Three-Dimensional Structure and Temporal Evolution of Submesoscale Thermohaline Intrusions in the North Pacific Subtropical Frontal Zone

a. Background and motivation

The three-dimensional structure and evolution of thermohaline intrusions remain elusive in spite of many observations, following the discovery of laterally coherent temperature inversions near the Gulf Stream by Spilhaus (1940). Based on thousands of bathythermograph records in the North Pacific, Roden (1964) found temperature inversions to be common throughout the North Pacific. Remarking on apparent differences in the origin of low- and high-latitude inversions, Roden pointed out that the strongest tropical and subtropical features are associated with water mass boundaries, “jetlike currents,” and the equator. He further speculated that the tropical inversions “may be due to turbulence.” Conductivity–temperature–depth (CTD) casts showed these temperature inversions to be hydrostatically stable due to salinity stratification (Roden 1964; Stommel and Fedorov 1967). Microstructure profiling resolved small “staircases” within many temperature–salinity inversions, composed of relatively homogeneous O(1 m) thick layers separated by sharp O(1 cm) thick interfaces (Gregg and Cox 1972). Such staircase structures have also been observed beneath the temperature–salinity maxima in the Gulf Stream (Gregg 1980), although less frequently than in the temperature inversions above these maxima. Sections of CTD profiles frequently feature intrusions sloping across density surfaces (e.g., Fedorov 1978; Gregg and McKenzie 1979), but we are aware of only one previous three-dimensional open-ocean mapping effort (Gregg 1980).

As noted by Roden (1964) and Stommel and Fedorov (1967), hydrostatically stable temperature–salinity inversions in the subtropics can result only from differential advection. From the singular nature of temperature–salinity staircases commonly observed within the inversions, it has been inferred that anomalies in stratification produced by double diffusion drive the necessary lateral advection. Moreover, profiles near fronts often contain multiple inversions extending over vertical intervals of tens or hundreds of meters (Joyce 1977), strongly resembling the structures produced in a laboratory tank when a disturbance was introduced into a diffusively unstable water column (Turner and Chen 1974). Ruddick and Richards (2003) and Ruddick and Kerr (2003) reviewed the extensive literature on observations and theory of intrusions, focusing on their links to double diffusion.

Double-diffusive and the closely related McIntyre instabilities (McIntyre 1970), however, are not the only potential sources of interleaving in the ocean. Frontal intrusions may also be generated by three-dimensional ageostrophic turbulence and linked directly to frontogenesis (Klein et al. 1998). Recent studies have focused on oceanic submesoscale dynamics, the spectral transition between the mesoscale (tens to hundreds of kilometers), where most of the ocean’s energy resides, and the microscale (millimeters to meters), where the actual dissipation of energy is thought to occur (McWilliams et al. 2001; Thomas et al. 2008; Smith and Ferrari 2009). Unlike mesoscale turbulence, submesoscale flow is essentially three-dimensional, so the vertical velocities associated with these features may be strong enough to have a local effect on both lateral and vertical fluxes of heat, salt, nutrients, and other tracers (Mahadevan et al. 2008; Thomas et al. 2008). Indirect evidence of vertically sheared submesoscale exchange is occasionally observed as intrusions or interleaving at the edges of mesoscale features (Tang et al. 1985; Schmitt et al. 1986; Armi et al. 1989; Hitchcock et al. 1994). It is a compelling possibility that such interleaving is the three-dimensional expression of submesoscale turbulence, conceptually similar to the complex structure of streaks and filaments revealed by surface observations. Generation of density-compensated thermohaline filaments with complex vertical structure as a result of lateral stirring of large-scale thermohaline gradients by geostrophic turbulence has been demonstrated in quasigeostrophic modeling by Smith and Ferrari (2009).

b. Experiment objective

To investigate the three-dimensional structure and evolution of frontal interleaving, an intensive field survey was conducted in the subtropical frontal zone (STFZ) north of Hawaii in July 2007, the STF07 experiment. The experiment focused on the outer edge of a mesoscale meander of the STFZ, clearly identified as a relatively warm filament in sea surface temperature imagery (Fig. 1). Within the filament, two thermohaline fronts (referred to as F1 and F2) were the apparent region of generation for interleaving features.

