Measurements by the Multi-Scale Profiler (MSP) at seven stations spanning the Straits of Florida characterize levels and patterns of internal wave activity and mixing in this vertically sheared environment. Contrasting properties suggest five mixing regimes. The largest and most vast is the interior regime, where the background flow has an inverse Richardson number (Ri−1) ranging up to 0.55, shear is dominated by fluctuations that are 1–4 times stronger than in the open ocean, and turbulent diffusivities are similarly moderate at (1–4) × 10−5 m2 s−1. The high-velocity core of the current, near the surface at midchannel, is associated with weak mixing. To its west is a zone of high mean shear, where strong stratification results in background Ri−1 of only 0.4, fluctuations are weak, and diffusivity is moderate. Intermittent shear features beneath the core have mean Ri−1 > 1 and strong turbulence. Two regimes are related to channel topography. Adjacent to the steep eastern slope, finescale shear is predominately cross-channel, and turbulence varies from nearly the weakest to nearly the strongest. Within 100 m of the channel floor, turbulent stratified boundary layers are mixing at (2–6) × 10−4 m2 s−1 to account for one-half of the section-averaged diffusivity. Using existing finescale parameterizations, observed dissipation rates can be predicted within a factor of 2 for most of this dataset, despite significantly strong mean shear and generally anisotropic and asymmetric fluctuations. The exceptions are in the high mean shear zones, where total rather than fluctuating shear yields reasonable estimates, and in some of the more turbulent regions, where shear underestimates mixing. Given its overall moderate levels of turbulence and finescale shear, the Florida Current is not a hot spot for oceanic mixing.
The Florida Current is a highly sheared, energetic flow through confined topography. Such an environment has potential for strong mixing. Measurements from a transect across the Straits of Florida at 27°N characterize the levels and patterns of turbulence and shear in the current.
The background state of the global ocean is one of weak mixing. Measurements of viscous dissipation rates ɛ in the midlatitude Pacific pycnocline during the Patches Experiment (PATCHEX) yielded a diapycnal diffusivity, Kρ = 0.2ɛ/N2 (Osborn 1980), of only 4.3 × 10−6 m2 s−1 (Gregg and Sanford 1988). Similar microscale measurements during the North Atlantic Tracer Release Experiment (NATRE) yielded 1.1 × 10−5 m2 s−1 (Toole et al. 1994), consistent with the observed thickening of tracer streaks at the site (Ledwell et al. 1998). Presumably, turbulence at these sites was driven by internal wave shear, which for NATRE was at twice the spectral level of Garrett and Munk (1972, 1975; hereafter referred to as GM76). During PATCHEX, shear closely approximated GM76 conditions, for which the scalings of Gregg (1989) and Polzin et al. (1995) predict Kρ ≈ 5 × 10−6 m2 s−1.
Higher diffusivities occur where internal wave activity is enhanced by mesoscale features or by interactions with topography. For instance, the PATCHEX North dataset taken beneath a coastal jet off northern California—but well away from direct influences of topography, background shear, or atmospheric forcing—yielded Kρ = 3.9 × 10−5 m2 s−1. Near the steep slope of Fieberling Guyot between 700 and 1300 m, Polzin et al. (1995) found (6.7–12.4) × 10−5 m2 s−1; 10 times greater than that at similar depths farther from the guyot.
Stronger topographic effects lead to extreme values, such as 2.5 × 10−3 m2 s−1 in the Denmark Straits (Oakey and Elliott 1980) and 5.5 × 10−2 m2 s−1 in the hydraulically controlled flow through the Strait of Gibraltar (Wesson and Gregg 1994).
High mean shear can dominate turbulent production above the core of the Equatorial Undercurrent (EUC) in the central Pacific. Peters et al. (1988) found Kρ ranging from about 10−4 to over 10−3 m2 s−1. Parameterizations in terms of the mean Richardson number, Ri = N2/〈dU/dz〉2, account for much of the variability, particularly for Ri < 0.4. However, when the same site was reoccupied over two years later, mean shear was weaker and was exceeded by internal wave shear, and dissipation rates and diffusivities were 10 times lower (Peters et al. 1994) and were correlated to total, rather than mean shear (Peters et al. 1995).
The Florida Current is an excellent setting to study all of these mechanisms of enhanced mixing. The conditions of strong flow, nearby topography, and vertical and lateral shear are in sharp contrast to the remotely forced ocean pycnocline. Because the current is part of the Gulf Stream, it is important to investigate its levels of turbulence and mixing.
In this paper we relate observed turbulent dissipation and finescale shear to each other and to attributes of the background flow. First, the collection and treatment of the measurements are discussed (with some details in the appendix), and the background environment is described using these as well as historical observations. Patterns and levels of dissipation and shear are presented, and their relationship is tested against the internal wave scalings to assess the turbulent mechanisms. Five mixing regimes are identified, their distinguishing characteristics are compared, and their contributions to the Florida Current are analyzed.
The survey was conducted from the R/V Endeavor between 3 and 17 June 1990 along 27°N, where the current fills an 80-km-wide, 800-m-deep channel between Florida and Little Bahama Bank (Fig. 1). The primary instrument was the Multi-Scale Profiler (MSP), a freely falling dropsonde carrying CTD, velocity, and turbulence sensors (Winkel et al. 1994, 1996). It was deployed during daylight hours, from 0700 to 1900 local time (1100–2300 UTC). Most of the 80 MSP drops were made at seven stations spanning the channel (Table 1 and Fig. 2). Profiling routinely came to within 5–15 m of the bottom, judging from telemetry pinged to the ship to track and recover the MSP. Time between drops was 1.5–3 h, depending on station depth. Nighttime measurements by a SeaBird CTD (Seim et al. 1999) and continuous velocity profiles from the vessel's RD Instruments ADCP supplement the MSP data.
