Deep-Sea Research, Vol. 32, No. 5, pp. 599 to 61 I, 1985. 0198-0149/85 $3.00 + 0.00 Printed in Great Britain. © 1985 Pergamon Press Ltd.

N O T E

F e a t u r e s o f m e s o s c a l e edd ies in the deep m i d - o c e a n o f the wes tern

N o r t h Pac i f ic

SHIRO IMAWAKI*

(Received 20 December 1983; in revised form 5 June 1984; accepted 18 September 1984)

Abstract--Velocities were measured by moored current meters at abyssal depths (4000 and 5000 m) at five stations in mid-ocean of the western North Pacific near 30ON, 146°40'E. The observed daily mean velocity field is almost uniform vertically at these abyssal depths. The observed level of low-frequency eddy kinetic energy is moderate in its geographical distribution over the sub- tropical gyre. Time-space correlation diagrams for the zonal and meridional components of velocity show a clear tendency of the westward phase propagation with a speed of several centimeters per second.

A composite of a few plane waves which have periods of dominant current fluctuations for most stations is fitted successfully to the observed velocities; the fitted waves account for variations of the relative vorticity and its local change estimated at the central station, as well as variations of velocities at all stations. The fitted waves have velocity amplitudes of 2 to 3 cm s -~, periods of 40 to 150 days, wavelengths of 200 to 500 kin, with a westward phase propagation; these properties are in the range of typical mesoscales observed at abyssal depths in the North Atlantic and the North Pacific. For these waves, the dispersion relation for barotropic Rossby waves over flat bottom topography holds approximately, though the waves are probably temporary. Therefore, a consider- able fraction of the observed mesoscale eddies is accounted for by a few temporary, linear, barotropic Rossby waves.

INTRODUCTION

MID-OCEAN mesoscale eddies, which are present all over the world ocean, may play an important role in the dynamics of the general ocean circulation and the transport of water properties. Their kinetic and potential energies are high near strong flows (e.g., western boundary currents and equatorial current systems) and low in the interior of subtropical gyres. An enormous amount of work has been carried out to describe and attempt to understand mesoscale eddies (MODE GROUP, 1978; WUNSCH, 1981; ROBINSON, 1983; SCHMITZ et al., 1983).

Mid-ocean mesoscale eddies are attributed to barotropic and/or baroclinic Rossby waves as follows. A considerable fraction of current and temperature fluctuations observed in the MODE (Mid-Ocean Dynamics Experiment) area in the western North Atlantic is accounted for by a combination of two pairs of flat-bottom barotropic and first-mode baroclinic Rossby

* Geophysical Institute, Kyoto University, Kyoto 606, Japan.

599

600 s. IMAWAKI

waves (McWILLIAMS and FLIERL, 1976), although some limitations of the linear wave-fit are pointed out (MCWILLIAMS, 1976a; RICHMAN et al., 1977; MODE GROUP, 1978). In the Gulf Stream recirculation region in the North Atlantic, a linear barotropic Rossby wave beneath the thermocline, modified by bottom topography, has been observed (PRICE and ROSSBY, 1982). The dominant annual and interannual baroclinic fluctuations detected from upper layer temperature records in the North Pacific are mostly accounted for by linear, first-mode baroclinic Rossby waves (KANG and MAGAARD, 1980). In the eastern equatorial Pacific, an indication of existence of a first-mode baroclinic Rossby wave trapped at the equator is shown by near-bottom current measurements (HARVEY and PATZERT, 1976). Near-bottom current fluctuations in the central North Pacific may have some features of Rossby waves, namely, the westward phase propagation and particle orbits transverse to the propagation direction, though the fluctuations do not fit the dispersion relation for flat-bottom barotropic Rossby waves (TAFT et al., 1981).