This study addressed operational and scientific questions:

1. Can submesoscale frontal intrusions be mapped in three dimensions and followed over a period of time? Having only one ship available, our approach was predicated on 1) using satellite sea surface temperature (SST) images as guides to frontal structures in the thermocline and 2) surveying the immediate vicinity of the features of interest that were tracked using a neutrally buoyant subsurface Lagrangian float.

2. What three-dimensional shapes and spatiotemporal scales characterize intrusions in the front? Do they have highly variable shapes and scales or are they relatively uniform?

3. Where do intrusions occur on the front in relation to velocity and shear as well as to temperature and salinity? Are there preferred locations or relations to velocity, for example, near-inertial shear? Do some parts of the front lack intrusions? Do intrusions occur as transient deformations or do they detach from the front?

4. What processes generate the intrusions? Are the driving mechanisms internal to the intrusions (e.g., double-diffusive instability) or external (e.g., the submesoscale turbulence cascade).

5. What diapycnal and lateral fluxes result from these features and where?

A few of these questions were addressed in a preceding paper (Shcherbina et al. 2009, hereafter SGAH09) that focused on the large-scale statistics of interleaving derived from the fields of diapycnal spiciness curvature. In particular, it was reported that the intrusions were most prevalent near the two curved thermohaline fronts located at the periphery of an anticyclonic meander in the STFZ. The vertical and cross-frontal scales of the intrusions were on the order of 10 m and 5 km, respectively. The slopes of these features were highly variable and typically not consistent with double-diffusive intrusion origin. Here, we take a phenomenological approach complementary to SGAH09 and describe three-dimensional deformation of salinity fields associated with several prominent intrusions.

c. Tracking and mapping frontal intrusions

Tracking open-ocean frontal intrusions presents unique operational challenges and, to our knowledge, has never been done prior to this experiment. Even though intrusions are embedded in the fluid and follow its motion to a certain extent, they are not truly Lagrangian because their existence and location inherently depend on the difference in the advection of the neighboring layers. Owing to the practical limitations on the extent of a single-vessel survey in space–time, a quasi-Lagrangian observation strategy was adopted. With this approach, the evolution of intrusions was investigated using a series of three-dimensional surveys in the reference frame following a tracked Lagrangian float (D’Asaro 2003).

This paper focuses on 20 days of the STF07 experiment (7–26 July 2007) when several frontal intrusions were tracked and measured extensively. The time line of the cruise, listing the instrument deployments, is shown in Fig. 2. It is further subdivided into four cruise segments—Alpha, Bravo, Charlie, and Delta—corresponding to the distinct regions of the frontal zone surveyed.

The following strategy was used to locate and track the intrusions within the front.

1. The general location of the front was identified using the satellite sea surface temperature data.

2. Precise location and subsurface thermohaline structure of the front was obtained using a long (∼100 km) zonal tow of the Shallow Water Integrated Mapping System (SWIMS) (Klymak and Gregg 2001; Alford et al. 2005), a depth-cycling towed instrument platform.

3. When a section of a front with noticeable interleaving was found, a large-scale (25 km × 25 km) “radiator” grid pattern centered at the front was surveyed with SWIMS to establish the rough three-dimensional context of the observed features.

4. A Deep Lagrangian Float (D’Asaro 2003) was then deployed in the vicinity of the intrusion to track its general advection. Trajectory of the float advection has been charted using acoustic tracking and shipboard velocity measurements (see appendix A).

5. While tracking the float for 2 to 3 days, a series of smaller radiator- and star-shaped SWIMS surveys (∼10 × 10 km) around the float and Modular Microstructure Profiler (MMP) drops were executed to map the small-scale structure and evolution of the intrusions. The patterns were intentionally distorted to compensate for the predicted water mass advection over the duration of the tow and ensure systematic sampling in the advected frame of reference.

Particular features targeted by this study were advected along the arc of a mesoscale anticyclonic meander at a rate of about 0.3 m s⁻¹, covering about 180 km per week (Fig. 1). For example, even though the Alpha and Bravo segments have similar geographic coordinates, they represent different realizations of the frontal structure due to advection. To compare observations of the water mass structure, an advected reference frame (ARF) was adopted.

Mesoscale advection was predominantly tangential to a circular arc centered at 29°47′N, 158°34′W (hereafter, point C) and aligned with the filament, as evident from shipboard ADCP observations (Fig. 3) and float deployments: in a cylindrical coordinate system with origin C, standard deviation of radial float displacement was only about 0.7 km, compared to the tangential displacements on the order of 50–100 km. ARF coordinates (s, r) essentially describe tangential arc length (clockwise) and radial distance relative to a certain water parcel being advected along the arc of the meander. The details of the ARF construction based on shipboard and float observations are given in appendix B. Comparison of ARF coordinates allowed us to identify corresponding features in different surveys.