Representative profiles from MSP drops are shown in Fig. 3. Finescale hydrography was measured by SeaBird temperature and conductivity sensors, finescale horizontal velocity by a two-axis Neil Brown acoustic current meter (ACM), and turbulent velocity by a pair of airfoil probes. The low noise of the ACM enables it to resolve fluctuations from scales of 1 km down to 0.5 m; however, it detects only relative flow, so the platform motion must be reproduced to yield oceanic velocity (Winkel et al. 1996). Absolute velocities, estimated by comparison with ADCP profiles, are generally accurate to within 0.1–0.2 m s−1. East and north components, u and υ, are essentially across- and along-channel. Viscous dissipation rates ɛ were computed at 2-m depth increments from airfoil spectra, and were then averaged in 10-m bins to form ɛ10 profiles.
Finescale velocity and density profiles are assumed to represent internal wave fluctuations superimposed on a subinertial background. As discussed in the appendix, the background flow and stratification were estimated by time-averaging of vertically smoothed drop profiles, yielding station-mean profiles 〈ũ〉, 〈υ̃〉, and 〈〉. The smoothing was necessary because most stations were occupied for just a few days during which about 10 drops were made (Fig. 2), and time-averages were not adequate; owing to subinertial variability at stations 1, 2, and 7, even fewer drops spanning less time were included in their separate mean profiles for before 10 June versus after 9 June.
Fluctuation profiles u′ = u − 〈ũ〉 and υ′ = υ − 〈υ̃〉 for each drop (Fig. 4) were first-differenced over 10-m intervals, and the resulting squared shears S′210 = S′210x + S′210y were time-averaged to form shear variance profiles 〈S′210〉 at each station. Similar treatment of u and υ yielded total variance profiles 〈S210〉. Mean shear has squared amplitude 〈S̃〉2, to which 〈S̃x〉 = Δ〈ũ〉/10 m as well as 〈S̃y〉 = Δ〈υ̃〉/10 m contributes.
Although the sampling was hardly synoptic, station-mean profiles are consistent with historical observations, and will be used to illustrate the subinertial background. For stations 1, 2, and 7, paired mean profiles were averaged together to form single profiles for display. For contour plots of mean hydrographic fields, CTD averages at 5-km intervals were included between MSP stations.
b. Large-scale structure
The bottom on the channel's west side is smooth at 27°N, gently sloping down across isobaths that parallel the current (Fig. 1). The channel shoals from 800 m off Miami to 740 m at the terminus of the straits, 40 km north of the survey site. Midchannel depth at 27°N is just over 750 m (Fig. 5). On the east side, the bottom between the 720-m and 620-m isobaths is bumpy and uneven, and then is fairly smooth where the cross-channel slope steepens to 0.025 at 500 m. The east bank rises sharply from 450 m, initially sloping up at 0.11 and reaching 0.32 toward the surface. The channel narrows from the south with the steep wall of Little Bahama Bank oriented 20° west of north, resulting in convergence in the cross-channel flow (Leaman et al. 1987).
The high-velocity core of the current is near the surface on the channel's west side, where northward speeds exceeding 1.6 m s−1 are attained (Fig. 5a). The velocity maximum stays near the surface to the west, but deepens eastward. Vertical shear is highest at the base of the core and on its west side. Toward the east, shear is more uniform but diminished in the deeper waters; above 150 m, its sense is negative.
The axis of the current divides anticyclonic flow on its east from cyclonic flow on its west. The lateral shear is characterized by the Rossby number, Ro = ∂xυ̃/f, where f = 6.6 × 10−5 s−1 at 27°N. Magnitudes are highest on the cyclonic side, with Ro varying from 0.7 to over 1 in the upper 100 m. On the anticyclonic side Ro is negative, with magnitude diminishing from 0.5 at the surface to 0.1–0.2 at depth. By definition, Ro = 0 at the current axis.
Mean isotherms and isopycnals slope up toward the west (Figs. 5b,d), in the proper sense for thermal wind balance with the vertical shear. At any given depth, the east side is warmer than the west side. The salinity maximum between 100 and 200 m is saltier toward the east (Fig. 5c). Water colder than θ = 6°C or denser than σθ = 27.5 kg m−3 seldom penetrates the Straits of Florida north of Miami.
The temperature–salinity relation varies across the channel, with relatively fresher water at a given density on the west side (Fig. 6). Schmitz and Richardson (1991) find that the fresher water, including that overlying the salinity maximum, originates in the equatorial or southern Atlantic; the higher salinities are traced to subtropical water from the North Atlantic, which subducts under the southern water mass as they collide in the northern Tropics before entering the deeper passages of the Caribbean. For the 12°–24°C temperature range, most of the transport originates in the North Atlantic, including a thick layer of 18°C water. Leaman et al. (1995) conclude that much of the 18° water enters through Northwest Providence Channel (NWPC) and through Santaren Channel (east of Cay Sal Bank; Fig. 1) via Old Bahama Channel, bypassing the Caribbean route argued by Schmitz and Richardson (1991). Deeper, most of the water colder than 12°C comes from the South Atlantic, with the notable freshening influence of Antarctic Intermediate Water (AAIW) in midchannel.
c. Conditions during MSP survey
The Florida Current flows persistently through the survey site, but exhibits considerable variability in its strength and its structure. The Subtropical Atlantic Climate Studies (STACS) program of the 1980s employed a variety of measurement systems to monitor the current's heat and volume transport past this location (Molinari 1985). PEGASUS dropsonde profiles yielded a mean transport of 31.7 ± 3 Sv (1 Sv ≡ 106 m3 s−1) (Leaman et al. 1987), and moored current meters (Lee et al. 1985) and submarine cables (Larsen and Sanford 1985) gave similar results. Transport fluctuations on weekly scales were comparable to the yearly variation of 4 Sv. Velocity and temperature varied most strongly on the west side of the channel (near MSP stations 1 and 2), often in association with meandering of the current core (Leaman et al. 1987).