Observations of the vorticity balance have been carried out in several areas as follows. Estimations of the vorticity balance from observations of float trajectories at 1500 m depth in the MODE area, as well as vertical density profiles, show that a 10-day mean balance is highly nonlinear but a 60-day mean balance is marginally linear (McWILLIAMS, 1976b). Analysis of current meter data at 1500 m depth in the same area shows that the advection of planetary vorticity accounts for only a half of the local change of relative vorticity estimated at 4-day intervals, indicating that the fluctuations are not explained by barotropic Rossby waves (BRYDEN and FOFONOFF, 1977). In the Atlantic North Equatorial Current region, however, the local change of relative vorticity is found to be balanced, in the thermocline as well as in the deep layer, by the advection of planetary vorticity, although only for the lowest- frequency band with periods of 81 to 324 days (KEFFER, 1983).

These studies suggest that the dynamics of mid-ocean mesoscale eddies differ at various locations, depths, and temporal and spatial scales and that further examinations are required to understand the eddy field. The purpose of this paper is to describe some features of mesoscale eddies at abyssal depths in mid-ocean of the western North Pacific as observed by moored current meters at five stations in a relatively limited region. Here the term 'mesoscale eddies' refers to current fluctuations with typical temporal scales of weeks to months and typical spatial scales of tens to hundreds of kilometers; neither eddies with particular dynamics nor only flows with closed streamlines are implied.

OBSERVATION SITE

The site is centered at 30°N, 146°40'E with a water depth of about 6200 m; there are no pronounced features in the bottom topography (Fig. 1). The site is about 400 km from the Izu-Ogasawara Ridge and about 500 km south of the Kuroshio Extension; it is on the indistinct southern boundary of the broad, west-southwestward flowing Kuroshio Countercurrent at shallow depths (JAPAN OCEANOGRAPHIC DATA CENTER, 1975), and in an inferred sluggish northward flow at abyssal depths (MANTYLA, 1975). Like the MODE area in the western North Atlantic, the present site is located between a strong current region and the interior region. Previous current measurements at this site indicate the existence of a westward propagating fluctuation with a period of about 100 days and a zonal wavelength of about 200 km (IMAWAKI et al., 1984).

Mesoscale eddies in the deep mid-ocean 601

N 140 160"E 4_[0: o¢°%e~r~,.._~ . . ............ ,. ........... ~ ..................

~i~:~,~,.. ~ , ~ . . , . ~ : : : : ~ -~¢.~ !::~ ~-'.:~:~?,~ ~ ~:~:'.-~:~?.~::"-.":~-:'-'..: ~:~:~:.~,.'~:.~ :::~.-' ~.~.~:~:~:~::~:~:, ~.,.'..'..:::

20

lt, S" E

RC

o 0

"

N.i.i!iii.i.i.i.i.i.ii o l i 6 147

32"N

31

30

29 148

Fig. 1. Configuration of the mooring array with a sketch of bottom topography. Shaded areas indicate water depth of <6000 m. Contour intervals are 500 m. In the physiographic inset, the loca- tion of the present observation site 121 is shown in relation to the Kuroshio system and the Izu-Ogasawara Ridge; the approximate climatological mean path of the Kuroshio system (JAPAN OCEANOGRAPHIC DATA CENTER, 1975) is shown by shading and the horizontal extent of the ridge

at 3000 m depth by dotted lines.

CURRENT MEASUREMENTS

The configuration of the mooring array used for the present velocity measurements is shown in Fig. 1. Zonal and meridional station spacings are either about 45 or 90 km. Such an irregular configuration was used so that fluctuating currents could be observed at two spatial scales and their horizontal extent estimated.

Each subsurface mooring had two Aanderaa RCM-5 current meters at nominal depths of 4000 and 5000 m. Measurements were restricted to abyssal depths because mooring technology at that time was not able to provide measurement platforms at shallow depths. Moorings were deployed in early October 1978 and recovered in mid-March 1979. Good quality records were obtained over a 152-day common period from all current meters except one at 4000 m at Sta. TA.

ANALYSES OF DATA

The data were sampled at 30-min intervals. The raw data are dominated by diurnal and semidiurnal fluctuations, which are removed by taking daily mean averages for the analysis of low-frequency fluctuations; the theoretical period of the local inertial oscillations at the site is about 1 day (23.4 to 23.9 h).