Three-dimensional distributions of hydrographic parameters in ARF were obtained with level-by-level isopycnal mapping using the thin-plate smoothing spline technique (appendix C). Semi-Lagrangian (SL) depth z_SL, defined as the mean depth of a given isopycnal (Alford et al. 2005), was chosen as the working vertical coordinate to minimize the aliasing of relatively fast distortions in the thermohaline field by internal waves.

a. Shapes of corrugated isohaline surfaces

Intrusions in the STFZ were manifested as corrugations in isohaline surfaces where they shoal across the F1 and F2 fronts toward the outside of the meander. In some cases (especially in Bravo and Delta segments) individual intrusions were prominent and coherent enough to motivate following them closely to investigate the details of their structure and evolution. In others (e.g., in Alpha and Charlie segments), the corrugation was weaker and less regular. Below, we present the structures that were covered in sufficient detail to be certain of their general topology. At the same time, they are representative of the range of features encountered during the survey.

Early in the cruise (segment Alpha, 5–12 July), only a few intrusions of small extent were observed. An example of a typical shape of isohaline surfaces within the front during this period is shown in Fig. 4. Despite somewhat corrugated appearance of the isohaline surfaces, no pronounced folds with salinity inversions characteristic of strong intrusions (SGAH09) were evident. The cross-frontal extent of the most prominent folds (e.g., near s = 110 km) did not exceed 3 km, and they did not extend downfront enough to appear on more than one cross-front section. In search of more substantial intrusions, the survey was moved upstream to the area showing a stronger sea surface temperature front in satellite imagery (Fig. 1a).

The first substantial deformation of isohaline surfaces was encountered on July 13 (Fig. 5). On the vertical profiles, the deformation had a local salinity minimum near σ_θ = 24.6–24.7 kg m⁻³ (z_SL between 55 and 65 m). This prominent intrusion and its vicinity (segment Bravo) were targeted specifically in subsequent surveys to document its evolution over the following days (Fig. 6). Shaped like a broad sheet, it extended in the alongstream direction for Δs = 30 km from s = −15 to +15 km in the float-relative arclength coordinates, and for approximately Δr = 10 km across. The apparent gap in the intrusive sheet between s = 1 and 5 km may be a sampling artifact, as discussed further in appendix D. The property distributions for the “core” of the Bravo intrusion are described in section 2b. This sheetlike intrusion was observed throughout the Bravo survey 13–18 July in the same ARF vicinity and density range (Fig. 6), and possibly as late as 19 July (see Fig. 7 below). The shape and extent of the intrusion changed little during this period. Unfortunately, the small changes between the surveys could not be linked conclusively with the evolution of the feature. A mismatch could arise from the error of interpolating three-dimensional fields from nonrepeatable survey tracks. Evolution of the intrusions is further discussed in section 2d.

Segment Charlie, immediately upstream of Bravo (s = −30 km), was surveyed 18–21 July (Fig. 7). A hint of the upstream edge of the intrusion Bravo is evident at s = −15 km, z_SL = 70 m, allowing cross referencing with Figs. 5 and 6. A smaller and shallower low-salinity intrusion near r = 1 km, σ_θ = 24.5 kg m⁻³ (or z_SL = 60 m) appeared at s ≤ −20 km and had an alongfront extent of about 20 km. Cross-front penetration of this feature was considerably less (<2 km) than the Bravo intrusion.

Another variant of these interleaving features was observed in the vicinity of the second thermohaline front (F2) near the outer edge of the meander (segment Delta). In ARF, this area was situated about 100 km upstream and 80 km radially outward from the earlier surveys. Intrusions in this area also appear as deformations of the front, although their character is markedly different (Fig. 8). In contrast to the sheets observed earlier in Bravo and Charlie segments, intrusions in the Delta segment had elongated tongue shapes, extending cross-stream toward the center of the meander for 10–15 km. The smaller alongstream extent of these tongues was not resolved by the survey, as it was a fraction of the 5-km separation between the parallel tracks. At least two distinct tongues were surveyed—a shallow one at σ_θ = 24.1 kg m⁻³, s = −95 km, and a deeper one at σ_θ = 24.6–24.8 kg m⁻³, s = −100 km. The shallow tongue was situated at about 40-m depth, immediately beneath (but not extending into) the mixed layer. Both tongues persisted throughout the Delta survey. Their fragments were observed during four consecutive surveys on 23–24 July (Fig. 9), although it is difficult to assess changes in their structure given the relatively sparse sampling.