The total transport inferred from the MSP mean profiles is 31.6 ± 4 Sv (given uncertainties in absolute velocities and interstation interpolation), with cross-channel distribution similar to that for STACS shown in Fig. 8 of Leaman et al. (1989). Transport by temperature was also comparable, except in the two warmest bins: STACS reported an 8.6-Sv peak at 24.5°–27°C but no warmer flow, while MSP found only 3.9 Sv in this bin but another 3.8 Sv above 27°C (Fig. 7). The MSP survey resolved the peak in the layer containing 18° water, most of which was transported through the east half of the channel, consistent with STACS findings.
The subinertial background specific to this study had features not highlighted in the historical observations. Some of this is due to the finer vertical resolution of MSP, but mostly it relates to the established variability of the current. Of particular interest was an eastward shift in the current's axis that evolved throughout the occupations of the three western stations. Some relevant aspects of the hydrography will be described before discussing the meandering.
Interleaving of the fresher western water with the saltier midchannel water is evident near the salinity maximum, between 100 and 150 m, in many drops at stations 2 and 3. Centered about local minima in salinity profiles were layers 5–20 m thick, which appear in θ–S plots between the characteristic western and central-to-eastern water masses (as for station 2a in Fig. 6). Weaker intermingling was found above 100 m at all stations. Well below the salinity maximum, intrusions of slightly saltier water occurred at various depths in drops of stations 3–5. The deepest of these involved AAIW as the fresher water mass.
2) Boundary layers
Homogeneous or minimally stratified boundary layers extend down from near the surface in all drops. The maximum penetration varies with station (and drop) from 10 to 55 m (Fig. 5a). Data from these layers are excluded from subsequent analysis.
Bottom homogeneous boundary layers (HBLs) were found in many drops, but not all. Because MSP profiles stopped 5–15 m above the bottom, the thicknesses of these layers are uncertain. The shallowest HBL encounter at each station is indicated on Fig. 5a. At stations 1 and 7, little if any HBL was apparent, as stratification reached the bottom of all but a few drops. Station 2 had HBLs in some drops, but they were thinner than those at stations 3–5; the thickest, at over 60 m, occurred at station 4. A CTD survey during the experiment revealed a benthic front between stations 2 and 3, where the density of the HBL jumped abruptly by 0.2 kg m−3 (Seim et al. 1999).
Atop many of the observed HBLs were turbulent layers or interfaces, which were typically more stratified and sheared than the water above (and below). These turbulent stratified boundary layers (TSBLs) account for much of the mixing in the channel, as will be discussed later. The strongest occurred at station 3 within the deep shear region and at station 7 at the base of the east channel wall (Fig. 8).
3) Shift of current axis
Midway through the MSP cruise, from 9 to 11 June, the current underwent a 2-Sv drop in transport while its core moved 10 km east toward midchannel. According to submarine cable monitoring, transport averaged around 32 Sv just before the shift and 30 Sv just after (J. Larsen 1995, personal communication). Transects through the three western MSP stations yielded ADCP profiles that show the position and structure of the stream. Within the 1.5 m s−1 velocity contour, the flow was relatively pluglike, and that portion of the core was near station 2 on 7 June before moving east of station 3 by 11 June (Winkel 1998). Between these dates, variations are evident in the shear structure at and below the base of the core.
The evolving subinertial flow complicated the separation of data from the western stations into background and internal wave components. Forming two sets of mean profiles for stations 1 and 2—one for drops before 10 June and another for those on or after 10 June (Fig. 2)—removed much of the variability. Most dramatic was the change in northward velocity at station 2 (Fig. 4); although the flow was still evolving during the second occupation, the profiles are much more similar to one another than to those of the first occupation. Regarding station 3, in the two drops made after 10 June—and nearly two days apart—the deep shear and vigorous TSBL found in the earlier 10 drops were absent; these two were excluded from analysis.
Changes in density profiles and θ–S relations are consistent with the eastward shift. For stations 1–3, later profiles are denser at all depths than earlier profiles, as if the background structure had moved offshore. The later θ–S relation for station 2 is characteristic of the west Florida Current (Schmitz and Richardson 1991), whereas earlier drops exhibited interleaving with the saltier midchannel waters (Fig. 6). After 10 June, such interleaving was found at station 3 where θ–S curves from the later drops zigzag between the western fresh and the central salty characteristics.
Conditions also changed at eastern station 7 in the week between its two occupations. Mean density and velocity profiles differed, and water was fresher near the surface and saltier at middepth the second time around. Mixing and internal wave activity above the TSBL were much stronger after 10 June. There is no evidence to establish whether these changes are directly linked to the shift in the current, or instead to unrelated variability near Little Bahama Bank (see Leaman and Molinari 1987).
3. Patterns of turbulence and shear
Turbulent mixing in the Florida Current is represented by vertical diffusivities computed from MSP measurements of dissipation and stratification. Distributions are presented by contouring station-mean profiles across the channel. General tendencies are noted, and areas of strong or weak activity are emphasized. Patterns of turbulence are compared to those of finescale shear components to understand which processes were at work.