Table 1 shows the general statistics of the daily mean velocities for the 10 records from the five stations. It also includes a time-space average, which is an average of the 10 records weighted with respect to the duration of measurements and is considered to be a

602 S. IMAWAKI

Table 1. Statistics o f daily mean velocities. Synbols u and v denote the eastward and northward components, respectively; overbars denote temporal averages over the record lengths and primes deviations of daily mean values

from their record length averages; K M and K E denote, respectively, the kinetic energies per unit mass for the mean flow and the fluctuations. Time-space average is an average o f the ten records weighted for the duration of

measurements

Station Depth Duration ff F K M u '2 v '2 K E u'v' No. (m) (days) (cm s -t) (era 2 s -2) (cm 2 s -2) (cm 2 s -2)

RA 4000 166 1.1 0.3 0.6 5.6 8.0 6.8 -2.2 5000 153 1.2 --0.2 0.8 5.6 8.2 6.9 -3.0

RB 4000 168 0.1 -0.4 0.1 9.0 9.6 9.3 0.3 5000 168 -0.0 -0.4 0.1 8.0 9.2 8.6 -0.1

RC 4000 164 -1.2 2.1 3.1 9.4 14.4 11.9 1.4 5000 164 -1.8 2.0 3.7 9.6 12.0 10.8 1.4

TA 4000 61 2.0 -4.1 10.4 6.6 4.1 5.3 -2.1 5000 166 3.1 -5.3 18.7 7.2 5.7 6.4 1.9

TD 4000 168 -1.3 0.8 1.1 2.7 3.5 3.1 0.3 5000 160 -0.3 0.7 0.3 3.5 3.8 3.7 -0.1

Time-space 1538 0.1 -0.2 0.03 6.7 8.1 7.4 -0.1 average

representative value at this site. The statistics are similar to each other at 4000 and 5000 m depths at every station except Sta. TA. The general agreement suggests that the velocity field is almost uniform vertically at these abyssal depths. The kinetic energy KM per unit mass for the mean flow is small, except for Sta. TA, where a remarkable mean flow with bottom intensification exists (TAIRA, personal communication). The kinetic ~nergy KM estimated from the time-space average mean flow is trivially small. The kinetic energy KE per unit mass for the low-frequency eddies (with frequencies less than one cycle per day) varies from 3 to 12 cm 2 s -2 with a time-space average of 7.4 cm 2 s -2. The values of time-space average KM and Ke are in good agreement with values of KM and Ke estimated from about 3-year con- tinuous measurements at 5000 m depth at Sta. RB (IMAwAKI and TAKArqO, 1982), which are statistically significant at a fixed station. The meridional variance is a little larger than the zonal variance.

The sequence of 10-day interval snapshots of 10-day mean current vectors at 5000 m (Fig. 2) shows features like a cyclonic swirl on days-13 t o - 3 and an anticyclonic swirl on days 37 to 47, which seem to pass through the array westward. To examine a tendency of the phase propagation, as well as the overall temporal and spatial scales, contour maps of time- space correlations for the zonal and meridionai components of velocity as functions of the temporal and spatial lags are presented (Figs 3 and 4). Zonal correlation along 30°N latitude, estimated from 5000 m depth records at Stas RA, RB, and TA, is shown in Fig. 3, whereas, in Fig. 4, meridional correlation along 146°40'E longitude, estimated from records at RA, RC, and TC, is shown.

The typical temporal scale is estimated to be 88 days from four times an average of first zero-crossing values at the zero spatial lag. The typical spatial scale, however, cannot be estimated, because first zero-crossing values at the zero temporal lag vary widely from 60 km to more than the maximum spatial lag of 135 km. The westward phase propagation is clearly seen in the zonal direction (Fig. 3). Its speed is estimated to be about 2 cm s-' for the zonal component and about 7 cm s -I for the meridional component. In the meridional direction, no

- 83

°33

17

t

I ,

t

-73

-23

27

0

/

%

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- 63

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37

P

/

/.