b. Core properties

The Bravo intrusion was surveyed in great detail, allowing resolution of the complex lateral evolution pattern of hydrographic properties within its core. The core of an intrusion can be traced using the extrema of diapycnal spiciness curvature τ_σσ (SGAH09). This parameter, calculated as a second derivative of spiciness with respect to potential density along a vertical profile, is an indicator of water mass interleaving: its high absolute values indicate sharp interfaces between dissimilar water masses. The lateral extent of the low-salinity intrusion core was defined as the area where the value of the associated τ_σσ maximum exceeded 10 m³ kg⁻¹. Intrusion thickness was defined as the density difference between the core and the underlying negative curvature extremum. Here τ_σσ was calculated from the temperature and salinity profiles low-passed with a filter with half-width of 0.1 kg m⁻³ (see SGAH09 for details). Properties of the Bravo intrusion core defined in this way are shown in Fig. 10.

The intrusion core had a shape of an elongated shallow bowl, shoaling toward either side of the front, as well as downstream. This shoaling was evident in both the depth of the core (Fig. 10a) and its density (Fig. 10b). Characteristic cross-frontal slopes of the intrusion core, determined by statistically robust plane fits to various areas of Fig. 10a, are given in Table 1.

The maximum cross-front intrusion extent of about 11 km was obtained between s = −10 and −5 km. This central area was characterized by the highest values of diapycnal spiciness curvature as well (Fig. 10c). Conversely, the intrusion thickness (Fig. 10d), defined as the density difference between the core and the underlying negative curvature extremum (SGAH09), was relatively low there.

The salinity of the intrusion core (Fig. 10e) generally increased toward the intrusion tip (r < 0) at a rate of (9.3 ± 0.7) × 10⁻⁶ m⁻¹. This increase was more pronounced near the downstream tip of the intrusion (−5 < s < 0 km) where it reached 3 × 10⁻⁵ m⁻¹, the value close to the maximum isopycnal cross-frontal salinity gradient.

Dissolved oxygen concentration within the core (Fig. 10f) monotonically decreased toward the tip of the intrusion at a rate of (2.4 ± 0.2) × 10⁻⁵ mL L⁻¹ m⁻¹. The observed changes in oxygen concentration could not be attributed entirely to the effect of temperature on oxygen solubility: no more than 25% of the oxygen content variance could be explained by the corresponding changes in temperature.

c. Area of deformation

To address the effectiveness of the lateral tracer dispersion associated with the intrusions, their scale needs to be characterized. Estimating the scale of a simple fold such as the Bravo intrusion (Fig. 5) is straightforward, but becomes progressively ambiguous as the complexity of interleaving increases, for example, multiple tongue intrusions in segment Delta. A convenient proxy can be derived using the area of isohaline surfaces A_s, which increases as the surface becomes multiply folded. We choose to disregard the vertical coordinate in calculating A_s, so its value is not affected by the tilt of the surfaces. The difference between the area of a given isohaline surface A_s and the area of its projection on the horizontal plane A_s⁰ divided by two is the average area covered by folds of this isohaline surface within the domain (Fig. 11a):

View Expanded

This value is a two-dimensional analog of mixing length, and will be called the area of deformation of a given isohaline. Parameterization of isosurface deformation through A*_s is most appropriate for the surveys that encompass a single feature in its entirety (e.g., Bravo in Fig. 5). If the survey covers multiple features or, conversely, only a part of the feature (e.g., Fig. 5), A*_s becomes sensitive to the size of the survey area. A complementary measure, the deformation ratio A_s/A_s⁰, would be more suitable in these situations. The latter, however, may be sensitive to the area of featureless margins of a survey.

