The relationship of low-frequency deep variability near the HEBBLE site to Gulf Stream fluctuations

Marine Geology, 99 (1991) 303-317

303

Elsevier Science Publishers B.V., Amsterdam

The relationship of low-frequency deep variability near the HEBBLE site to Gulf Stream fluctuations E l i z a b e t h B. W e l s h a, N e l s o n G . H o g g a a n d R o s s M . H e n d r y b

aWoods Hole Oceanographic Institution, Woods Hole, MA 02543, USA bAtlantic Oceanographic Laboratory, Department of Fisheries and Oceans, Bedford Institute of Oceanography, Dartmouth, N.S. B2 Y 4A2, Canada (Received April 1988; revision accepted September 1989)

ABSTRACT Welsh, E.B., Hogg, N.G. and Hendry, R.M., 1991. The relationship of low-frequency deep variability near the HEBBLE site to Gulf Stream fluctuations. In: A.R.M. Nowell (Editor), Deep Ocean Sediment Transport. Mar. Geol., 99: 303-317. Current meter measurements from two recent moored array experiments on the Continental Rise and in the Gulf Stream south of Nova Scotia are examined to determine horizontal and vertical structures of energetic time variable motions; the intent being to put the so-called "abyssal storms" observed at the HEBBLE site into the context of the larger-scale energetics of the region. Empirical orthogonal functions are used to examine characteristics of the motions as a function of frequency. One array spanned the Continental Rise and the Stream. In many low-frequency bands, motions exhibit properties of nearly barotropic topographic Rossby waves and are coherent over the array. Phase propagation of the waves is to the southwest, indicating onshore energy propagation. Data from a second current meter array within the Stream are examined to determine source region structure and relationship to Rise variability. In most frequency bands, Stream motions are too complex to be clearly separable into empirical modes, but a significant mode does exist in the band centered at 30 days. Westward propagation is observed in the meridional component of the velocity at 4000 m depth and the associated zonal wavenumber matches that observed on the Rise. The hypothesis that westward propagating meanders can directly excite far field motions is explored and found to be consistent with observations in the 30-day band.

Introduction A typical d e e p c u r r e n t r e c o r d f r o m the C o n t i n e n tal Rise a n d Slope in the western N o r t h A t l a n t i c shows s u p e r i m p o s e d on the m e a n flow n e a r l y c o n t i n u o u s l o w - f r e q u e n c y v a r i a b i l i t y m o s t often a s s o c i a t e d with t o p o g r a p h i c waves, b u t s o m e t i m e s with the d e e p s i g n a t u r e o f the G u l f S t r e a m on a n o r t h e r n excursion. T h e s t a n d a r d d e v i a t i o n s are well in excess o f the w e s t w a r d m e a n s causing very large i n s t a n t a n e o u s velocities to the west a n d w e a k e r flow reversals. I n s o m e areas, such as the H E B B L E site, these m o t i o n s are so energetic t h a t they have been called " a b y s s a l s t o r m s " o r " b e n t h i c s t o r m s " ( H o l l i s t e r a n d M c C a v e , 1984; W e a t h e r l y a n d Kelley, 1985). A s far as the ocean c u r r e n t s are c o n c e r n e d , " a b y s s a l " is n o t the a p p r o p r i a t e adjective as we shall see t h a t they fill the entire water column. 0025-3227/91/$03.50

This p a p e r examines the structure o f the m o t i o n s on the C o n t i n e n t a l Rise a n d explores its relationship with the G u l f Stream, using d a t a f r o m two recent m o o r e d arrays. In 1983 a n d 1984, the A b y s s a l C i r c u l a t i o n E x p e r i m e n t ( A B C E ) was cond u c t e d yielding 17 m o n t h s o f c u r r e n t a n d tempera t u r e m e a s u r e m e n t s f r o m b o t h regions. P r i o r to this e x p e r i m e n t , the G u l f S t r e a m h a d rarely been s a m p l e d c o n c u r r e n t l y with m o t i o n s on the C o n t i nental Rise. A d d i t i o n a l l y , as p a r t o f the Statistical and Mapping Experiment (SME) a current meter a r r a y was d e p l o y e d in the G u l f S t r e a m j u s t to the east o f the A B C E a r r a y a n d o v e r l a p p e d it in time. B o t h t h e A B C E a n d S M E are d e s c r i b e d in s o m e detail by H o g g et al. (1986). T h e r e is evidence f r o m earlier e x p e r i m e n t s t h a t the source o f the l o w - f r e q u e n c y m o t i o n s on the Rise is offshore. T h o m p s o n (1977) inferred the energy flux at site D to be directed s h o r e w a r d .

© 1991 - - Elsevier Science Publishers B.V.

