1. Introduction

The Programme Ocean Multidisciplinaire Meso Echelle (POMME) program was conducted in 2000–01 to study the role of mesoscale eddies in the formation and subduction of 11°–13°C mode waters in the northeast Atlantic Ocean (Mémery et al. 2005). Third in a series of four cruises, POMME 2 was conducted from the end of March 2001 to the beginning of May 2001, with two ships, the RV L’Atalante and the RV D’Entrecasteaux. Figure 1 shows the mesoscale eddy field obtained through a reanalysis of the outputs of the Système Océanique de Prévision Régionale en Atlantique Nord-Est (SOPRANE) quasigeostrophic (QG) model, which assimilates altimeter data, combined with the hydrological measurements gathered by the two ships during the first leg of POMME 2 (Assenbaum and Reverdin 2005). This figure reveals that, despite the POMME region being an area of rather low eddy kinetic energy, the large-scale circulation is completely dominated by mesoscale eddies that strongly interact.

The main properties of such a turbulent eddy field have been theoretically and numerically elucidated (Hua and Haidvogel 1986; Hua et al. 1998; McWilliams 1984). Its streamfunction is characterized by elliptic regions that principally identify mesoscale eddies (i.e., dominated by the relative vorticity) and hyperbolic or stirring regions (i.e., dominated by the horizontal strain and deformation processes) located between the eddies. Mesoscale eddies are characterized by large horizontal velocity on their edges and vertical velocities with a quadripolar or more complex structure extending from their center to their periphery. Such eddies involve significant sea surface height (SSH), thermohaline, and density anomalies. On the other hand, stirring regions are the locations where the anomalies of any properties (temperature, salinity, and potential vorticity) ejected from the eddies are usually elongated into thinner and thinner filaments (Lapeyre et al. 1999) by the large mesoscale strain rate and are ultimately horizontally mixed. In those regions the SSH, thermohaline, and density contrasts are rather weak.

In situ oceanic experiments have so far focused on the eddy regions since these elliptic and energetic regions are easily detectable (in particular from satellite) because of their strong SSH and thermohaline contrasts (see, e.g., Martin and Richards 2001; Shearman et al. 1999). Very few experiments have been dedicated to the stirring regions. Only a few experimental studies (Abraham et al. 2000; Ledwell et al. 1993) have highlighted the efficiency of the deformation and strain field to produce, in a short period, long and thin horizontal filaments. Nevertheless these stirring regions are often considered as anemic in terms of vertical velocity. Still, some theoretical and numerical studies in the atmosphere (Hakim et al. 2002; Held et al. 1995; Juckes 1994) have pointed out the energetic vertical velocity field in the stirring regions. Our hypothesis is that their arguments, based on the frontogenesis processes associated to the horizontal stirring of small-scale horizontal filaments of density, should be valid not only for the atmospheric fluid but also for the oceanic fluid. Testing of this hypothesis necessitates, for the design of an appropriate in situ experiment, knowing how to discriminate hyperbolic and elliptic regions.

Several exact criteria have been proposed to partition such a turbulent eddy field into elliptic and hyperbolic regions (Klein et al. 2000; Lapeyre et al. 1999). However the simplest one [the Okubo–Weiss (OW) criterion (Weiss 1991)] has been chosen because of the spatial resolution of the SOPRANE data. The OW criterion is defined as

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where ω = ∂υ/∂x − ∂u/∂y is the relative vorticity, and σ_n = ∂u/∂x − ∂υ/∂y and σ_s = ∂υ/∂x + ∂u/∂y, respectively, are the normal strain and shear deformation rates. Here, u and υ are the horizontal velocity components, respectively, along the x and y directions. The hyperbolic regions (i.e., dominated by the deformation rate) are those where Q² > 0 and the elliptic (or eddy) regions (i.e., dominated by the relative vorticity) are those where Q² < 0.

During POMME 2, it was decided to conduct a high-resolution survey to get data to diagnose the vertical velocity field in an area located between eddies where the horizontal stirring processes should be efficient. The design of the survey was greatly facilitated by the availability in real time of the SOPRANE outputs principally based on altimeter data. SOPRANE is a quasigeostrophic model that assimilates altimeter data and also available in situ data (Assenbaum and Reverdin 2005). The model geometry is a one-tenth regular grid with a 10-layer vertical discretization extending from 24° to 54°N and from 35°W to the 200-m isobath of the European shelf. The location of the survey was chosen in a region where the OW criterion, Q² (calculated from the SOPRANE streamfunction and using the geostrophic approximation), was significantly positive. The direction of the sections was chosen to be perpendicular to the streamlines provided by SOPRANE outputs in order to fully sample the horizontal gradients of the thin elongated structures. Despite the eddy field evolution between the end of leg 1 (11 April) and the beginning of leg 2 (18 April), data collected in the three westerner sections are still well located within a deformation area that favors the formation of elongated density structures (Fig. 2).