Figure 11b shows the distribution of A*_s over a range of isohaline surfaces for each of the four observation segments. The isohalines chosen to illustrate these intrusions (Figs. 4 –9) were among the most deformed examples. The area of deformation in Bravo segment peaks at 200 km², consistent with the 30 km × 10 km estimate of the intrusion’s extent, given its irregular shape. Confirming inspection of isohaline plots, deformations in Alpha and Charlie segments are weaker. In contrast, areas of deformation in segment Delta are substantially higher and peak at lower salinities, further highlighting the difference between the fronts F1 and F2. Deformation ratio A_s/A_s⁰ of these isohalines shows similar behavior (Fig. 11c).

d. Evolution of the vertical structure

The SWIMS surveys were designed to pass repeatedly over the tracked Lagrangian float deployed in the vicinity of a particular intrusion. This float recorded a Lagrangian time series of salinity, temperature, and pressure at 30-s intervals, while closely following the motion of the surrounding seawater (D’Asaro 2003). SWIMS and MMP profiles taken within 500 m of the float illustrate the evolution of vertical structure in areas Bravo, Charlie, and Delta within the frontal zone (Fig. 12). Float deployment Alpha spanned only 24 h and is not shown. It should be kept in mind that float-referenced observations are “Lagrangian” only with respect to the layer in the immediate vicinity of the float. Note also that using the semi-Lagrangian depth as a vertical coordinate removes the effects of isopycnal heaving and vertical strain; remaining variability can be attributed to sheared isopycnal advection and, possibly, mixing.

The largest intrusions likely persisted longer than they were tracked: for example, the Bravo intrusion was observed, at least partially, between 13 and 20 July. Consequently, the lifespan of these features is on the order of days, perhaps even weeks.

The structure of the intrusions did change during the tracking period owing to differential advection. Isopycnal variability in the vertical profiles was relatively weak during the Bravo float deployment (Figs. 12a,b), becoming much more pronounced during the Charlie and Delta deployments (Figs. 12c–f). Partially, this may be due to the weaker rms baroclinic velocities during the Bravo deployment (4 cm s⁻¹) compared to 6 cm s⁻¹ during subsequent segments. Smoother lateral salinity structure of the Bravo intrusion (cf. Figs. 5 and 8) may also have been a factor.

Deviation of hourly salinity profiles from the mean showed signs of variability on time scales close to the inertial period T_in = 2πf ⁻¹ = 23.2 h. Inertial variability of the salinity profiles was particularly pronounced during the Charlie segment (Fig. 13). This variability was largest at σ_θ ≈ 24.6, and 25.1 kg m⁻³ (z_SL ≈ 59 and 100 m, respectively), while salinity at the float (σ_θ = 24.9 kg m⁻³, z_SL = 85 m) remained relatively constant as the float tracked its surrounding water. Temporal salinity variations above and below the float were negatively correlated (correlation coefficient −0.34, significant at 60% with approximately eight degrees of freedom). The diapycnal wavelength of these oscillations was O(0.8 kg m⁻³), corresponding to about 80 m in the vertical.

a. Structure of the mesoscale meander

During 7–26 July 2007, the survey focused on the outer edge of a mesoscale feature, identifiable as a relatively warm filament in sea surface temperature imagery (Fig. 1a). Within the filament concentration of intrusions near the two thermohaline fronts (referred to as F1 and F2) suggests that these were the regions of formation for interleaving features.

Average radial structure across this arc of the meander is shown in Fig. 14. Salinity (Fig. 14a) and temperature (not shown) decrease with depth and radius, forming two distinct fronts: F1 near r = 158 km and F2 near r = 195 km. The fronts are partially compensated and barely noticeable in the density structure (Fig. 14b).

Throughout the STFZ, salinity decreases with depth, making most of the water column mildly susceptible to double-diffusive salt-fingering instability. The relative importance of the double-diffusive effects is expected to be related to the vertical density ratio, R_ρ = (αθ_z)/(βS_z), where θ is the potential density, S is the salinity, and α = −ρ⁻¹(∂σ/∂θ)_S,p and β = ρ⁻¹(∂σ/∂S)_θ,p are the coefficients of thermal expansion and saline contraction, respectively (St. Laurent and Schmitt 1999). Mean hydrographic structure observed during the experiment typically has R_ρ between 3 and 5, with a median of 3.9. Such high density ratios (R_ρ > 2) suggest weak susceptibility to salt-fingering instability, while not excluding it completely.