Station-mean profiles of diffusivity 〈Kρ〉 = 0.2〈ɛ10〉/〈N210〉 are computed using unsmoothed mean stratification to match the scale of the dissipation estimates. Finescale shear stability is discussed in terms of squared Froude numbers 〈F̃r〉2 = 〈S̃〉2/〈Ñ2〉 and Froude variances 〈Fr210〉 = 〈S210〉/〈Ñ2〉 and 〈Fr′210〉 = 〈S′210〉/〈Ñ2〉. The smoothed stratification matches the scale of the mean shear. Stratification over 80- to 160-m-thick intervals is represented by the vertical average 〈N210〉. To reduce notational clutter, angle brackets are excluded from station-mean profiles henceforth, unless required in specifications and definitions.
Over much of the section, mixing seems to be driven by the internal wave field, based on the similarity of observed dissipation rates with those predicted by the scalings of Gregg (1989) and Polzin et al. (1995). West of the core, the maximal mean shear was stabilized by high stratification, but it did influence turbulent production. Topography appears to affect internal waves and mixing at the easternmost station.
a. Vertical diffusivity and turbulent dissipation
Averaged over all MSP stations, Kρ = 6.7 × 10−5 m2 s−1, including TSBLs near the bottom, and avoiding homogeneous boundary layers at the surface and bottom. Such diffusivity implies moderate but not strong mixing by oceanic standards.
Turbulence was not distributed uniformly across the MSP section. Most of the high diffusivities occurred in the TSBLs, which occupy only 7% of the total record; their average Kρ = 4.2 × 10−4 m2 s−1 is 10 times the average in the remainder of the stratified water. Further variability is revealed in cross-sectional contour plots.
The highest diffusivities, Kρ > 10−4 m2 s−1, are mainly within 100 m of the bottom, but are also scattered at lesser depths (Fig. 9a). They are associated with elevated dissipation, ɛ10 > 10−8 W kg−1, found below 200 m within moderate stratification of N210 < 10−4 s−2 (Figs. 9b,c). Similar high ɛ10 occur above 200 m outside the core, but result in Kρ of only (1–10) × 10−5 m2 s−1 owing to the larger N210. Lower ɛ10 values inside the core yield minimal diffusivities of (0.7–7) × 10−6 m2 s−1. Elsewhere, weak-to-moderate Kρ of (0.4–10) × 10−5 m2 s−1 tend to follow patterns of ɛ10.
The high Kρ and ɛ10 near the bottom are due to TSBLs, which vary in character and thickness with station and from drop to drop. Some lie atop HBLs, others extend at least to the bottom of the drop. The strongest are marked by shear, stratification, and especially dissipation that are elevated in contrast to waters immediately above. Those of stations 3 and 7 are 30–70 m thick. (See the examples in Figs. 3 and 8). At station 2, they appear as 2–15-m-thick interfaces that cap mixed or weakly stratified bottom layers (i.e., where N < 0.002 s−1); the few detected at station 1 are similar but thinner. At stations 4–6, TSBLs tend to be 10–30 m thick, lying atop HBLs that are up to 60 m thick. Section maxima of ɛ10 > 10−7 W kg−1 occur in the HBLs of stations 4 and 5 and in the TSBL of station 3 (Fig. 9b).
b. Finescale shear
Patterns of finescale variance are examined to understand the observed distribution of turbulence and mixing. The subinertial background shear S̃2 can generate turbulence directly, or it can affect the downscale transfer by altering or reinforcing the internal wave field. Internal wave levels are represented by the fluctuating shear variance S′210 and its Froude counterpart Fr′210.
1) Mean shear
The highest S̃2, in excess of 10−4 s−2, are found above 150 m adjacent to the west side of the core and in the TSBL of station 3 (Fig. 10a). For these regions, and also for the local maximum near 220 m at station 2, the northward component dominates the eastward. The maximum mean shears of 0.01–0.018 s−1 are comparable to those in the Gulf Stream off New England (Gregg and Sanford 1980) and above and below the EUC in the Pacific (Peters et al. 1995). Lesser S̃2 of (1–10) × 10−5 s−2 occur deeper at stations 1 and 2, within and under the central core, and at station 7 near the surface and the bottom; in the latter two areas, the east mean component contributes significantly. A vast region of S̃2 < 10−5 s−2 covers much of stations 4–7.
Areas of F̃2 > 0.5 are of limited extent: they occur at the base of the shallow high S̃2 of stations 1 and 2, within the deeper high S̃2 of stations 2 and 3, deep in midchannel, and immediately below the central core (Fig. 11a). Maxima exceeding 1 occupy TSBLs at stations 3 and 4. Moderate 2 of 0.2–0.5 occur over most of stations 1 and 2, in the lower 100–200 m of stations 4 through 7, and at middepths of stations 3 and 4. Most of the upper waters of the three easternmost stations—and the highly stratified core—have 2 < 0.2, including large areas with 0.05 or less.
2) Fluctuating shear variance
The basic pattern in Fig. 10b is that S′210 > 10−4.5 s−2 above 200 m and S′210 < 10−4.5 s−2 below 200 m. Exceptions are in the TSBL of station 3 and in the core at station 4, which have S′210 respectively higher and lower than those nearby. Minima of less than 10−5 s−2 occur deep at station 6 and above the TSBL of station 7. Over most of the section, S′210 is at least twice the mean component; only in western regions where S̃2 > 3 × 10−5 s−2 does the mean exceed S′210.