304

Hogg (1981) used a ray tracing technique on data from the Rise Array to locate the position of the source of observed topographic waves and found it to coincide with a meander of the Gulf Stream. Johns and Watts (1986) also deduced a shoreward flux of energy associated with topographic waves off Cape Hatteras just east of where the Gulf Stream leaves the Continental Rise. A number of theories implicate Gulf Stream rings as the topographic wave source. In a numerical study of rings, McWilliams and Flierl (1979) found that wave dispersal is a decreasing function of the nonlinearity of the vortex. As Gulf Stream rings are highly nonlinear it was concluded that the rather slow dispersal of baroclinic Rossby waves from rings is insignificant. However, with the inclusion of nonlinear coupling between modes, they found that barotropic dispersal could provide significant energy to the wave field. Louis and Smith (1982) noted that the dynamics of Gulf Stream rings are linearized over significant bottom slopes, thereby enhancing the dispersal of Rossby waves. They calculated the expected evolution of the radiation field and found that the bursts of topographic wave energy observed near the shelf break north of the ABCE region by Louis et al. (1982) were consistent with this theory. In addition to theories which implicate Gulf Stream rings, there are several which suggest that the Stream itself might be a source for energy in the far field. One such mechanism is radiating instabilities from a jet (Talley, 1982, 1983a, b). The radiating modes resemble Rossby waves in the far field with slowly decaying amplitudes away from the current. Other researchers have examined the effects that a meandering Stream might have on the surrounding field. Most studies have concentrated on the steady forced response of the ocean interior to specified meander forcing. In both linear (Pedlosky, 1977) and nonlinear (Malanotte-Rizzoli, 1984) studies of this type it was found that for Rossby waves to penetrate the ocean interior, the phase speed of the meanders must be westward to match the free Rossby wave speeds. In more recent investigations which include the effects of a time-dependent boundary, or growing and pulsating meander amplitudes, it was found that pulses of transient Rossby waves can radiate from both

E.B. W E L S H ET AL.

stationary and eastward propagating meanders and become important far from the jet in both the linear and the nonlinear cases (Malanotte-Rizzoli et al., 1987, 1988; Hogg, 1988). An examination of the ABCE and SME data provides additional evidence that the Gulf Stream is generating the observed motions on the Continental Rise. In the next section, using empirical orthogonal functions in the frequency domain, the vertical and horizontal structure of the ABCE region will be described. In the following section, the Gulf Stream will be examined using data from both experiments and the possibility of Stream forcing of far field motions will be explored. Conclusions will follow in the final section. The ABCE data

The positions of the current meter moorings from both the ABCE and the SME are shown in Fig. 1. As this paper concentrates on deep motions on the Rise and their relation to Gulf Stream variability, only moorings 775-780 are used in the ABCE analyses. Tables 1 and 2 list the instruments, their locations, depths and lengths of operation for both experiments. Figure 2 shows the current records from the full depth moorings 775, 776, and 780 along with temperature at 500 m corrected for mooring motion as in Hogg (1986). Moorings 775 and 776 were located in the northern branch of the Northern Recirculation Gyre (as described in Hogg, 1983 and Hogg et al., 1986) and therefore exhibit relatively strong southwestward mean flows. Mooring 780 was in the Gulf Stream throughout most of the experiment. Consequently, mean flows at the uppermost instruments are to the east but, in addition, the records from this mooring and the SME moorings show that the eastward flow extends to the level of the deepest instruments. A description of the deep mean fields is given in Hogg et al. (1986). This section focuses on the current variability. The vertical structure of the low-frequency motions in Fig. 2 is visually striking and similar to all previous observations made near the Stream at 55°W (Schmitz, 1980) and the Kuroshio (Schmitz, 1984). Motions at mooring 776, which is close to

305

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the HEBBLE site and away from the Stream, are virtually depth-independent and show that the socalled "abyssal storms" are not confined to the near-bottom but fill the whole water column. In what follows we shall try to quantify this structure and relate the variability at this mooring to motions at other locations, in particular the Gulf Stream.

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7751 7752 7753 7762 7764 7765 7766 7771 7772 7781 7791 7802 7804 7805 7806

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# Day~ 506 506 424 507 507 507 507 506 506 523 506 507 507 507 507

Depth (m) 497 1390 3987 518 1512 4011 4789 4002 4871 4002 40@5 513 1009 1506 4004

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-62.06 -61.59 -61.59 -61.50 -60.72 - 6 0 33 -60.33 - 6 0 33 -60.33

Methods Empirical orthogonal functions can be an effective means of describing large amounts of data if most records are coherent with one another and dominated by one or two processes. The method was applied in the frequency domain to obtain information about time scales and phase relationships between contributing series. For a discussion of empirical orthogonal functions refer to Wallace and Dickinson (1972). Cross-spectra were calculated between all temperature and velocity records by dividing time series into seven overlapping pieces 120 days in length which were then Fourier-transformed and Hanned. Elements of the cross-spectral matrix were normalized by the square root of the product of the component variances to prevent the modes