This paper briefly describes in the next section the data collected during the survey from a towed SeaSoar (Pollard 1986). Data from a ship-mounted Acoustic Doppler Current Profiler (ADCP) were also available and are described in Lherminier et al. (2005, manuscript submitted to J. Geophys. Res.). Section three describes the vertical velocity field diagnosed from the high resolution SeaSoar data in combination with altimeter data (processed through the SOPRANE model). Discussion and conclusions are offered in the last two sections.

2. The 3D density field

The high-resolution survey was conducted from 18 to 20 April 2001 with a SeaSoar (Pollard 1986) towed by RV D’Entrecasteaux. The survey consisted of nine meridional sections (Fig. 2), which were completed within 50 h. Pressure, conductivity, and temperature were sampled by a Seabird SBE911 + CTD located within the SeaSoar, which oscillated following a classical sawtooth path between around 15 and 330 m, in a 2.5-km cycle. ADCP data were collected at the same time using a hull-mounted 75-kHz RDI profiler. Each 50-km-long section (Fig. 2) was carried out during a period of about 4 h. The sections are 10 km apart. After initial processing of the data we have mostly used those between 50 and 300 m since fewer data are available above 50 m. This translates for the SeaSoar data into an along-track resolution of 2 km near 50 and 300 m and 1.25 km at middepth. Vertical resolution of the SeaSoar data is less than 1 m between 15 and 330 m. High-frequency motions (tidal and inertial motions) are assumed to be weak in this area. Indeed analysis of the velocity data obtained between 40 and 400 m on a mooring close to this area [located at 42°N, 18°W (Briand et al. 2003)] have revealed high-frequency motions (obtained using a low-pass filter) with an RMS value less than 1 cm s⁻¹ during the period 12–25 April.

The data have been interpolated onto a regular grid (3 m × 2 km) using standard objective analysis (Rudnick 1996; Shearman et al. 1999). Objective analysis (OA) requires the specification of a spatial correlation function. A 2D (y, z) correlation Gaussian function, involving in particular a decay scale on the horizontal and one on the vertical, has been used. The vertical decay scale is chosen arbitrarily to be 3 m because of the density of the measurements on the vertical (their resolution is less than 1 m). To determine the appropriate value of the horizontal decay scale, we have calculated the spatial correlation of the data at each vertical level. Then the Gaussian function has been fitted to the correlation data using a least squares method (Rudnick 1996; Shearman et al. 1999). The resulting horizontal decay scale varies slightly with depth. Its value is 3.3 km (±1 km) and the zero crossing occurs at 5.2 km. The OA has been carried out, using these decay scales, to interpolate the data onto the regular grid. The OA allows for the computation of the error expected at an objectively analyzed point. All the gridded data have an error covariance well less than 10% of the data variance. A sensitivity study to the decay scale on the horizontal (involving a variation of up to 25%) has not revealed any significant change in the results.

The mesoscale context involves an anticylonic eddy in the south and a cyclonic eddy in the north (Fig. 2) separated by a large-scale meridional density gradient of the order of 0.5 kg m⁻³ over 80 km. Figure 3 shows density along the nine sections. Sections 1 to 3 (20.13°, 20°, and 19.87°W), located in the western part, are those where the OW criterion has the largest values. In the present analysis we focus on the data from these sections since they are those in a region of strong gradient formation. These three western sections were completed within 13 h, a time short enough for the mesoscale eddy field to be assumed as stationary. This assumption is confirmed by Fig. 4, which shows that the small-scale elongated features of the temperature field from these three sections are well lined up along the SOPRANE streamlines. It was found that this holds at any depth. This is not true for the density field from the eastward sections that were sampled about two days later. The reason is that, in the meantime, the eddies evolved slightly, which has been confirmed by the subsequent SOPRANE outputs. Between 50 and 300 m these three western sections display the existence of small-scale (with a width up to 10–20 km) horizontal meridional structures elongated in the zonal direction. They are strongly baroclinic and involve alternately lighter and denser water with a pronounced thermohaline signature: light water corresponds to salty and warm water; and dense water to fresher and colder water. The corresponding density anomalies are not larger than 0.05 kg m⁻³.

The small-scale horizontal density structures have a depth scale smaller than 300 m (Fig. 3). These characteristics are such that the Burger number¹ is close to 1, which is the magnitude for the structures in hydrostatic and geostrophic equilibrium (Pedlosky 1987).