Contouring Fr′210 reveals the relative strength of the fluctuating shear by removing the dependence on mean stratification (Fig. 11b). Maxima exceeding 1 lie beneath the core, and deep at stations 3–6. Moderate Fr′210 of 0.5–1 cover most of stations 2–5 below 150–200 m, and the lower 100–200 m of stations 6 and 7. Weaker Fr′210 occur at stations 6 and 7 away from the bottom, and within and west of the lower core. The lowest values, less than 0.2, are in the upper core, reminiscent of the minimal diffusivity there (Fig. 9a). Note also similar middepth patterns of west-to-east weakening in Fr′210 and Kρ.
3) Total shear variance
Patterns of total shear variance (Fig. 10c) are similar to those of the fluctuating component, except where mean shear is high. The most notable difference is the larger expanse of S210 > 10−4 s−2, including the regions of high S̃2 west of the core and deep at station 3. Thick intervals of Fr210 > 1 appear under the core and deep at stations 2–7 (Fig. 11c). Over most of the section, 0.5 < Fr210 < 1. Minima of Fr210 < 0.5 occupy only the upper core and some upper waters of stations 6 and 7.
4) Comparison with GM76
Fluctuating shear variance in these data is generally 1.5–3 times the GM76 counterpart of Fr210GM = 0.33. The greatest excesses lie under the central core and deep in midchannel. Only in the current core are variances below GM76 levels.
The shear deviates from GM76 assumptions of vertical symmetry and horizontal isotropy. Clockwise variance is 2–4 times the anticlockwise component over much of the section, and is the lesser only shallow at station 7 (Fig. 12). Cross-channel shear variance is more than twice along-channel in the upper 200 m of stations 5 and 6, and particularly at station 7 where it is up to 4 times higher. There are regions where along-channel shear variance is greater than cross-channel, but only in the TSBL of station 3 is it twice as high.
c. Internal wave scalings of dissipation
Similarities in the patterns of Kρ and Fr′210 suggest that mixing is modulated by the strength of the internal wave field. The parameterizations of Gregg (1989) and Polzin et al. (1995) predict how dissipation rates produced by low-wavenumber shear will vary with non-GM76 conditions. Gregg employs the 10-m first-differenced shear for
where N0 = 0.005 24 s−1, and with ɛ0G = 7 × 10−10 W kg−1 established empirically to match assorted observations within a factor of 2. Polzin et al. focus on the low-wavenumber band up to kc, the point at which Fr′2(kc) = 0.7 in the fluctuation spectrum (which occurs at kcGM = 0.1 cpm for GM76), such that
where ɛ0P = 6.7 × 10−10 W kg−1 is the GM76 expectation [their Eq. (11)] for N = N0 at 27°N. The observed shear-to-strain ratio Rω = Fr′2(kc)/St2(kc) is used in
to account for non-GM76 frequency content (higher-order terms are necessary if Rω < 1.1); C = 1 with Rω = 3 for GM76. Strain-based corrections are addressed in Winkel (1998), but are excluded here because they are minor (0.8 < C < 1.5) in regions where strain estimates are reliable (at stations 3–6 below 200 m).
Both scalings are based on the analytic model of Henyey et al. (1986) of the downscale energy flux from internal waves evolving within a background shear consisting only of larger-scale internal waves. However, Polzin et al. (1996) estimate that subinertial shear contributes significantly to the modeled flux in flows with mean Fr2 exceeding 0.05 (i.e., Ri < 20). A simple way to include mean shear contributions in ɛiwG and ɛiwP is to use total Froude variances and spectra in place of the fluctuating quantities. This approach also establishes upper bounds for the scalings, in that it avoids underestimation of internal wave shear related to the uncertain removal of subinertial flow from the measurements.
Within 100-m intervals at each station, observed average ε compared with ɛiwG and ɛiwP computed first with the fluctuating shear and then with the total shear. IntervalɛiwGare vertical averages of 10-m gridded ɛiwG, which were generated via (1) from station profiles 〈Fr′210〉 or 〈Fr210〉 and N2 = 〈Ñ2〉. To evaluate ɛiwP via (2), kc was inferred by accumulating interval spectra until Fr′2(kc) = 0.7 or Fr2(kc) = 0.7, and N2 was taken as〈N210〉; GM76 frequency content was assumed by fixing Rω = 3.
Ratios ε/ɛiwP for the fluctuating shear case are contoured in the upper panel of Fig. 13; the same features occur for ε/ɛiwG computed with Fr′210 (not shown). For most of stations 3–6—about 63% of the section—agreement to within a factor of 2 is realized. Above 200 m at station 5 and above 120 m at station 7, ɛiwP underestimates ε by factors of 2–4. Over the two western stations and most of station 7, ɛiwP is 4–8 times too low, and more than 8 in a few spots (including the TSBL of station 3). Use of total shear variance results in higher estimates and better agreement with ε in regions of high mean shear. Ratios ε/ɛiwG, computed with Fr210, are now within a factor of 2 over most of stations 1–3 (Fig. 13, lower panel). Station 7 also shows improvement, although beneath 100 m the scaling still falls short. Elsewhere, the favorable comparison with fluctuation-based ɛiwP (upper panel) is conserved, aside from small regions within and under the core where ɛiwG > 2ε. Computation of ɛiwP using total Froude spectra yields similar results (not shown) except in regions of high mean shear or strong turbulence, where the spectral representation of large-scale shear variance is inadequate (Winkel 1998).
The fair agreement, overall, of ɛiwP and ɛiwG with observed dissipation rates was not anticipated. The background conditions of strong flow, nearby topography, and vertical and lateral shear are in sharp contrast to the remotely forced ocean pycnocline that Henyey et al. (1986) assume in their simulations and model. Close matching of ε by ɛiwP (computed with fluctuating shear) occurs even in broad regions where mean shear is such that 2 > 0.2. Regardless of the processes driving the downscale energy flux, the resulting dissipation here is predicted with the same skill—to within a factor of 2—that Gregg (1989) claims for ɛiwG. The high mean shear zones are an exception, but there it takes only a reasonable substitution of total for fluctuating shear variance to compute acceptable estimates.
