIAL MOTION OFF OREGON
1.0
than 0.048 cph and greater than 0.077 cph, tapering linearly
within the edges(0.002 cph wide) of the filter. The band passed
by the filter lies entirely betweenthe semidiurnaland the diurnal tidal frequencies.For computationalefficiency,we filtered
only 2048 hours of the long records,1408 hours of the Ocelot
0.8
F•rst Period
'-' 0.6•).•
0
"'
0
records, and 1280 hours of the Puma records. In each case,
there were at least 32 Fourier componentswithin the band
o
(n
5967
0.4
passedby the filter.
The possibilityof peak smearingdue to the sharp filtering
was testedby usinga synthetic1024-hour serieswith 5, 10, or
o
15 cyclesof motion at 0.0625 cph, with the remainder of the
seriesset to zero. Like Kundu [1976], we found that peak
0
25
50
75
I00
125 km
smearingis lesspronouncedwhen the number of cycleswas
Ax
greater:When the input seriescontainedmore than 10 cycles,
Fig. 8. The squared coherenceat 0.0625 cph between pairs of
the amplitudeof the band-passed
output did not vary greatly
current meters with roughly horizontal separation: Skunk 100 m,
from the input series.The phaseof the near-inertialmotion was
I•opard 70 m, Ocelot 141 m, Puma 64 m, and Elephant 89 m. The
90%, 95%, and 97% significancelevelsare 0.44, 0.53, and 0.58, respec- not alteredby the band-passfilter, regardlessof the number of
tively.
cycles.
The time seriesof the eastward component of the bandpassedcurrent at all current meters(Figure 9) showsthere is
there was significantcoherencebetweenonly a few vertically
somenear-inertialmotion throughoutmost of eachrecord.The
separatedpairs.The spacingof the currentmeterswastoo large
energyseemsto occur predominantlyin burstsor 'events'of
to resolve vertical wavelengthsof the magnitude (50-500 m)
generallyobservedin the ocean.Although we could have ob- severaldays duration. Someof theseeventsappear to begin
tained estimates by assuming particular values of integral impulsivelyand decaygradually,but othersincreasegradually
wavelengthsbetween current meters, the choice would have and persistfor more than a week. The maximum value (39
been completelyarbitrary, and, hence,the resulting estimates cm/s) of the band-passeddata occurredat Leopard 70 at the
end of October.At eachcurrentmeter,the band-passed
northwould be meaningless.
ward currentis verysimilarto the eastwardcomponent,except
that it is 90øout of phase(e.g.,Figure 10).
BAND-PASSED DATA
The time seriesof the band-passeddata (Figure 9) demonTo examine the time variability of the near-inertial motion, strateexplicitlysomeof the conclusions
drawn from the specwe followedKundu's[1976] exampleand usedthe techniqueof tral analysis:The strongestnear-inertial currentsoccur at the
band-passingrather than complex demodulation.(While the offshoremoorings,and at eachlocationthe amplitudegenerlatter has the advantage of using both componentsof the ally decreases
with depth.During the firstperiod,October13 to
original vector time series,the former has the advantage of December5, the near-inertialmotion is very persistentat the
showingthe currentvariability more clearly.In a caselike ours, offshoremooringsand lesspersistentover the continentalshelf.
where the motion in the near-inertialfrequencyband is essen- At mostcurrentmeters,the largestamplitudesoccurduringthe
tially circularand clockwise,the two techniquesgiveequivalent first period rather than the second.During the secondtime
results.)The current records were band passedby using a period,November20 to January12, there is very little nearnarrow filter centeredat 0.0625 cph, the most common fre- inertial energyover the continentalshelf.
quency of the near-inertial peak in the autospectra.The proDuring each period of high near-inertialenergy,the phase
cedurewas to determinethe Fourier componentsof each cur- differencebetweenthe band-passedcurrent vectorsat Skunk
rent record by using a Sande-Tukey fast Fourier transform, 100m and Leopard70 m, and betweenLeopard70, and Ocelot
pass100% of the energyin the frequencyband between0.050 141m, remainedfairly constant(Figure 11).During the strong
and 0.075 cph, and suppressall of the energyat frequenciesless near-inertial event of October 27 to November 13, Skunk 100
z
rr02
od
A
i
TABLE 2. Horizontal East-West(Cross-Shell)WavelengthsCalculatedFrom PhaseDifferencesat 0.0625cph, for Current Meter Pairs With
Nearly Horizontal Separations.