If we assume hydrostatic and geostrophic equilibrium, we can estimate the zonal current from the density field using the classical thermal wind equation:

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where ρ is the density anomaly; g and ρ₀ are, respectively, the gravity and density constants; and z is the vertical coordinate. The spatial resolution in y for the density field is high enough to calculate such a zonal current. The ADCP divergence-free field at 330 m is used as a lower boundary condition for the integration of (2). It is recovered by solving a Poisson equation forced by the relative vorticity estimated directly from the ADCP data (Pollard and Regier 1992). Results for the three sections (Fig. 5a) display an eastward current in the whole area in agreement with the SOPRANE streamlines (Fig. 2). However Fig. 5a clearly displays both horizontal and vertical variations of this zonal current. The horizontal variations involve meridional bands with a width of approximately 10 km and variations up to 30 cm s⁻¹. The vertical structures involve velocity variations of about 20 cm s⁻¹ over 200 m.

We have attempted to compare these geostrophic currents estimated from the SeaSoar data with those obtained from the ADCP data [smoothed and gridded using an objective analysis (Lherminier et al. 2005, manuscript submitted to J. Geophys. Res.)]. Figure 5b displays the zonal current deduced from the divergence-free ADCP data. Comparison of Figs. 5a and 5b shows that the minima and maxima of the large-scale (y, z) structures of the zonal current are at approximately the same locations with similar magnitudes. It is noted, however, that only a qualitative comparison can be made since the ADCP data are not very reliable at some levels because of some technical problems on the instrument.

3. The vertical velocity field

Using the density field of the three sections analyzed before, we have attempted to estimate the vertical velocity (w) through a simplified 2D version of the classical omega equation [i.e., the quasigeostrophic form of the Sawyer–Eliassen equation (Hoskins et al. 1978; Pollard and Regier 1992; Rudnick 1996)], that is,

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with w = 0 (w_z = 0) at z = 0 (z = –330 m) for the surface (deep) boundaries. Periodic conditions are chosen at the lateral boundaries for the sake of simplicity and since the rhs of (3) is dominated by small horizontal scales. Integration of (3) uses finite differences in both directions. This 2D version of the omega equation is based on the assumption that the x variations of any quantity in our data are much smaller than their y variations (Pollard and Regier 1992). This assumption is all the more reasonable since small-scale structures in the area considered are permanently stretched and elongated along the x-oriented streamlines instead of being contracted. Solving (3) requires us to estimate its rhs term using the experimental data. It is noted that this term should involve an additional component [(2g/ρ₀)(u_y · ρ_x)_y] (Pollard and Regier 1992). In our case a first calculation has shown that its contribution is less than 7% and consequently only that related to υ_y is considered. Density gradients on the rhs of (3) are directly retrieved from the SeaSoar data. Velocity gradients have been estimated using the SOPRANE streamfunction. The reason is that the QG dynamics is nonlocal (Hua and Haidvogel 1986; Scott 2006), which means that the production of small-scale gradients of any active or passive tracer is driven by the flow at larger scales. Consequently in our hyperbolic region, it is the large-scale part of the velocity gradients that drives the growth of the small-scale horizontal density gradients and therefore the vertical velocity field emerging as a response to this growth (Giordani et al. 2005; Klein et al. 1998). In the present situation, the SOPRANE outputs capture the large-scale part of the velocity field well since they are based on altimeter data that resolve the large scales well. The resulting vertical velocity field, superimposed on the density isolines, is shown on Fig. 6.

To strengthen these results, we have performed a sensitivity analysis to the estimation of the horizontal velocity gradients. Two other integrations of (3) have been done using, first, the horizontal velocity gradients directly estimated from the “ADCP” divergence-free field at different levels, second, a constant value for the horizontal velocity gradients. The constant value (υ_y = –u_x = σ = 5 × 10⁻⁶ s⁻¹) for the horizontal velocity gradients represents the large-scale limit. The results (Fig. 7) using both estimated velocity fields conspicuously display the same w patterns as those using the SOPRANE data. This confirms the assumption of the dominance of the large-scale part of the velocity field. Despite this quite good comparison, the solution with the SOPRANE data (Fig. 6) is considered more reliable. Indeed, because of the very low resolution in the x direction, getting the streamfunction from other data such as the ADCP or SeaSoar data requires us to take into account at least eight sections (and not only the three sections analyzed in this study), which produces a loss of synopticity (as mentioned in section 2). Besides, the solution with the SOPRANE data represents the lower limit of the three ones in terms of w magnitude (see Figs. 6 and 7), which further strengthens our conclusions.

Figure 6 clearly reveals a strong correlation between density and vertical velocity, with the vertical velocity positive in lighter filaments and negative in denser filaments. One important characteristic is that the w field in the three sections displays vertical bands alternately positive and negative. These bands have a 5–10-km width. They are coherent from one section to the other, which indicates that the w field involves horizontal structures elongated in the x direction. Another important characteristic concerns the magnitude of the vertical velocity within these elongated structures: it reaches values up to 20 m day⁻¹ between 100 and 300 m. This magnitude of the vertical velocity associated to density anomalies of 0.05 kg m⁻³, when compared to the 30–40 m day⁻¹ associated to 0.4 kg m⁻³ anomalies found by Pollard and Regier (1992), highlights the importance of stirring regions for the vertical velocity field triggered by a turbulent eddy field.