4. Mixing regimes
The regional variability of turbulent and finescale characteristics in the flow can be examined by specifying five mixing regimes (Fig. 14). Shear instability appears to be the primary turbulent mechanism in all regimes; contrast occurs in the level and composition of the shear that drives the mixing.
Interior (N): This is the large region of moderate Kρ and Fr′210, in which both fluctuating and total shear variance are good indicators of ɛ.
High mean shear zones (S): In these areas of maximum mean shear, dissipation rates exceed those anticipated from fluctuating shear; total shear variance is a better indicator here.
Current core (C): The weakest diffusivities of the section are found near the surface in the high-velocity axis of the current. The weak fluctuating shear slightly overpredicts ɛ.
East channel wall (E): Fluctuating shear is predominately cross-channel, suggesting that the nearby topography is affecting the internal wave field. Dissipation is sometimes weak and sometimes strong and tends to be underpredicted by the scalings.
TSBLs: The highest Kρ occur in these energetic layers, which are often interfaces or transition zones between HBLs below and interior waters above.
Determination of regime boundaries was guided by features in the station-mean profiles. Contrast among the regimes is enhanced by examination of parameters computed on designated vertical intervals. Most deliberately chosen were the interval bounds for all high mean shear zones (HMSZs), for the weakly mixing core, and for the TSBL deep at the east wall (Fig. 14).
Each analysis interval is characterized by quantities vertically averaged from 10-m station-mean profiles (such as ε) or derived from interval spectra. Most interval thicknesses are 100 m, the uppermost at stations 5 and 6 are 160 and 150 m, respectively, and others are 80 or 90 m to fit a regime's extent. A total of 38 were defined, including intervals for the separate occupations of stations 1, 2, and 7. For example, the HMSZs at station 2 changed after 9 June (Fig. 4). Most TSBLs were too thin or too variable to be assigned analysis intervals; those at stations 3 and 7 were appropriate, but they are considered in the context of the HMSZs and the east channel wall, respectively.
The interior lies in an active and variable subinertial environment, and has turbulence and finescale variance similar to a moderately forced oceanic pycnocline (Table 2). Interior N210 and ε pairings cluster at intermediate diffusivities, while S̃2 are indistinct from non-HMSZ regimes in range and stability (Fig. 15).
Observed dissipation rates are anticipated fairly well by the fluctuation scalings (Fig. 16). This result is robust, whether comparing ɛiwP (with Rω = 3) or ɛiwG. Of the 21 intervals, all but one have ε matched by ɛiwP within a factor of 2.1. When ɛiwG is computed with total shear variance, the outlier is in closer agreement, while ε in seven intervals is overestimated by factors of 2.1–2.7.
Finescale shear in much of the interior differs from that assumed for the internal wave interactions parameterized by ɛiwG and ɛiwP. For fluctuating variance in the low-wavenumber band, east components generally exceed the north ones by 1–2 times, and clockwise components often more than double—and always exceed—the anticlockwise (Figs. 17c,d). Despite such variable composition in interior Froude spectra, Winkel (1998) shows that they are consistent in shape and level with the scaling of Polzin et al. (1995). Subinertial shear is significant in many intervals, especially in the six where mean F̃r2 > 0.25 accounts for 25%–43% of the total Fr210 > 0.95 (Fig. 17a).
b. High mean shear zones
Mean shears here are the highest observed in the section (Fig. 15) and are predominately northward (Fig. 17b). Dissipation rates are high, and are 3.7–33 times those predicted by fluctuating shear (Table 2). Total shear variance does, however, provide a fair estimate of ε (Fig. 16). Decomposition of shear is uncertain because of the highly fluctuating subinertial flow. Even so, computed mean F̃r2 are more than one-half of the measured total Fr210, in contrast to the interior's lesser ratios (Fig. 17a).
Two intervals—from deep station 2 and the TSBL of station 3—are distinct in that their ε and Kρ are the highest over all the regimes, and that they alone have F̃r2 > 1 (Table 2). These turbulent zones were of limited duration, and were affected by a shift or adjustment of the current's axis.
The other four intervals are shallow at stations 1 and 2, where strong stratification moderates high S̃2 and ε to yield, respectively, F̃r2 and Kρ comparable to interior levels (Table 2). This region is probably a persistent feature of the current, although its strength and position may vary.
Fluctuating shear, regardless of its nature, is a poor measure of dissipation in this regime. Nor does the moderate to strong mean shear account for all the turbulent production. The best indicator is the total shear, when applied in the ɛiwG formulation. This suggests that the magnitude of the downscale energy flux is independent of whether the shear is composed of energetic internal waves in a quiet background (as assumed in the scalings), or of weaker waves in an energetic background (as in this regime).
c. Current core
The weakest diffusivities are found in the current core, where low dissipation occurs within high stratification (Fig. 15). Total shear is also among the weakest, with Fr210 < 0.5 (Fig. 17, abscissa). Fluctuating shear variance is close to GM76 levels (Table 2), and dissipation is slightly less than the scalings anticipate (Fig. 16). The high ratio of clockwise-to-anticlockwise variance distinguishes fluctuating shear in the core (Fig. 17d). The excess clockwise variance corresponds to a peak in core Froude spectra, which fall off more steeply than GM76 thereafter (Winkel 1998).
d. East channel wall
Profiles at station 7 are within 2 km of the channel's east side, which for internal waves is virtually a wall owing to its steep slope. This regime is marked by its proximity to topography and, above the TSBL, by its predominately eastward shear variance (Figs. 12 and 17b,c). The strong turbulence on 13 June is in sharp contrast to the weak activity on 6 June (Table 2).