SecondPeriod (Nov. 20 to Jan. 12)
First Period (Oct. 13 to Dec. 5)
Current
Separation
Meter
Pairs
Distance,
km
S 100-L 70
S 100-O 141
52.3
66.4
Coherence
Squared
Phase
Difference
N
0.64
0.57
331ø q- 21ø
78ø q- 25 ø
0
1
S 100-P 64
95.6
S 100-E 89
115.3
0.73
91ø+__17ø
2
13.9
0.57
115ø _+25 ø
0
L 70-0
141
Wavelength,
km
m
J
Coherence
Squared
57
55
0.30
--
0.10
50
0.03
Phase
Difference
N
Wavelength,
km
163ø q- 49 ø
2
21
21 ø q- 31ø
2
21
20 ø q- 25ø
1
19
44
L 70-P 64
43.1
m
L 70-E 89
62.8
0.63
128ø q- 22ø
1
46
0.48
0.16
O 141-E 89
P 64-E 89
48.9
19.7
0.68
--
25 ø + 20 ø
1
46
--
0.57
The 80% confidence
intervalis shownfor phase'N is the assumed
numberof integralwavelengths
betweeneachpair.
5968
ANDERSON ET AL.' NEAR-INERTIAL MOTION OFF OREGON
•0•cm/sec
S
-Ii. .,
I00
S 600
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vv
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..................................................
I0
20
30 I
I0
October 1977
20
I
November
I0
20
December
30 I
I0
January 1978
Fig. 9a
P
64
............................
....
-...............
P 164
0[......................................
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AAAAA,,AAA.
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..............
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^AAAAAAAAAAA
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q½-:'•';:--:-:::#•
•-::•::;:
........
vvvv
.......v,.................
vVg
v......
.....
^AA
.............................
AAAA
.......
.,rAy
.,,.,AAA...AAAhAAAAAAAI
•.,•..,,.AAhA.AA,,AAA,,,,.,,..,,AAAA,,•,AAA
......A,,^..
.......AAA,__AAA
....,.v,,,
....,v,
....................
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g
E 89
,o
•o
October 1977
•o,
,o
•o
,
November
K•
•0
December
•0,
;0
January 19•
Fig. 9b
Fig. 9. Theband-passed
timeseriesof theeastward
component
of thecurrentat thecurrentmetersat (a) Skunk,Leopard,
and Ocelot,and (b) Puma and Elephant.
ANDERSON
ET AL.' NEAR-INERTIAL
MOTIONOFF OREOON
50T
5969
Leopard
70m BandPassed
I
•
•l•J•,
]',,•,•.
Fig. 10. A 10 day (Oct. 27 to Nov. 6) segmentof the band-passed
eastward(u) and northward(p)componentsof current
at Leopard70 m. The approximatelyequalamplitudeof the componentsand the 90ø lag of u behindp indicateclockwise
circular motion.
m lagsbehindLeopard70 m by about 330ø,and Leopard 70 m
lagsbehind Ocelot 141 m by about 120ø;thesenumbersagree
very well with the phasespectrafor the first period (Table 2).
Thus, the horizontal wavelengthestimateof 50 km seemsto be
valid throughout the 20-day duration of strong near-inertial
motion beginningabout October 27.
Several current meters showed high near-inertial energy
during December 13-28 (Figure 9). At Leopard 70 m, there
seemto be two separatenear-inertialeventsthat begin about
December 13 and December 24; the near-inertial energy at
0
Skunk 100 m seemsto be marc nearly continuous.The phase
differencebetween Skunk 100 m and Leopard 70 m varies
considerablyduring this period: It is about 180ø on December
14-16, about 75ø on December 18-22, and about 270ø on
December24-28; only the first of theseagreeswell with phase
spectrafor the secondperiod (Table 2). Thus, the near-inertial
phasedifferencebetweena pair of current metersseemsto bc
well defined and fairly constant during a particular nearinertial event but varies considerablyfrom one event to another. To the extent that differencesin phase reflect different
2ø
t
141
-2
$60
240
L 70-0
141
120
:
:
:
:
:
................................................