The tangential velocity V_s is overwhelmingly clockwise (positive), forming two narrow surface-intensified jets near r = 162 and 189 km with the speeds reaching 0.4 m s⁻¹ (Fig. 14d, Fig. 15a). Based on the deeper-reaching 75-kHz ADCP observations (not shown), V_s decreased exponentially below the core with an e-folding scale ∼180 m, reaching 0.11 m s⁻¹ at 250 m depth. Below that, the decay in velocity weakens, with an e-folding scale of 650 m. Tangential advection is very small (<0.06 m s⁻¹) at 600-m depth. Anticyclonic tangential advection was largely in thermal-wind balance with the density field (Fig. 16). Relative vorticity ζ = −dV_s/dr − r⁻¹V_s associated with the radial shear within the two jets over O(10 km) horizontal scales reached −0.2f and +0.4f (Fig. 15c). Large-scale vorticity associated with the meander itself, ζ₀ = −r⁻¹V_s, was O(−0.01f ).

Even though tangential flow dominated the circulation, the relatively weak radial advection drives the cross-frontal growth of the intrusions. Radial velocity V_r was nearly zero within the jet cores, increasing slightly toward both the smaller and larger radii (Figs. 14d and 15b). Assuming two-dimensional dynamics, radial variation of V_r suggests the presence of bands of convergence (r ≈ 155 and 175 km) and divergence (r ≈ 170 and 190 km), with the strain rate χ = r⁻¹d(rV_r)/dr exceeding ±0.1f (Fig. 15d).

Strong radial variability of V_s indicates that the eddy was not in solid-body rotation (Fig. 15a). In fact, the velocity distribution is closer to that of a nested pair of the so-called circular pulsons, analytical approximations developed for inertially oscillating warm-core frontal eddies with radially symmetric parabolic isopycnals (Rubino et al. 1998).

Substantial deformation of the thermohaline features due to differential tangential advection can be expected. A tangential velocity difference of 0.15 m s⁻¹ between the initially radially aligned water parcels at r = 160 km and r = 170 km would result in their separation at a rate of 13 km per day. Over the 6-day survey period this separation would reach O(80 km). A similar V_s difference of 0.15 m s⁻¹ across the top 100 m (Fig. 14e) would result in similar rate of separation of parcels initially aligned vertically. These estimates illustrate that the evolution of the intrusions is necessarily affected by the structure of mesoscale [O(100 km)] advection, governed by geostrophic turbulence within the STFZ.

The fields of mean and rms vertical shear (Figs. 14e,f) were dominated by radial velocities, which were considerably more variable than tangential ones (cf. Figs. 14c,d). As expected, strongest shear variability occurred at the base of the mixed layer at 40–50-m depth. There was no apparent association of high shear with the localization of the intrusions. Furthermore, no particular enhancement of shear variance in the vicinity of F1 and F2 fronts consistent with near-inertial wave trapping (Kunze and Sanford 1984) was observed, possibly due to these fronts being narrower than the lateral coherence scale of the waves.

b. Effect of cross-front differential advection

The relationship between the hydrographic and velocity fields surveyed concurrently during the experiment can be investigated by prognostic simulation of cross-frontal tracer advection. The evolution of the hydrographic structure advected by cross-front ADCP velocities is used here to test whether the observed thermohaline intrusions could have been created by the observed velocity fields.

In a simple prognostic simulation, an initial salinity distribution on a cross-frontal section is advected by a velocity field, varying in a prescribed manner in time and space. Because the full three- and four-dimensional fields of salinity and velocity distribution are not available, two simplifying assumptions need to be made. First, the intrusions are considered to be purely two-dimensional, having infinite alongfront extent. With this assumption, alongfront gradients are neglected and the evolution of the intrusions is driven solely by cross-front velocities. Sheetlike intrusions, such as the intrusion Bravo, naturally lend themselves to such simplification. Second, the velocity field is assumed laterally homogeneous, varying only with time and depth. With this assumption, we can extrapolate the velocity profile measured by the shipboard ADCP onto the full extent of the cross-front section. This simplification is reasonable for radial velocity, which, unlike the tangential component, shows little coherent cross-front variability (see section 3a; Fig. 14d).

Using these assumptions, we simulate the evolution of frontal zone stratification in the Lagrangian segment Bravo between 13 and 20 July 2007. The initial salinity distribution was taken from the cross-frontal section near ARF s = 14 km occupied during the SWIMS deployment 11 on 13 July (Fig. 17a). Insignificant salinity inversions present in this section were eliminated from initial conditions by low-pass filtering and sorting in the vertical (Fig. 17d). Cross-frontal advection was then simulated by time integration of the radial velocities, which produced relative shifting of various layers of the section. Barotropic advection, moving the section radially without distorting its structure, was neglected.