/

-53

-3 -%

/

47 % ,

-43 \

b

7

57

i N , ~ i

0emil0 ~_ 0 km 100

Fig. 2. Sequence of horizontal distribution of the 10-day mean velocities (with record-length averages removed) at 5000 m depth from 9 October 19"/8 (day -83) to 26 February ]9"/9 (day 57). The figure at the upper left corner in each panel indicates the serial day starting from ! January

1979. RA the central mooring is located at 29°59'N, i46°41'E.

"~100

a

g so t / )

-40

[~ c m s "1

E-W, U a

-2b 0 2b

E-W, V ~7 cm s "1 a i i

i:U:i!!i o ~

40 -40 -20 0 20 4O Time tag (days) Time tag (days)

Fig. 3. Time-space correlation diagrams for (a) the zonal and (b) the meridional components of velocity, estimated from 5000 m depths records at Stas RA, RB, and TA, separated zonally at 30°N

latitude. Sample slopes arc also shown.

Fig. 4.

N-S. U a N-S, V

"E I~

? i .

0 . . . . . . . . -60 °20 0 20 40 -40 -20 0 20 40

Time Lag (days) Time Lag (days)

As in Fig. 3, but for Stas RA, RC, and TD, separated meridionally at 146°40'E longitude.

604 S. IMAWAKI

phase difference is found for the meridional component, and the phase propagation is not clear for the zonal component (Fig. 4).

PLANE WAVE FIT

]MAWAKI (1983), using the same data set as the present one, shows that the 10-day mean local change of relative vorticity is almost accounted for by the advection of planetary vorticity. This suggests that the fluctuations under consideration might be explained by linear, barotropic Rossby waves, though observed features like a swirl (Fig. 2) and different speeds of westward phase propagation in zonal and meridional components (Fig. 3) cannot be explained by a single Rossby wave, In the present study, plane waves existing during the observation period are detected and their properties such as periods, wavelengths, and phase velocities are compared with the dispersion relation for barotropic Rossby waves; here the observed velocities are assumed to be mostly accounted for by a sum of mean velocities and current fluctuations associated with a composite of a few waves.

Figure 5a shows time-series of the observed daily velocities at 5000 m after smoothing by a 5-day running-mean procedure to eliminate short-term fluctuations. Periods of the dominant fluctuations of the zonal and meridional components are estimated by the maxi- mum entropy method (MEM) of spectral analysis (ULRYCH and BISHOP, 1975), which is very effective for estimation of periods from a relatively short time-series. The results of this method (Fig. 6) show three periods of fluctuations dominant for most stations, namely,

0 10 cmls (~ ~

I I , I I I I , i i I

. ~ , ~ . . ~ p , . _ .,~, , Jz .~_ TA

....... -~ " - , . , ~ ' - - m . , ~ - ~ TD

N

I I I L I I I I L

~. . . , ,~ __. ._ ,~m~ __.~ RA

~ - - . . ~ , , ~ . , , m , , m ¢ l I R B

i , , , ~ RC

~ , ~ , ¢ ~ 1 TA

' ' ' b . . . . " ' 6 . . . . -100 100 -100 100 T ime ( d a y s ) T i m e ( d a y s )

Fig. 5. Time-series of (a) the velocities observed at 5000 m depth at the five stations from 6 October 1978 (day -86) to 2 March 1979 (day 61) and (b) the velocities associated with a composite of three fitted waves as shown in Table 2 and Fig. 8. Each stick represents a daily current vector (upward north). The abscissa is time in days starting from 1 January 1979. In (a), the velocities are smoothed by a 5-day running-mean procedure and the mean velocities estimated in the wave-fit are

subtracted.

Mesoscale eddies in the deep mid-ocean 605

i , , . , ¢ • , , , * . . . . * . . . .

Q. /

u 10 3 ~ ' ¢q " 1'I' "N/

IU f . i1\ ~ !: i , "\ !

, . - i£--.~

/ /

181 . - " / /

a, / I ",

"o 0" " " I ' ,~ >,I, "--~ /

® 17: . . . . . . / / ~ ,

/ / RA \ U "*"~" / i "- .I / - - - RB :':

.- I . . . . . . . . RC \ - . - TA \ ' -

,o' . . . . To ii i 200 150 100 50 0

P e r i o d (days )

Fig. 6. Spectral peaks of the zonal and meridiona] current fluctuations observed at 5000 m depth at all stations estimated by the maximum entropy method of spectral analysis. Arrows indicate the three common periods. Peaks of zonal components arc indicated by I , A , and • (with thick lines) For periods of 15 I, 9.7, and 44 days, respectively, and peaks of meridional ones by A and O (with

thin lines) for periods of 9"7 and 44 days, respectively.