L 7O
-40
$60
-• 240
S I00-L
70
*'• 120
I0
20
October
•)
I
I0
20
November
•) I
I0
20
December
January
2o
S I00
Fig. 11. Thehourlydifference
in direction
between
theLeopard
70m andtheSkunk100m or Ocelot141band-passed
current
vectors.
I0
5970
ANDERSON
ET AL.' NEAR-INERTIAL
MOTIONOFF OREGON
i2
dynes/cm
W•nd
Stress
Magnitude
Nov
Dec
Jan
Elephant 23m
..........
......
JAAAAAfiAAAfiAA
....
nAA.AAAhAIA.AAA,
...... ........
nAAA..
........................
,lb,..
Leopard 70rn
Fig. 12. Themagnitude
of theNewport
windstress,
andthemagnitude
andcastward
component
of thePollardand
Millardmodel,
andcastward
components
oftheband-passed
current
atElephant
23m(inthemixed
layer),
andLeopard
70
m (about30m belowthemixedlayer).
wavelengths,
thesevariationsimply that the wavelengthof
near-inertialmotionsvariesconsiderably
betweendifferenten-
mooringsin late OctoberandearlyNovember.Sincethemodel
ergeticepisodes.
is very sensitive to small-scalevariations in the wind field
WIND
FORCING
Thegeneration
ofnear-inertial
motionin themixedlayerby
energetic near-inertial motion observed at the three offshore
[Pollard,1980],we mightexpectpoor agreement
betweenobservedcurrentsand modelresultswhenever
thereare strong
atmospheric
frontsin theregion.
Frontalpassages
wereverycommonoff Oregonduringlate
October
and
early
November
(Figure13):betweenOctober23
successfully
by PollardandMillard [1970].Althoughmostof
with low pressure
cenour currentobservations
werewellbelowthemixedlayerand andNovember15, 17frontsassociated
the nearestwind observations
weremadeon the Newport tersof varyingsizeandintensitypassedeastwardovertheSUS
southjetty 85 km southof the array,we usedthe Pollardand array. Many of thesefrontal passageswere recordedin the
Millard modelto obtaina qualitativeestimateof the currents Newport pressuredata and causedclockwiserotation of the
that might havebeengeneratedby the observedwinds.The windat Newport(Figure13).Sincetheextentof theSUSarray
was115km,thearrivaltimeof eachfrontwouldnot generally
modelequationsare
be the sametime at all moorings.Whereverthe rotationof the
u,--fv = •:"/(pZ)- cu
(1) near-inertialmotioncausedby eachfrontalpassagewas in
v, + fu = •:'/(pZ)- cv
(2) phasewith the pre-existingnear-inertialmotion,therewouldbe
constructive
interference
[Pollard,1970] whichwouldincrease
wheref is thelocalinertialfrequency,
u andv areeastwardand the near-inertialenergy.To look for phaseshiftsin the obnorthward
components
of thecurrent,c is thedamping
coef- servednear-inertialmotion,wecalculated
the phasedifference
ficient,p isthewaterdensity,x0:",•:Y)
is thewindstress,
andZ is betweenthe band-passed
currentvectorsand a referencevector
the mixedlayerdepth.The windstress,
x = Cap,,JVJV,was rotatingclockwise
at 0.0625cph:vectorswith no phaseshifts
computed
fromtheNewporthourlyvector,V, thedensityof will have a constantphasedifferenceif they have the same
air,p• = 1.25x 10-3gm/cm
3,anda dragcoefficient,
Ca= 1.5 frequency
as the reference
vectoror a linearlyincreasing
and
local wind forcingat siteD in the North Atlanticwasmodeled
x 10-3.Weassumed
a constant
mixed
layerdepthof25m.We decreasing
phasedifference
if theirfrequency
is slightlydifferuseda simplefinitedifference
formwith a 4-s timestepto ent.Timeseriesof thisphasedifference
for Leopard70 m and
computehourly valuesof the modelcurrent.