2

The Statistical and M a p p i n g Experiment hlst. 5571 5572 5573 5574 5581 5582 5583 5584 5592 5593 5594 5601 5602 5604 5611 5612 5614

Start Date # Days Depth (m) WaterDepth 5~7-83 5-07-83 54:)7-83 5-07-83 5-08-83 9-29-83 5~8-83 5--08-83 5-08-83 5M}8-83 5-08-83 5-11-83 5-11-83 5-11-83 5-11-83 5-11-83 5-11-83

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308

from being dominated by the input series with the highest dimensional values. Eigenvalues and eigenfunctions were calculated from the resulting matrices. If an empirical mode explains more than twice the variance of the next mode, as indicated by the relative magnitudes of the eigenvalues, then probably one wave type dominates in that band (Wallace and Dickinson, 1972). If there also exist significant coherence amplitudes between the modal series and the data series from instruments which are not randomly distributed then it is plausible that the mode is physically meaningful. Once their significance were confirmed using these criteria, the modal structure was examined by constructing a variance ellipse for each record from the amplitude and phase values for each velocity component given by the eigenfunctions. The structure of the first mode was examined in several frequency bands. In the preliminary analyses, temperature was found to be generally incoherent with the modes. Therefore, the normalized cross-spectral elements involving temperature were reduced to 10% of their actual values in the determination of the coherence matrix, thereby allowing for a more accurate description of the current variability. Vertical structure

The method of empirical orthogonal functions was first used to examine the vertical structure at each location sampled by moorings 775, 776, and 780. Lowest modes were significant in most lowfrequency bands at each of the three moorings. The 120-, 30- and 17-day bands will be described giving information about motions over a broad range of time scales. Current ellipses, superposed on the bathymetry, are shown in Fig. 3 for the 30day band. At mooring 775, the energy is bottom intensified as is readily apparent in the current records (Fig. 2a). Amplitudes at moorings 776 and 780 are nearly constant with depth except at 500 m, where the amplitudes are significantly larger. This is attributed to the presence of a surface intensified Gulf Stream at each of these moorings, which should have an especially large effect on modal structure at mooring 780 as motions there are dominated by Stream activity. The high degree

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of vertical coherence is especially of interest at mooring 780 because it again indicates that the Stream extends coherently to the level of the deepest instrument, consistent with the findings of Hall and Bryden (1985) from the " G U S T O " (Gulf Stream Observations) mooring near 68°W. To understand the structure at mooring 776 it is useful to examine the current records along with the 500-m temperature record (Fig. 2b). The bottom velocities show two types of disturbances. Weak and brief eastward flows are associated with much stronger eastward bursts of current and warm temperatures at 500 m. These events extend throughout the water column and can be attributed to the presence of the Gulf Stream or a ring at the mooring. The second class of motion is barotropic or slightly bottom intensified with little or no corresponding temperature disturbance at 500 m and dominates the westward bursts. Weatherly and Kelley (1985) suggest that these two kinds of disturbances result from the same phenomenon. They used 20-month records from deep current meters near mooring 776 along with satellite data from the National Weather Service to determine the position of the Gulf Stream. Most

309

LOW-FREQUENCY DEEP VARIABILITYAND THE GULF STREAM

of the eastward and one of the westward events present in their current records coincided with the presence of a Gulf Stream event overhead which, if sufficiently barotropic, could extend to the bottom and cause a reduction in amplitude or displacement of the westward current. When the Stream is n o t over the mooring, Weatherly and Kelley (1985) hypothesize that the westward current regains its full strength and a "burst" of energy occurs. Our contention is that these westward bursts result instead from Rossby wave-like motions, which are probably forced by the Gulf Stream and propagate shoreward through the area ultimately becoming the topographic waves seen so clearly at mooring 775 (Fig. 2a). This supports the conjecture of Grant et al. (1985) and the full depth mooring at our disposal shows that these motions near the H E B B L E site are only very weakly bottom-trapped. The 500-m temperature record allows for a more accurate determination of the presence or absence of Gulf Stream events at the mooring site than does the satellite data, because the surface front is often displaced from the position of the subsurface front (Weatherly and Kelley, 1985). The record shows the presence of Stream events at mooring 776 during approximately 30% of the experiment (Fig. 2b) as determined by the number of days that the temperature at 500 m exceeded the mean temperature. If the Weatherly and Kelley assertion were correct then the remaining 70% of the record should show the strong westward current with relatively less variability. However, the flow is highly variable during these periods and includes a number of strong events comparable in intensity to the reversals ascribed to the Gulf Stream. The mean westward flow appears to be weaker than the 15 cm s- t needed by Weatherly's and Kelley's scenario as well. At 4000 m it is just - 7.5 cm s- 1, as calculated from days when the temperature at 500 m was below the mean temperature. The current bursts are typically - 1 5 to - 2 0 cm s-1, and sometimes as large as - 35 cm s- ~, and therefore cannot be attributed to lateral meanderings of a quasi-uniform current. Finally, as will be demonstrated in the next section, bottom motions are coherent over the entire array including mooring 775 which is out of range of the Stream. This