151 + 16, 97 + 9, and 44 + 4 days. Another explanation might be that there are two dominant fluctuations with periods of 115 + 28 and 44 + 4 days. However, the composite of two plane waves with these periods can explain only 34% of the observed eddy kinetic energy. Further, periods of peaks for meridional components are about 100 days for the longer period peaks, while those for zonal components are much longer. Therefore, oscilla- tions with the above-mentioned three periods are considered to exist simultaneously during the observation period.

The composite of three plane waves with these periods is fitted to the observed velocities at the five stations. The error norm is defined as the summation, at all stations, of squared vectorial differences between the observed velocities and mean velocities plus velocities associated with the composite of waves. Values of amplitudes, wavenumbers, phase propaga- tion directions, and initial phases of the three waves, as well as mean velocities at the five sta- tions, are determined by the procedure of FLETCHER and POWELL (1963) for minimization of the error norm. The results are shown in Table 2 and Fig. 5b.

The fitted waves have velocity amplitudes of about 2 cm s -I , wavelengths of about 200 to 300 km, and the westward component of phase propagation. The relationship of the current fluctuations associated with the composite of waves with the observed fluctuations (Fig. 5)

e~

Z

~, ~ ' . ~ o

~ E

~z

0 ~

T?

/

0

0

0

6

. ~ < ~

=..- Z ~ o ~

Mesoscale eddies in the deep mid-ocean 60"/

is as follows. The vectorial correlation coefficient between the original data and the composite of fitted waves is 0.69 on average over five stations; here the vectorial correlation coefficient C is defined by C = ~ / (v# 2 ~)1/2, where vd is the observed velocity minus the estimated mean velocity, v/is the velocity associated with the composite of fitted waves, and an overbar denotes the temporal average. The amplitude ratio of the composite of fitted waves to the data is 0.71 on average; here the amplitude ratio a is defined by a = (~/v~ ),/2 ; thus the composite of waves accounts for 51% of the observed eddy kinetic energy. Features like a swirl observed in Fig. 2 and major features in time-space correlation diagrams of Figs 3 and 4 are reproduced, although counterparts to these figures are not shown here.

The relationship of the relative vorticity associated with the composite of fitted waves with the observed relative vorticity (IMAWAKt, 1983) is as follows (Fig. 7a); both are estimated from finite differencing of the current fluctuations at the five stations. The maximum cross- correlation of the relative vorticity between the data and the composite of fitted waves is 0.94 at a time lag of only 1 day (with a phase lead of the composite), and the r.m.s, amplitude ratio of the composite of fitted waves to the data is 0.82. The relationship of the local change of relative vorticity associated with the fitted waves to the observed one is as follows (Fig. 7b). The maximum cross-correlation of the local change of relative vorticity between the data and the composite of fitted waves is 0.82 at a time lag of only 1 day (with a phase lead of the data), and the r.m.s, amplitude ratio of the composite to the data is 0.69. Therefore, the fitted waves account for the observed relative vorticity field very well.

A • T 11 U

odd

'o

'5

+1: "5 -1

O

> - 1 0 0 ' " ' " " 6 . . . . . . . . . 1 0 0

T ime ( d a y s )

Fig. 7. Time-series of (a) the relative vorticity and (b) its local change at RA, the central station, estimated from finite differencing of t ic current fluctuations at the five stations. Solid lines indicate those observed (IMAWAKI, 1983) and dotted lines those associated with a composite of fitted waves.

The abscissa is time in days as in Fig. 5.

608 s. IMAWAKI

The agreement between the data and waves is best in the relative vorticity as shown above. This is partly due to the fact that the observed velocities may contain local fluctuations that cannot be resolved by the present waves, which express only fluctuations accompanied with vorticity fluctuations of comparatively large horizontal scales. It is also because the contribu- tion of wave No. 3, whose fitting is not sufficient in the present case, is small in relative vorticity due to its smaller wavenumber. Similarly, weaker agreement between the data and fitted waves in the local change of relative vorticity is partly because the contribution of wave No. 3 is not small in the local change of relative vorticity due to its larger angular frequency.