After four days of advection (corresponding to 17 July), a prominent low-salinity intrusion was formed at about 45 m SL depth (Figs. 17b,e). The structure of this intrusion is qualitatively similar to that of intrusion Bravo observed during the SWIMS deployment 15 on the same date at s = 7 km (Figs. 17c,f). At that time, the simulated differential shift between the 45- and 60-m layers reached 3.7 km (Fig. 18), similar to the extent of isohaline retroflection observed during the deployment 15 (4–5 km). It is interesting to note that the maximum differential displacement relative to the 50–60-m layer (>10 km) was reached near 33-m depth (Fig. 17b), yet the strongest low-salinity “intrusion” (as seen by the distortion of isopycnals) appeared at least 10 m deeper. Apparent absence of the intrusion in the upper layers is a result of weaker cross-front salinity gradients found in the mixed layer. This illustrates the critical and nontrivial dependence of the vertical structure of an intrusion on the vertical shear and on both lateral and vertical tracer gradients. Thus simple inference of an advection history based solely on the appearance of the intrusive features may be misleading (SGAH09).

The growth history of cumulative differential radial advection between the intruding layer and the underlying water (Fig. 18) suggests that both inertial and low-frequency processes contribute to the evolution of intrusions. Inertial oscillations cause relative displacement of the layers with amplitudes up to 2 km. The time scale of subinertial advection was probably longer than 20 days, though not adequately resolved with these observations. The maximum rate of low-frequency differential advection was O(10⁻² m s⁻¹), or 1 km day⁻¹. The vertical structure of inertial and subinertial advection, determined by an empirical orthogonal function analysis (not shown), was similar—both showing a reversal in the flow near 45 and 80 m.

We do not imply that our kinematic simulation realistically predicts the formation of the intrusion Bravo during 13–17 July 2007. In fact, this intrusion had probably existed prior to 13 July, albeit slightly farther upstream (see section 2a; Fig. 5). The simulation results, however, do show that the structure of the observed velocity field was favorable to the formation of intrusions of realistic scales. Note that Fig. 17b also illustrates the important observation (Woods et al. 1986) that purely isopycnal lateral advection is capable of creating features slanted across isopycnals. Consequently, no process leading to Lagrangian density change necessarily needs to be invoked to explain such slopes that may be observed.

a. Summary

Frontal intrusions were followed and their evolution mapped in three dimensions. At least two substantially different types of intrusions were observed: sheets and tongues. The sheets were O(10 m) thick, protruding about 10 km into the warm, saline side of the front, and were coherent for 10–30 km along the front. Having about the same thickness and cross-frontal extent as the sheets, tongues extended less than 5 km along the front. Two tongues were found together. All the intrusions were attached to the front; no isolated lenslike structures were observed. Intrusions originated from the isohalines of 34.8 to 35.0, appearing most often at the steepest part of the front. On the other hand, these isohalines were devoid of intrusions for at least a 50-km stretch elsewhere along the front.

All of the intrusions persisted as long as we followed them, several days to one week. Because they evolved so slowly, neither their formation nor decay were documented. Prognostic kinematic simulation of deformation of the cross-front hydrographic structure by the observed advection (section 3b) produced features similar in scale, location, and shape to the observed sheetlike intrusions. This suggests that they could have been produced by distortion of the thermohaline field by observed velocities. Consequently, the dynamic formation of these intrusions is at least partially observable, in contrast to the flows driven by double-diffusive instabilities that are too weak for ADCP field observation. The evolution of the intrusions appears to occur on inertial [O(24 h)], and subinertial [O(10 days)] time scales.

b. Observational technique

Single three-dimensional maps of intrusions extending over submesoscale distances (several tens of kilometers) can be made over the course of several hours, once the local orientation of the front is determined from SST imagery or a large-scale survey. It is possible to construct a sequence of such maps by tagging and tracking the feature of interest with a physical, or with a “virtual” float if the mesoscale flow is predictable. Strong and persistent vertical and lateral shears over scales comparable to those of the intrusion make Lagrangian tracking of a particular water parcel irrelevant over prolonged periods of time. The synoptic differential advection of water parcels in an intrusion was approximately 10 km day⁻¹. Depending on lateral thermohaline gradients, this advection may enhance, eliminate, or displace the intrusion as a whole, or it may leave it unchanged.