suggests a larger-scale process than was proposed by Weatherly and Kelley to explain the deep variability. Horizontal structure

To determine whether the fluctuations described in the previous section are locally generated or are a larger-scale phenomenon possibly related to Gulf Stream variability, the 4000-m records from all moorings in the ABCE were used to calculate deep empirical modes. Figure 4 shows the percent variance as a function of frequency explained by the first three modes. In the bands with central periods exceeding 15 days, first modes tend to be significant, suggesting that larger-scale processes may dominate motions at longer periods. Significant modes exist in the three bands centered at 120, 30, and 17 days and these bands will again be described. Figure 5 shows the current ellipses and coherence amplitudes calculated from the first mode for each band as well as a summary chart of the deep eddy and mean kinetic energies. In the 120-day band, the orientations of the ellipses are quite uniform over the array (i.e. along the isobaths) and all series are coherent with the modal series except those at mooring 775 where neither component is coherent. Ellipse orientations change significantly in the 17-day band in the manner of topographic waves (see e.g. Hogg, 1981) and, even in this band, most records are coherent with the modal series. Some interesting findings are the apparent relationship between the motions on the Rise and the motions at the Gulf Stream mooring, 780, and the near uniformity of the amplitude of the motions over the array. tO0

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The evidence from bottom photographs suggests that the most intense "abyssal storms" occur at the foot of the Rise in depths between about 4400 m and 5100 m (Tucholke et al., 1985). The mean and eddy kinetic energy distributions (lower right panel of Fig. 5), on the other hand, increase substantially toward the south (i.e. toward the Gulf Stream) from a plateau in the neighborhood of mooring 776. Figure 6 illustrates phase propagation of the motions in the 30-day band. Because the bottom slope changes over the array, a linear relationship between phase and cross-slope distance should not be expected even for linear plane waves. The slope varies less in the along-slope direction and an approximate along-slope wavenumber is indicated. Phase propagation is to the southwest with respect to the isobaths in this and the other two bands.

The motions described above exhibit many of the properties of topographic Rossby waves. Figure 7 illustrates some of these as a function of period and bottom slope (i.e. mooring number). The dispersion relations were calculated numerically from the linearized potential vorticity equation using parameters and profiles of buoyancy frequency from the locations of moorings 780, 776, and 775. For a given zonal wavenumber, k, the meridional wavenumber,/, increases considerably as the slope increases, and as motions are perpendicular to the wavenumber vector they should become more along isobaths. The three figures show how this alignment is a function of frequency. More rapid enhancement of l occurs for waves with lower frequencies and these motions tend to be more along isobaths, a property observed in the data. In particular, for the 30-day band the

LOW-FREQUENCYDEEPVARIABILITYANDTHEGULFSTREAM

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L780

Fig. 7. Dispersion relations for the near barotropic mode calculated numerically using estimated parameters for the three moorings in the 120-, 30- and 17-day bands. To the right of the dispersion curves the vertical structure is shown for each location. A zonal wavenumber of -0.01 km -1 was used in the calculation. Mooring labels for the curves are as in the 120-day band. show that the motions in many low-frequency bands are coherent over the entire array which includes a mooring in the Gulf Stream. The amplitudes of the motions at 4000 m are relatively uniform over the array, but the enhanced bottom trapping on the upper Rise indicates that there is some decay o f energy over the full water column to the north. The waves exhibit many of the properties of topographic Rossby waves with an associated shoreward flux of energy indicating that they might be forced in the vicinity of the Gulf Stream.

Gulf Stream variability The current records from the SME moorings and from nearby ABCE mooring 780 allow an exploration of the structure of the Gulf Stream jet and its near field over a zonal span of 170 km and a meridional span of 110 km, with a focus on the possibilities of generating topographic waves. As detailed in the Introduction, both the Gulf Stream and detached Gulf Stream rings have been pro-

312

posed as possible sources of wavelike motions observed on the Continental Rise and slope to the north of the Stream, but the present measurements are among the first to provide horizontal and vertical coverage capable of yielding quantitative estimates of scales and propagation characteristics of current variability in the Gulf Stream itself. Following a brief overview, some of the details of this structure will be explored.