Wavenumber vectors of the three waves and dispersion relation curves of Rossby waves with corresponding periods (Fig. 8) indicate whether the dispersion relation for harotropic Rossby waves over flat bottom topography, o =-f3k/(k 2 + 12), holds for the fitted waves. Here o is the angular frequency, I] the meridional derivative of the Coriolis parameter, and (k, 1) the wavenumber vector in the (east, north) direction. In each panel of Fig. 8, the thin line surrounding the dispersion curve (heavy line) indicates the error bound estimated from the standard deviation of the estimated period of the dominant fluctuation. The thin line around the arrowhead of the wavenumber vector indicates the error bound estimated from values of the wavenumber for which the wave fit is 0.95 of the optimum fit. The dispersion relation holds for wave Nos 1 and 2 but not for wave No. 3.

A possible explanation for the deviation of wave No. 3 is as follows. In time-series of velocities at all stations (Fig. 5a), as well as the estimated relative vorticity and its local change (solid lines in Fig. 7), fluctuations with a period of about 44 days are seen clearly during the first two-thirds of the observation period but are indistinct during the final third. If a similar wave-fit is done for the first two-thirds of the period, the third wave, designated No. Y, has a smaller wavenumber, a similar phase propagation direction, and a little larger amplitude (Table 2 and Fig. 8c); its error bound (dotted lines) indicates that the dispersion relation holds fairly well. Therefore, a wave having properties similar to those of barotropic Rossby waves probably existed during the first two-thirds of the period, following which it

A I, '7

0

-2"

C l

i i i i

No. 1

-4 -3 -2 "1

b = i i =

No. 2 T=97d

-4 "3 -2 -I 0 -4 k (10 "2 km "1 )

C

i , , A

No. 3 T = 4 4 d

-3 -2 -!

Fig. 8. Wavenumber vectors of the fitted waves, Nos 1, 2, and 3, with periods of 151, 97, and 44 days, respectively, as well as dispersion relation curves of barotropic Rossby waves with corresponding periods. Thin lines surrounding the dispersion curve and the arrowhead of the wavenumbcr vector indicate the error bound. In (a), the error bound of the dispersion curve of baroclinic Rossby waves (dotted line) is also shown. In (c), O indicates the position of an arrowhead of the wavenumbcr vector (wave No. 3') in the case of wave-fit to the data of the first two-thirds of

the observation period; its error bound is shown by the dotted line.

Mesoscale eddies in the deep mid-ocean 609

weakened; however, the present wave-fit assumes a constant amplitude, resulting in estima- tion of a larger wavenumber and a smaller amplitude.

The dispersion relation for baroclinic Rossby waves, o -- - f3k/(Id + 12 + R f 2), definitely does not hold for the fired waves; here Rn is the nth mode internal radius of deformation. The possible shortest period of baroclinic Rossby waves at this site is estimated to be 162 days from the first-mode internal radius of deformation of 45 km (IM^wArd, 1981). Therefore, the periods of most of the observed oscillations are too short to be interpreted as baroclinic Rossby waves. The error bound of dispersion relation curve for baroclinic Rossby waves for wave No. 1 (dotted line in Fig. 8a) is far away from the observed wavenamber vector. The observed periods might be subject to Doppler shifting by the mean flow; the dispersion relation for baroclinic Rossby waves holds for wave No. 1 if a mean north- westward flow with a speed of about 0.5 cm s -~ exists. But such a systematic flow was not found at these abyssal depths during the observation period.

The r.m.s, amplitude of the local change of relative vorticity (estimated analytically from wave properties) associated with the composite of fitted waves is 0.6 x 10 -12 s -2 on average over the five stations, the advection of planetary vorticity is 0.4 x 10 -12 s -2 , and the advec- tion of relative vorticity or the nonlinear term is 0.1 x 10 -12 s -2. In general, the nonlinear term is not zero for the vorticity field of combined linear Rossby waves, but in this case it is small compared with the advection of planetary vorticity.