In the two middepth intervals of 13 June, Kρ exceeds 10−4 m2 s−1, levels matched only in the underlying TSBL and in the two turbulent HMSZs (Fig. 16). The higher value is from the interval centered at 190 m, in which ε was dominated by a vigorous event within a 20-m-thick mixed layer. Its high dissipation exceeds the predictions of the internal wave scalings, even when Fr210 is used for ɛiwG.
Finescale shear in the TSBL differs from that elsewhere at station 7. Northward mean shear contributes more than eastward to the high F̃r2 > 0.25 (Fig. 17b). Fluctuating shear is nearly isotropic but exhibits some clockwise rotation with depth (Figs. 17c,d). As in the energetic middepth interval discussed above, the high ε is underpredicted by the scalings (Fig. 16).
In the remaining five east wall intervals, fluctuating shear is a fair indicator of dissipation, especially when ɛiwP is modified for high-frequency content (Winkel 1998). The combined adjustments C(Rω) via (3) are moderate, ranging from 0.9 to 3.4 for the inferred Rω of 3.4–1.3. Higher-frequency internal waves are a reasonable expectation near the east wall, for which the critical reflection frequency is around 0.1–0.3N. Individual drop profiles of shear exhibit rectilinear behavior, indicative of higher frequencies than in the more elliptical profiles of the interior (Winkel 1998).
e. Turbulent stratified boundary layers
These near-bottom layers account for nearly one-half of the section-averaged Kρ, although they occupy only 7% of the total record. Most prominent are TSBLs that exhibit higher dissipation, stratification and shear than waters immediately above. The TSBLs of stations 3 and 7 are summarized in Table 2. Some drops from other stations exhibit TSBLs that are similar to, though thinner than, those at stations 3 or 7. Others are less turbulent or less distinct. Because TSBLs vary in character and in depth range from drop to drop, inter-regime contrast is enhanced by computing attributes for each drop's TSBL, and then averaging appropriately to form station statistics. This approach increases mean ɛ, Kρ, and Fr2 by only 50%–100% for stations 3 and 7.
The importance of mixing in the various regimes depends on the volume and properties of the affected water. Examination of transport in θ–S bins emphasizes that the interior is the dominant component, especially below 24°C (Fig. 18). To discuss contributions in terms of the source waters analyzed by Schmitz and Richardson (1991), transport and diffusivity are tallied by regime in four temperature bins (Table 3).
Surface boundary layers accounted for 3.2 Sv of the total 8.3 Sv warmer than 24°C; the remainder was in stratified flow concentrated near midchannel (Fig. 19). The weakly mixing core carried almost as much as the eastern interior. The combination of rapid flow and weak turbulence suggests that this water mass (beneath the SBLs) undergoes little modification as it transits the Straits of Florida.
The next deeper layer, 17°–24°C, contains North Atlantic water characterized by the θ–S curve from the salinity maximum through the 18°C water (Fig. 6). The MSP survey found such properties in 90% of the total 10.8 Sv, mostly in the eastern interior (Table 3). The remaining 10% occurred in the upper HMSZ (Fig. 18), consistent with reports of fresher, South Atlantic water on the channel's west side (Schmitz and Richardson 1991); some of this water intruded eastward into the core, weakly eroding its salinity maximum. There was a transport maximum east of midchannel between 17°C and 19.5°C (Fig. 19), comparable to that in Fig. 9a of Leaman et al. (1989). Diffusivities exceeding 10−4 m2 s−1 affected 0.7 Sv near the east wall, including 0.3 Sv of 17.5°–18.5°C straddling the upper TSBL; another 1.9 Sv of this 18° water flowed through the interior. Overall, Kρ was only twice the (1–2) × 10−5 m2 s−1 reported for the subtropical North Atlantic by Toole et al. (1994), so the Florida Current is not a hot spot for mixing of this water mass. The east wall could be an exception if the slower transit allows the stronger turbulence to affect the 18° water significantly.
Regarding the 12°–17°C layer, the interior accounted for 6.1 Sv of the dominant North Atlantic component. Around 1 Sv of South Atlantic water flowed through west of station 3, half in the interior and half in the deeper turbulent shear zone of station 2. Only 0.1 Sv trickled through the lower TSBL at the east wall, mixing with a mean diffusivity of 3.6 × 10−4 m2 s−1. The conclusion is the same as for the overlying layer: Given the predominant interior-regime conditions, the Florida Current is not an exceptional site for modifying this water mass.
Water in the deepest layer, 6°–12°C, comes mainly from the South Atlantic (Schmitz and Richardson 1991). Most of the transport was again in the interior, where turbulence was slightly stronger than in the warmer layers (Table 3). Antarctic Intermediate Water, categorized as the fresher 7°–10°C bins in Fig. 18, accounted for 1.4 Sv in the midchannel interior. Water colder than 7°C summed to 0.6 Sv, split evenly among midchannel flows in the interior, TSBLs, and bottom HBLs; the station 3 TSBL carried another 0.5 Sv of water above 7°C. This layer has the strongest mixing, but the smallest transport (Fig. 19). Also, much of this flow does not interact with the bottom in the deeper channel upstream of 25°N (Fig. 1), so the enhanced mixing in the TSBLs persists only for the 10-day transit through the shallower portion. Even so, the effects of friction and turbulent mixing are more important here than in the other layers.