Elephant
23 m (Figure13)showthatno shiftsin thephaseof
ThePollardandMillardmodelshowsa strongnear-inertial thenear-inertial
motionoccurred
at Leopard70m duringlate
response
to thewindstress
peaksof December
14andJanuary October/early
November,whileseveral
phaseshiftsoccurred
at
4 (Figure12),and a weakerresponse
to someof the weaker Elephant
23duringthesameperiod.Thissuggests
thatmostof
storms between November 7 and December 10. Near-inertial
the wind-generated
near-inertial
motionat Leopardin late
motionwasobserved
morefrequently
at Leopard70m thanin October/early
Novemberwasnearlyin phase,causingthe
thePollardandMillardmodelresults
(Figure12).Near-inertial strong persistent near-inertial currents there. On the other
motion occurredfrequentlyat Elephant23 m from mid- hand,someof thenear-inertial
motiongenerated
at Elephant
Octoberto early December,
but not immediately
after the may havebeenout of phasewith pre-existing
near-inertial
strongstormsof December
14andJanuary4, althoughbothof
thesestormsseemedto generatenear-inertialmotionsat Leo-
pard70 m. Themodelfailedto account
for thepersistent
and
motions,causingdestructiveinterferenceon about October 27
and again on November 4 and 6. Thus, the observations
stronglysuggestthat the strongand persistentnear-inertial
ANDERSON ET AL.' NEAR-INI•TIAL
MOTIO8 OFF OREC,O•
5971
I
45' N
/000rob
•'
40 ø
1020
I"W
I12øNøo•v
•...!.I
29
Oct
125 ø
130øW
125"
i:•o"w
125,
i:•o•w
1:•5o
IODec
/
I oooo /
130øW
/
•".'
I
/
125'
10401
I010
NEWPORT
980
Barometric
Pressure
mb
Oct.
Nov.
NI •WPORT
Dec.
Low-Poss
Jon.
Wind Direction
t........
/L/
360 ø'
lD :::::::::::::::::::::::::
LEOPARD
: ...........................
70rn
Phose Difference
40
ELEPHANT
23m
360 ø
18
i........................................
::............................
ELEPHANT23m
PhoseDifference
Dec,
Jori
Fig. !3. Examplesof the synopticatmospheric
pressur
e chartsfrom the period of the near-inertial'event'of late
October/earlyNovemberandtimeseriesof atmospheric
pressure
and the directionof the low-passed
(< 0.025cph)windat
Newport,withtheeastward
components
andthephasedifferences
of theband-passed
currentvectors
at Leopard70m and
Elephant
23m relativeto a reference
vectorrotatingclockwise
at 0.0625cph.
5972
ANDERSON ET AL.' NEAR-INERTIAL MOTION OFF OREGON
motionsobservedat the offshoremooringsin late October and
early November were generatedby the local wind. Without
directwind observations
over the moorings,this tentativeconclusion cannot be verified.
CONCLUSIONS
Near-inertial
motions were observed at all current meters in
an array of five moorings which spanned the continental
margin off Oregon betweenOctober 1977 and January 1978.
The currentmeterswerebetween23 and 1850m deep,in water
depths between 100 and 2500 m, at locations between 10 and
130 km from shore.Although almost all of the currentmeters
werebelowthe mixedlayer,largeamplitude(~ 20 cm/s)nearinertial motionswereobservedon severaloccasions.
The largest amplitude(> 30 cm/s)near-inertialmotionswere observed
at the shallowestcurrentmetersof the offshoremoorings;these
currentmeterswerein the pycnoclineat depthsbetween70 and
141m. Althoughtherewerecurrentmetersat shallowerdepths
(23 and 49 m) within the surfacemixed layer over the continentalshelf,therewasmuchlessnear-inertialenergythere.The
amount of near-inertial energy observedover the shelf was
similar to that observedthere in the summerof 1972, and the
amount of energyin the deep water was comparableto that
observed in the North Atlantic.
Most of the near-inertialmotion had a frequencyslightly
greater than the local inertial frequency,but someof it had a
frequencylessthan the local inertial frequency.The downward
frequencyshiftoccurredin the presenceof a strongnorthward
current.
The near-inertialmotion at somecurrent meterswas very
persistent(in one caseit persistedfor more than 15 days).In
this case,the amplitudeseemedto increasegraduallybeforeit
decayed.In other cases,the amplitude increasedimpulsively
with gradualdecay,asusuallyobservedelsewhere.
Spectralanalysisshowedthat the horizontal coherencescale
exceededthe extent of the array (115 km) in October and
Novemberand was about half the extent of ,thearray (i.e.,60
km) in Decemberand early January.Thesecoherencescalesare
much larger than thosepreviouslyobservedover the Oregon
shelfin summer.Estimatesof the horizontalwavelengthof the
motion changedfrom 50 km during the first half of the records
to about20 km duringthe second.Theseestimatessuggest
that
thereis significantcoherence
betweencurrentmetersseparated
by two wavelengthsor less.