DISCUSSION

The statistics of the observed velocities show that the site is located in mid-ocean apart from intense current zones. The kinetic energy for the mean flow is fairly small. The level of the kinetic energy for low-frequency eddies is higher than in the central North Pacific (TAFT et al., 1981) but lower than in the Kuroshio Extension (SCHMITZ et al., 1982; SCHMITZ, 1984). The level is moderate in its geographical distribution over the subtropical gyre and is compar- able with the level of eddy kinetic energy observed at an abyssal depth in the MODE area in the western North Atlantic (SCHMIrZ, 1978).

Time-space correlation diagrams for the zonal and meridional components of velocity show a tendency of the westward phase propagation with a speed of several centimeters per second, which is comparable with speeds observed in the deep layer in the western North Atlantic (FREELAND et al., 197.5; FREELAND and GOULD, 1976; FU et al., 1982).

In the preceding section, waves having properties of barotropic Rossby waves are identified for the first time from current meter data. The observed waves, however, do not seem to be fully periodic in time and space, as shown by the wave with a period of 44 days being predominant during the first two-thirds of the observation period, then becoming indistinct. No evidence for long persistence of individual waves is found in the subsequent long record at Sta. RB (IMAWAKI and TAKANO, 1982), although a considerable amount of kinetic energy is found in a particular band with 120- to 62-day periods, where, for example, wave No. 2 belongs. Therefore, it is appropriate to conclude that linear, barotropic Rossby waves existed temporarily at abyssal depths at the present site, and account for a consider- able part of the mesoscale eddies.

Periods and wavelengths of the identified waves are in the range of the typical temporal mesoscale (about 30 to 150 days) and spatial mesoscale (about 200 to 400 km), observed so far at abyssal depths in the North Atlantic and the North Pacific (FP.EELAND et al., 1975;

610 S. IMAWAKI

McWILLIAMS and FLIERL, 1976; RICHMAN et al., 1977; SCHMITZ, 1978; TAFT et al., 1981;

WUNSCH, 1981 ; Fuet al., 1982; IMAWAKI and TAKANO, 1982; SCHMITZ et al., 1982). The present da ta set provides little information on sources and sinks of eddies or waves,

but a hint is given by examinat ion of the direction of group velocity; in Fig. 8, the group velocity points from the intersection o f the wavenumber vector with the dispersion relation curve toward the center of the circle. The group velocity of wave No. 1 is directed to the

south, which is consistent with a supposit ion that the origin was located at the Kuroshio Extension, a candidate for the major source of eddy energy (RoaINSON, 1983). Group velocities of wave Nos 2 and 3 are directed to the northeast. It might be possible to consider that oscil lat ions originated in the southwest had passed over the I z u - O g a s a w a r a Ridge located about 400 km west of the site, but another explanat ion is also possible, namely that f luctuations originated in the southeast were reflected at the almost meridional ridge, and thus observed at the site.

Acknowledgements--The author thanks Prof. H. KUNlSH! of Kyoto University for helpful advice and encourage- ment. The current measurements were made by Prof. K. TAKANO of the University of Tsukuba, Prof. T. TERAMOTO and Dr. K. TAIRA of the University of Tokyo, and the author. The mooring operation was done on board R.V. Hakuho Maru of the University of Tokyo. Thanks are due to Messrs. M. SAWAMURA andS. SAKAI of Kyoto University, Dr. A. MASUDA of Kyushu University, and Dr. M. FUKASAWA of the University of Tokyo for valuable discussions. Dr. D. P. Henry of the University of Washington offered valuable suggestions for improving the text. The work was supported by the Ministry of Education, Science and Culture, and by the Science and Technology Agency, Japan.

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HARVEY R.R. and W.C. PATZERT (1976) Deep current measurements suggest long waves in the eastern equatorial Pacific. Science, Wash., 193, 883-885.

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IMAWAK! S. (1983) Vorticity balance for mid-ocean mesoscale eddies at an abyssal depth. Nature, London, 303, 606-607.

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