5. Summary and conclusions
Regions of high, moderate, and low turbulent activity have been identified, and relationships between finescale variance and dissipation have been investigated. Influences of background shear have been examined by separating velocity profiles into station-mean and fluctuating components. To accentuate the observed variety of background conditions and turbulent and internal wave activity, five mixing regimes have been designated (Fig. 14). Most of the stratified flow, that is, 73% of the total 28 Sv, has the following characteristics of the interior regime.
Fluctuating shear variance is 1–4 times higher than GM76 internal wave levels, and has larger contributions from the clockwise and cross-channel components than from their counterparts.
Similarly moderate values of turbulent diffusivity, (0.7–7) × 10−5 m2 s−1, are consistent via internal wave scalings with observed patterns and levels of fluctuating shear.
Total shear is determined more by fluctuations than by background flow, even though mean Fr2 range up to 0.55.
Turbulence and finescale quantities show no significant dependence on mean shear.
The remaining regimes are associated with specific areas in the flow or the channel. The high velocity core of the current transports nearly 4 Sv, and zones of high northward mean shear adjacent to the core carry 2 Sv.
The core has predominately clockwise shear variance at GM76 levels, and the weakest diffusivity in the current at 3 × 10−6 m2 s−1.
High mean shear is persistent in the upper western waters, where strong N2 results in background Fr2 of only 0.4 and diffusivity is moderate.
Intermittent features beneath the core with mean Fr2 > 1 have some of the strongest turbulence, Kρ ≈ 4 × 10−4 m2 s−1.
Total shear, determined more by the mean than by fluctuations, reasonably predicts turbulence when adapted to the finescale parameterizations.
The steep eastern slope interacts with 0.5 Sv, and TSBLs carry 1 Sv within 100 m of the channel floor.
Near the east slope, finescale shear is predominately cross-channel and turbulence varies from nearly the weakest to nearly the strongest;
TSBLs are typically more sheared, stratified, and turbulent than the waters immediately above, and at (2–6) × 10−4 m2 s−1 account for nearly one-half of the section-averaged diffusivity;
Shear tends to underpredict strong turbulence near the east slope and in some TSBLs, but yields a fair estimate where mixing is weaker and for the thick TSBL below the core.
These observations provide evidence that the Florida Current is not a hot spot for mixing. Diffusivities were above 10−4 m2 s−1 in just 2 Sv, while the core carried 4 Sv of weakly turbulent water. The remainder of the flow—whether in the vast interior or in the upper shear zone—exhibited shear variance and mixing rates only a few times greater than those found in the open waters of the Atlantic Ocean.
We are grateful to the Captain and crew of the R/V Endeavor and to the MSP team of Bob Drever, Jim Carlson, Earl Krause, Bill Hess, and Pat McKeown for their expertise in the collection of these data. Harvey Seim, Ren-Chieh Lien, Eric D'Asaro, and Kurt Polzin provided useful discussions regarding internal waves and turbulence. Two anonymous reviewers made valuable comments that improved the manuscript. The Office of Naval Research funded the collection and analysis of these MSP measurements.
MSP Data Processing
During the Florida Straits experiment, the MSP fell at 0.31 ± 0.02 m s−1 and rotated once every 23 ± 2 m during its free-fall descent. Drops ended when the ballast release was triggered at a programmed pressure, or when the return from an onboard continuous acoustic transmission indicated proximity to the bottom. Several sensors were carried by the MSP to measure water properties and to detect platform motion and position. Winkel et al. (1994) provide specifications of the sensor systems and details of the data processing, and Winkel et al. (1996) discuss the treatment and quality of the velocity and shear measurements.
For each MSP drop, standard processing generated profiles of horizontal velocity (u and υ), potential temperature (θ), salinity (S), and potential density (σθ) on 0.1-m depth grids. Dissipation rates (ɛ and χ) were estimated every 2 m for data within 2.4-m windows centered at each grid point. Velocity profiles came from the ACM data and initially contained unknown, depth-independent offsets. Through comparisons with concurrent ADCP profiles corrected for ship motion, the offsets were estimated to produce absolute velocities. This was most successful at stations 1, 2, and 7, where ADCP bottom tracking was reliable. At each of the other stations (3–6), the ship's velocity was estimated from GPS fixes for a few drops, but poor daytime GPS coverage prevented such efforts for most drops.
Three types of operations were used to compute station-mean profiles and statistics. Given profiles A(z), the time-mean profile for a set of drops is denoted 〈A〉, vertical smoothing with a low-pass filter is denoted Ã, and the arithmetic average over a depth interval (typically 100 m) is denoted A.
The background stratification was estimated by averaging drop profiles of N210, which were computed from temperature and salinity profiles over 10-m intervals. In some cases, particularly at station 7, resulting 〈N210〉 profiles exhibit structures that are likely too small in scale to be part of the background. Such fluctuations are smoothed out in 〈Ñ2〉, which was computed from drop profiles of N210 after they were passed through a 12.5-m boxcar filter prior to 10-m subsampling. Relative to the unsmoothed d〈σθ〉/dz, the mean density gradient associated with 〈Ñ2〉 has half as much variance in its 33-m fluctuations, and less than one-tenth for those 20 m or smaller.
The background flow is represented by 〈ũ〉 and 〈υ̃〉, the time-mean of velocities smoothed with a 22-m Bartlett window (to achieve the same scale attenuation as for 〈Ñ2〉). Smoothed drop profiles ũ and υ̃ were differentiated, then station means of these shear profiles were integrated and offset to the absolute velocities estimated from the most reliable ADCP comparisons.
Corresponding author address: David P. Winkel, Applied Physics Laboratory, University of Washington, 1013 NE 40th St., Seattle, WA 98105. Email: email@example.com