Descriptive overview The Gulf Stream did pass through the array during much of the measurement period, as shown by ocean surface feature analyses by the National Ocean Service of the National Oceanic and Atmospheric Administration (NOAA). The analyses for the period May 1983-December 1983 show a sequence of large meanders in the Stream between 55 ° and 60°W, and during this period at least six warm-core and two cold-core Gulf Stream rings either formed in the immediate vicinity of the array or moved into the area. One warm-core ring (NOAA designation Ring 38) formed over the array in September 1983 and was reabsorbed several months later without having ever broken completely free of the Gulf Stream. The subsequent period of measurements from January 1984 to April 1984 was characterized in the NOAA analyses by a relative absence of large meanders and by little ring activity in the vicinity of the array. Thermocline temperature measurements at central mooring 557 indicate that the Gulf Stream oscillated about the center of the array with n o r t h south displacement amplitudes of order 50 km during the first eight months of measurements, and then shifted north by approximately 50 km in December 1983 and remained relatively steady to the end of the record (Hendry, 1988). Daily averaged flows reached speeds of more than 90 cm/s at the nominal 500-m levels on moorings 561 and 557, and more than 80cm/s at moorings 560 and 558. The nominal 500-m level at mooring 780 only 55 km to the west of mooring 561 was about 100 m deeper than for the SME measurements and showed a maximum speed of 68 cm/s for daily averaged currents. At the 4000m level, maximum speeds of the daily averaged

E.a WELSH ET A L

currents ranged from 34 cm/s at mooring 780 to 44 cm/s at mooring 558. Record mean flows had speeds of 20-30 cm/s at the nominal 500-m level, declining to about 6 cm/s at the 4000-m level (see Fig. 1). The mean flows at all levels of all moorings were directed within 20 ° of 80 ° true, and at all moorings except mooring 780 changes in the orientation of the mean flow with depth were less than 11 °. At mooring 780, the mean flow at 4000 m was rotated by about 30 ° into the southeast quadrant compared to thermocline level flows, contrasting with the northeast deep mean flows at moorings to the east (Fig. 1). This short zonal scale variation may reflect a non-zonal orientation of the Gulf Stream during the particular measurement period, or the influence of one of the New England Seamounts some 100 km to the southwest on the deep flow at mooring 780. In the meridional direction, qualitative differences were observed between southernmost mooring 560 and the more northerly sites, consistent with the presence of a 50-km halfwidth Gulf Stream jet centered somewhat to the north of this mooring. For example, during the last four months of observations, mooring 560 showed weaker currents and warmer, less variable temperatures at the 500-m level characteristic of a Sargasso Sea setting (Fig. 8), while strong flows and large variations in 500-m temperature were seen at the 500-m level of mooring 780 (Fig. 2c). Temporal variations in flow dominated the records. The current fluctuations relative to individual record means had root mean square (rms) speeds ranging from approximately 40 cm/s at the 500-m level to 15 cm/s at the 4000-m level. The relatively energetic near-bottom flow variability is notable in the context of wave generation through the interaction of the time-varying flows with the sloping bottom, but the coupling of this variability to external topographic wave modes or to any other wave motions depends on the frequency and wavenumber content of the variability. This is explored in the following section.

Space-time scales and propagation tendencies Spectral analyses of the records from the composite Gulf Stream array were carried out using overlapped 120-day long data pieces and spectral

LOW-FREQUENCYDEEP VARIABILITYAND THE GULF STREAM

313

MOORING 560 20.6

' 'APR' 1983

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~12.6

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4010m

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CM/SEC 'APR' 1983

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Fig. 8. Temperature at 495 m and stick plots at mooring 560.

quantities calculated by further averaging over three frequency bands centered at 80, 30 and 17 days. The goal was to derive estimates of overall time and space scales, recognizing that the dominant processes are not time-stationary over the year of measurements and that the dynamics of Gulf Stream variability are far from linear as assumed by conventional spectral analysis theory. The 120-day subsampling acts as a filter to reject the lowest-frequency energy in the records, but the three frequency bands account for approximately 80% of the total variance in the original records. This variance is partitioned with approximately 50-60°/0 in the 80-day band, 30-40% in the 30day band, and about 10°/0 in the 17-day band. The 30-day band will be discussed in detail because it approximates the most energetic range of frequencies observed at deeper levels on the Continental Rise and slope to the north, outside the near field of Gulf Stream meanders. In similar spectral analyses of 4000-m records from moorings 775 and 776 in the ABCE array, the relative energy in

the 80-day band was much reduced and more than half the variance summed across the three bands appeared in the nominal 30-day band. To examine the vertical structure of flow in the 30-day band, normalized cross-spectra were used to compute empirical modes combining both u and v components from all available vertical levels on single moorings. Using central mooring 557 as an example, two modes together described 93% of the normalized variance in the eight input series (Table 3). The first mode, accounting for 58% of the variance, gave vertically in-phase clockwise rotating current ellipses oriented northwest-southeast, with phases in u or v components differing by at most 14°. The second mode, accounting for 35% of the normalized variance, gave similar vertically phase-locked current ellipses with counterclockwise rotation and a northeast-southwest orientation. Thus the most economical empirical description of the current fluctuations at a single mooring is one involving vertically in-phase motions such as would be produced by the mean-

314

E.B. WELSH ET AL.