The single-ship surveying mode had limited capacity to resolve variability of intrusions on the smaller [O(1 km)] and larger [O(10 km)] scales simultaneously. The need to alternate small- and large-scale survey patterns inevitably resulted in loss of spatial and temporal resolution, making the structure of the features ambiguous and reducing confidence in tracking.

c. Implications for lateral mixing

Coherent intrusions observed in STFZ are associated with cross-front transport of temperature and salinity and, therefore, are directly related to lateral mixing of tracers. It is presently not clear how this mixing can be parameterized.

Typical methods of estimation of lateral fluxes due to fine structure are based on the balance of lateral advection and vertical diffusion (Joyce 1977) and are not applicable here. Diffusive time scale H²/K of the large intrusions observed in STFZ is O(100 days), assuming thickness H = O(10m) and typical vertical eddy diffusivity K = O(10⁻⁵ m s⁻²), which is substantially longer than the presumed lifespan of the intrusions (days to weeks; see section 2d). Therefore, steady-state balance theory cannot be applied here.

At the same time, the evolution of intrusions during STF07 was not rapid enough to allow gathering of reliable statistics of their realizations during the month-long single-ship experiment. Consequently, statistical estimation of effective tracer diffusivity due to STFZ intrusions was also not possible. Moreover, it is not clear whether the dispersion of tracers attributable to these features can be described in terms of a diffusive (i.e., downgradient flux) model or whether a “transilient” model (Stull and Kraus 1987) that includes parameterization of nonlocal eddy transport is necessary.

The question remains whether the observed intrusions and associated tracer fluxes are purely random or at least partially deterministic. The large singular features observed during the STFZ experiment suggested predominance of low-salinity tongues and sheets extending toward the warm and salty side of the front. Absence of large features of opposite sign may be indicative of the asymmetry of the interleaving dynamics, common among submesoscale ageostrophic processes (Capet et al. 2008b). On the other hand, it could be purely coincidental, considering a relatively small sample of the observed structures.

d. Driving dynamics

Most intrusions observed in the STFZ do not have the characteristics of double-diffusive interleaving (SGAH09). An alternative explanation for the observed structures can be sought among the broad range of submesoscale frontal processes, known to create intricate lateral filamentation on scales of 1–10 km (Mahadevan and Tandon 2006). Among these processes is stirring by balanced geostrophic turbulence (McWilliams et al. 2001), spontaneous ageostrophic instabilities (Molemaker et al. 2005), nonlinear Ekman effects (Thomas and Lee 2005), and internal frictional effects (Garrett and Loder 1981). Since these processes tend to occur simultaneously (Capet et al. 2008a), conclusive differentiation between them requires detailed balance analysis through inverse modeling (e.g., Thomas et al. 2010) and is not feasible with the available data.

The process of intrusion formation in STFZ appears to be essentially similar to that of the submesoscale surface frontal cusps and filaments (A. Mahadevan, A. Tandon, and J.-L. Thiffeault 2010, unpublished manuscript), except that the resulting features have no surface expression due to the capping by the summertime mixed layer. Formation of thermohaline filaments of increasingly small vertical and horizontal scales is a common feature of mesoscale turbulent flows associated with the double cascade of density and spice variance (Klein et al. 1998; Smith and Ferrari 2009). Therefore, dynamics of the intrusions is inseparable from the dynamics of the mesoscale meandering of STFZ, which appears to be governed by well-balanced geostrophic turbulence (section 3a). This turbulence likely develops from the spontaneous instability of lateral density gradients within the winter mixed layer (Hosegood et al. 2006). Symmetric instability, which is a common source of mixed layer submesoscale turbulence (Boccaletti et al. 2007), may play an important role during the initial stages of this development. During the summertime STF07 surveying, however, potential vorticity was typically positive in the restratified mixed layer between 30 and 100 m (not shown, but can be inferred from Figs. 14 and 15), indicating that symmetric instability was weak relative to the slower, more balanced baroclinic modes. Mesoscale frontogenesis that creates sharp thermohaline fronts, such as F1 and F2 in STFZ, may trigger partial loss of balance when the strain rate S exceeds absolute vorticity A (Molemaker et al. 2005). Even though the time–space aliasing did not allow robust estimation of the strain rate in STF07, this condition, A − S < 0, was apparently satisfied in several locations on the anticyclonic side of F1 and F2. Evidence of inertial variability in the structure of the STFZ intrusions (section 2d) supports the potentially important role for unbalanced dynamics.