The near-inertialphasedifferencebetweena pair of current
meters varied considerably between separate near-inertial
events,even though the stratification remained much the same
throughoutthe period of observation.This suggests
that the
wavelengthis the resultof the particularcircumstances
generating the motion, rather than of the oceanicenvironment.
Because of the lack of current measurements
Pollard and Millard modelof local forcing,usingthe Newport
wind observations(85 km south of the array) as the forcing
function, indicates that some of the near-inertial motion ob-
servedbelow the mixed layer (e.g., at Leopard 70 m) was
generatedimpulsivelyby strongpeaksin the wind stress(e.g.,
December14 and January4). The strongand persistentperiod
of near-inertialmotion in late October and early November
may have beenthe resultof a sequenceof fronts that happened
to pass over the region in the proper phase for constructive
interference.Thus, our data are consistentwith the hypothesis
that the local wind can force strong near-inertial motions at
depthswell belowthe mixedlayer.
Acknowledgments.We wish to thank Barbara Hickey of the Universityof Washingtonfor providingthe data at Ocelot and Elephant.
We also thank Rick Romea and Jim Richman for their comments on
earlier drafts and JosephBottero and William Gilbert for assistance
in
the analysis.This study was completedwhile the first author was
studyingfor a degreeat Oregon State University.Financialsupport
was providedby the United StatesCoast Guard and by the National
ScienceFoundation throughgrantsOCE-7925019 and OCE-8026131.
REFERENCES
Fu, L., Observationsand modelsof inertial wavesin the deep ocean,
Rev.Geophys.SpacePhys.,19, 141-170, 1981.
Gonella,J., A local studyof inertial oscillationsin the upperlayersof
the ocean,DeepSea Res.,18, 775-788, 1971.
Johnson,W., Cyclesondemeasurementsin the upwelling region off
Oregon, Tech. Rep. 76-1, RosentialSchoolof Mar. and Atmos.Sci.,
Univ. of Miami Florida, 1976.
Kindle, J. C., The horizontal coherence of inertial oscillations in a
coastalregion,Geophys.
Res.Lett., 1, 127-130, 1974.
Koopmans, L. H., The SpectralAnalysisof Time Series,Academic,
New York, 1974.
Kroll, J., The propagationof wind-generatedinertial oscillationsfrom
the surfaceinto the deepocean,J. Mar. Res.,33, 15-51, 1975.
Kundu, P. K., An analysisof inertial oscillationsobservednear the
Oregoncoast,J. Phys.Oceanogr.,
6, 879-898, 1976.
Mooers,C. N. K., A techniquefor the crossspectrumanalysisof pairs
of complex-valuedtime series,with emphasison propertiesof polarizedcomponentsand rotationalinvariants,DeepSeaRes.,20, 11291141, 1973.
Munk, W., and N. Phillips, Coherenceand band structureof inertial
motionin the sea,Rev.Geophys.,
6, 447-471, 1968.
Pollard, R. T., On the generationby winds of inertial wavesin the
ocean,DeepSeaRes.,17,795-812,1970.
Pollard,R. T., Propertiesof near-surface
inertialoscillations,
J. Phys.
Oceanogr.,10, 385-398, 1980.
Pollard, R. T., and R. C. Millard, Comparisonbetweenobservedand
simulatedinertialoscillations,
DeepSeaRes.,17, 815-821, 1970.
Schott, F., and W. Diiing, Continental shelf waves in the Florida
Straits,J. Phys.Oceanogr.,
6, 451-460, 1976.
Thompson,R. O. R. Y., Coherencesignificance
levels,J. Atmos.Sci.,36,
2020-2021, 1979.
Thomson,R. E., and W. E. Huggett,Wind driveninertial oscillations
oflarge spatialcoherence,Atmos.Ocean,19, 291-306, 1981.
Webster,F., Observationsof inertial-periodmotionsin the deepsea,
Rev. Geophys.,6, 473-490, 1968.
in the mixed
layer and the absenceof direct wind measurementsover each
mooring, we could not rigorouslytest the hypothesisof local
generation of the near-inertial motions. However, the simple
(ReceivedJuly 6, 1982;
revisedJanuary31, 1983;
acceptedMarch 21, 1983.)