TABLE 3 Amplitudes (cm/s), coherence values and phase lags of u and v velocity components associated with the first two empirical modes in the 30-day band at mooring 557a inst. 5571 5572 5573 5574 inst. 5571 !5572 5573 5574

M o d e l : 30 days depth a m p u 445 10.7 850 6.9 1355 6.2 3959 5.3 Mode 2 : 3 0 days depth] a m p u 445 14.9 850 3.2 1355 4.6 I 3959 3.2

(explains 58%of the variance) cohu phu ampv cohv .32 0 22.0 .57 .56 4 9.5 .60 .62 5 7.9 .69 .63 1 5.7 .65 (explains 35%of the variance) cohu p h u a m p v c o h v .55 0 16.6 .33 .41 -12 7.6 .39 .35 -7 5.2 .30 .22 -4 3.3 .22

phv -141 142 -146 -155 phv 40 24 25 17

aThe percentage of normalized variance explained by each mode is shown in the table. The 95% confidence level for coherence amplitudes with zero true coherence is 0.59.

dering of a jet (or the passage of G u l f Stream rings) extending from shallow to deep levels with reduced speed at depth but without change in direction. The analysis was extended to include groupings of G u l f Stream moorings to investigate the properties of horizontally coherent structures in the 30day band. Various combinations were tried, and particular results involving the zonally oriented subset of moorings 780, 561, 557 and 559 are discussed below as a synopsis of the major results. Individual current components at moorings separated by the basic 55 km zonal spacing in general did show significant coherence in the 30-day band, and empirical modal analysis provides an effective overview. Empirical modes were computed combining u and v components from a single thermocline level (500 m or 800 m) and the 4000-m level at the four selected moorings. As pointed out by Wallace and Dickinson (1972), in cases where more than one coherent structure exists in a particular frequency band, the results of an empirical analysis depend critically on the specific selection of sensors. Using only one thermocline level equalizes the relative importance of deep and thermocline variability in the analysis, and minimizes the effects of differences in data recovery at different moorings. The 500-m and 800-m levels are highly correlated and the normalized cross-spectra used in the analysis disregard any differences in absolute am-

plitude, so the choice of either level to represent thermocline variability is somewhat justified. The results for the first mode, explaining 47% of the combined normalized variance of the 16 input time series, are shown in Table 4. The mode is dominated by zonal flow variations, and the zonal components show a systematic increase in phase lag from mooring 780 to more easterly sites at both thermocline and deep levels. This structure can be interpreted as a wavelike motion with zonal wavelength on the order of 1200 km and eastward phase propagation on the order of 40 km/day. The meridional component is less coherent with the dominant empirical mode. There is a hint of vertical structure in the v component, with a tendency for higher coherences at 4000 m. The uncertainties in the phases of the v components are large, but the numerical values of the phase lags suggest a wavelike structure with shorter zonal wavelength on the order of 300 km and with a contrasting westward phase propagation of order 10 km/day. The differences in the zonal and meridional components point to the existence of several spatially coherent structures in the 30-day band, with different structures tending to dominate each component. To explore this possibility, empirical modes were computed separately for u and v components at each of the thermocline and 4000-m levels (Table 5). The first u component modes account for 83% and 75% of the total variance at thermocline level and 4000-m levels, respectively, and TABLE 4 Amplitudes (cm/s), coherence values and phase lags of u and v velocity components associated with the most energetic empirical mode in the 30-day band at thermocline (500 m and 800 m) and 4000-m levels at moorings 780, 561,557 and 559a inst. 7802 7806 5611 5614 5571 5574 5592 5594

Mode 1 : 3 0 days (explains47%of the variance) depth amp u eoh u ph u amp v coh v ph v 507 10.3 .63 0 10.9 .35 33 4004 5.0 .51 17 5.0 .39 68 479 18.6 .78 30 8.7 .12 38 3993 5.4 .62 21 5.6 .50 -65 445 11.5 .40 46 7.0 .06 102 3959 5.6 .71 48 3.2 .21 -146 878 5.2 .45 49 6.9 .57 151 3988 4.4 .66 50 5.1 .61 144

aThe mode explains 47% of the normalized variance in the 30day band. The 95% confidence level for coherence amplitudes with zero true coherence is 0.59.

LOW-FREQUENCY DEEP VARIABILITY AND THE GULF STREAM

TABLE 5 Amplitudes (cm/s), coherence amplitudes and phase lags as for Table 5, but showing the most energetic empirical modes computed separately for zonal (u) and meridional (v) components and separately for thermocline and 4000-m levelsa

inst. 7802 5611 5571 5592

depth 507 479 445 878

inst. 7806 5614 5574 5594

depth 4004 3993 3959 3988

Mode 1 : 3 0 days, Thermoeline u (83%) u (53%) iampu :eohu phu ampv cohv 12.9 .71 0 15.9 .63 22.7 .95 30 21.2 .87 9.4 .88 43 3.8 .21 6.8 .80 53 5.6 .39 Mode 1 : 3 0 days, 4000 m u (75%) v (69%) ampu eohu phu ampv cohv 5.6 .64 0 6.5 .64 6.0 .75 45 5.9 .59 6.2 .85 82 5.1 .64 4.7 .75 85 6.3 .89

phv 0 30 68 -173

phv 0 -23 -110 162

aThe percentage of normalized variance explained by each mode is given in the table. The 95% confidence level for coherence amplitude with zero true coherence is 0.56 for the thermocline records and 0.59 for the 4000-m records.

both show eastward phase propagation with zonal wavelengths comparable to those suggested by the combined analysis. The results for the zonal variability are thus quite robust. The two v component modes show different behaviors. The thermocline level v component first mode explains 53% of the total variance and resembles the thermocline u component mode in that it shows eastward phase propagation, although it is somewhat localized to the westernmost two moorings in the sub-array. The 4000-m v component mode shows spatially uniform amplitudes and coherences, and quite clearly indicates the westward phase propagation hinted at in the combined mode. The inferred zonal wavelength is of order 400 km, giving a phase speed near 13 km/day for the nominal 30day periodicity. In summary, as far as spatial propagation is concerned, the most efficient empirical description shifts to considering zonal and meridional components separately. The single long-wave structure dominating the propagation of u component variability appears to extend from thermocline to deep levels with little change of phase and propagates rapidly to the east. Thermocline v component variability seems to be dominated by one mode which also propagates to the east, but deep v component variability is dominated by a second

315

mode which has short zonal scales and propagates to the west. The westward propagating mode is of special interest to the question of generation of topographic waves because its structure is quite similar to that of the topographic waves observed to the north. Hendry (1982) discussed the propagation characteristics of low-frequency deep flow variability from moored observations at 4000 m and deeper in a 90-km scale zonal array near 40.5°N and 55°W. This site seemed to be located somewhat to the north of the mean axis of the Gulf Stream in that the observed mean zonal flows were to the west. Both u and v components showed westward phase propagation tendencies, in contrast to the results at 60°W, but there was a similar disparity in the horizontal scales of u and v component variability which suggested that there were several organized structures in the deep flow at 55°W. Field work presently being undertaken under the sponsorship of the Office of Naval Research in the Gulf Stream Synoptic Prediction program should allow a much more comprehensive understanding of this interesting structure. The increased understanding of the scales of variability in the near field of the Gulf Stream provided by the combined ABCE/SME observations should allow progress to be made in constructing realistic models of the generation of topographic waves of special relevance to the H E B B L E area. Conclusions Using current meter data collected in the Abyssal Circulation Experiment, deep motions from a region including the Gulf Stream and extending north to the base of the Continental Rise have been described. Gulf Stream variability was examined by supplementing the ABCE records with data collected in the Synoptic Mapping Experiment. The possibility that Rise motions are associated with Stream variability was then explored. Bottom motions at mooring 780, in the Gulf Stream, are usually to the east and are most often the deep manifestations of a vertically coherent Stream event. Motions at mooring 775, the northernmost mooring, are wavelike and bottom intensified with fluctuations sometimes reversing the

316 direction o f the w e s t w a r d m e a n flow at the deepest i n s t r u m e n t level. M o t i o n s at m o o r i n g 776 are o f two types. The first is clearly related to the passage o f a G u l f S t r e a m event over the m o o r i n g site. Such events are surface intensified a n d usually reverse the direction o f the b o t t o m flows. The second type is a nearly b a r o t r o p i c d i s t u r b a n c e that does n o t coincide with the presence o f a G u l f S t r e a m event at the m o o r i n g site. The empirical m o d e s o f vertical structure s u b s t a n t i a t e w h a t is visually a p p a r e n t in the c u r r e n t records. In an analysis o f the deep h o r i z o n t a l structure over the region s a m p l e d by the A B C E instruments, m o t i o n s at 4000 m were f o u n d to be c o h e r e n t over the entire array, including the G u l f S t r e a m region, in a n u m b e r o f frequency bands. A c o m p a r i s o n with t o p o g r a p h i c wave t h e o r y revealed that the o b s e r v e d m o t i o n s exhibit p r o p e r t i e s o f nearly b a r o tropic t o p o g r a p h i c R o s s b y waves. The direction o f phase p r o p a g a t i o n is to the southwest in all bands, indicating that energy p r o p a g a t i o n is directed s h o r e w a r d . This is suggestive o f forcing in the vicinity o f the G u l f Stream. W e s t w a r d p r o p a g a t i o n was also f o u n d at the 4000-m level within the G u l f S t r e a m b u t only for the m e r i d i o n a l c o m p o n e n t . A c o m p a r i s o n o f the w e s t w a r d p r o p a g a t i o n in the S t r e a m to t h a t associa t e d with waves on the Rise shows the alongi s o b a t h w a v e n u m b e r s to be c o m p a r a b l e . In a d d i tion, it is the m e r i d i o n a l c o m p o n e n t o f the velocity at the G u l f S t r e a m m o o r i n g from the A B C E a r r a y which was coherent with m o t i o n s on the Rise in the 30-day band. H o w e v e r , e a s t w a r d p r o p a g a t i o n o f m e a n d e r s is usually o b s e r v e d in satellite d a t a and, therefore, empirical m o d e s were c o n s t r u c t e d from all records from four G u l f S t r e a m m o o r i n g s to e x a m i n e the vertical structure o f the w e s t w a r d p r o p a g a t i n g features. This analysis i n d i c a t e d that the w e s t w a r d p r o p a g a t i o n is o b s c u r e d at the u p p e r level by surface intensified e a s t w a r d p r o p a g a t i n g features. The discovery o f w e s t w a r d p r o p a g a t i o n within the deep S t r e a m m i g h t be seen to a d d some weight to the idea t h a t the S t r e a m can directly force the external wave field. H o w e v e r , this sense o f p r o p a g a t i o n c o u l d also arise f r o m the wave field, generated b y some o t h e r m e c h a n i s m , acting b a c k on the Stream. In o u r study we have n o t yet been

E.B.WELSHET AL. able to distinguish between cause a n d effect with any certainty.

Acknowledgements E.W. a n d N . H . a c k n o w l e d g e the s u p p o r t o f the Office o f N a v a l R e s e a r c h t h r o u g h c o n t r a c t s N00014-85-C-0001, NR083-004, N00014-84-C0134, NR083-400, N00014-82-C-0019 a n d N R 0 8 3004. This is c o n t r i b u t i o n n u m b e r 6591 o f the W o o d s H o l e O c e a n o g r a p h i c Institution.

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LOW-FREQUENCY DEEP VARIABILITY AND THE GULF STREAM

Numerical simulation of transient boundary-forced radiation, Part II. The modon regime. J. Phys. Oceanogr., 18: 1546-1569. McWilliams, J.C. and Flierl, G.R., 1979. On the evolution of isolated, nonlinear vortices. J. Phys. Oceanogr., 9: 11551182. Pedlosky, J., 1977. On the radiation of mesoscale energy in the mid-ocean. J. Mar. Res., 24: 591-600. Schmitz, W.J., Jr., 1980. Weakly depth-dependent segments of the North Atlantic circulation. J. Mar. Res., 38:111-133. Schmitz, W.J., Jr., 1984. Observations of the vertical structure of the eddy field in the Kuroshio Extension. J. Geophys. Res., 89: 6355-6364. Talley, L.D., 1982. Instabilities and Radiation of Thin Baroclinic Jets. Ph.D. thesis, Joint Program in Oceanography and Ocean Engineering, Woods Hole Oceanographic Institution, 233 pp.

317 Talley, L.D., 1983a. Radiating barotropic instability. J. Phys. Oceanogr., 13: 972-987. Talley, L.D., 1983b. Radiating instabilities of thin baroclinic jets. J. Phys. Oceanogr., 13: 2161-2181. Thompson, R.O.R.Y., 1977. Observations of Rossby waves near site D. Prog. Oceanogr., 7: 135-162. Tucholke, B.E., Hollister, C.D., Biscaye, P.E. and Gardner, W.D., 1985. Abyssal current character determined from sediment bedforms o n the Noval Scotian Continental Rise. Mar. Geol., 66: 43-57. Wallace, J.M. and Dickinson, R.F., 1972. Empirical orthogonal representation of time series in the frequency domain, Part I. Theoretical considerations. J. Appl. Meteorol., 11: 887-892. Weatherly, G.L. and Kelley, E.A., 1985. Storms and flow reversals at the Hebble site. Mar. Geol., 66: 205-218.