4. Discussion

The 3D dynamics that explains the diagnosed vertical motions within the small-scale density filaments elongated by a large-scale strain field, u_x = α > 0, simply involves the restoration of the thermal wind balance [represented by (2)] within these filaments.

Indeed, because of the filaments elongation, the density gradients (ρ_y) that bound them increase, but at the same time their associated along-front vertical current shear (u_z) decreases, which causes a thermal wind imbalance (Klein et al. 1998; Spall 1995). Appearance of this imbalance is highlighted by the terms (involving α) on the rhs of the equations for u_z and ρ_y (derived from the zonal momentum and density equations assuming the QG approximation):

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where υ′ is the ageostrophic meridional velocity. The terms (involving α) have exactly the same magnitude (using the factor g/fρ₀) but the opposite sign. As a consequenc, these terms, alone, lead to an exponential increase (decrease) of ρ_y (u_z), which breaks down the thermal wind balance (2). Then the resulting thermal wind imbalance causes motions to depart from geostrophy and thus induces an ageostrophic circulation (w and υ′). In QG approximation the role of this ageostrophic circulation is to instantaneously restore the thermal wind balance, which is expressed by the last terms on the rhs of (4) and (5): υ′_z acts to increase u_z and in particular to accelerate the upper along-front flow and w_y acts to decrease ρ_y. The omega equation in (3), which simply results from the combination of (2), (4), and (5), contains all these dynamics. The rhs of (3), which is just related to the y-derivative of the first terms on the rhs of (4) and (5), represents the force that tends to destroy the thermal wind balance. The two terms on the lhs of (3), which are related to the last terms on the rhs of (4) and (5), represent the other force due to the ageostrophic motions that opposes the first one.

This frontal dynamics usually occurs on a scale close to the width scale of the density fronts. When the width scale of the elongating filaments is close to that of the density fronts that bound them, the vertical velocity should be almost homogeneous within the filaments (as depicted on Fig. 8). Such 3D dynamics of the elongating filaments suggests a simple relationship to quantify the apparent anticorrelation that emerges in Fig. 6 between the density anomalies related to the filaments and the diagnosed vertical motions. Using the omega equation, a simple expression can be derived with L and D, respectively, the width and depth scales of the filaments, Δρ, a scale for their density anomalies, and σ, a scale for the strain field. This expression is

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If we use the appropriate values related to our experimental data, that is, N/f = 40, L = 10⁴ m, D = 200 m, and σ = 5 × 10⁻⁶ s⁻¹, (6) becomes

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with w in meters per day and Δρ in kilograms per meter cubed. To check this linear relationship (7), after removing the large-scale meridional gradient from the observed density field, we have plotted the resulting small-scale density anomalies and the diagnosed vertical velocities (Fig. 9). The anticorrelation between the two quantities is remarkable, and the regression calculation leads to a factor of −300, a value close to the estimation (−250) deduced from the scaling (6). Thus, the strong anticorrelation between the w field and the small-scale density anomalies is easily explained by the elongation of the small-scale density filaments by the large-scale strain field as detailed above. The consequence (as depicted in Fig. 8) is that, for an elongating filament, the vertical velocity will tend to decrease the density anomaly inside the filament (Hakim et al. 2002).

The main characteristics of the w patterns revealed by this high-resolution experimental survey agree with previous estimations (Paci et al. 2005) of the w field issued from numerical simulations (with a 5-km resolution) in the POMME region. The only differences for the period considered (A. Paci et al. 2006, personal communication) concern the w amplitude (almost 2 times as large in our study) and the width of the w structures (almost half as small in our study). These differences can be principally attributed to the 3D dynamics of the small-scale density filaments (as small as 5–10 km) that are better resolved in the present study than in the numerical simulations. Thus these experimental results strongly confirm and emphasize the dynamical importance of the small-scale density structures (permanently elongated and contracted) in the stirring regions and the necessity to explicitly take them into account.

5. Conclusions

POMME 2 has offered the opportunity to implement an original strategy to conduct a high-resolution experiment in a specific area within a region dominated by the presence of a large number of mesoscale eddies strongly interacting. To our knowledge, it is the first time that altimeter data coupled with a simple model have been used for the design of such a specific experiment. The availability of such data allowed us to discriminate in real-time hyperbolic from elliptic regions that have quite different properties. Both classes of regions are worth detailed in situ investigations, but each one requires a specific strategy that cannot be used for the other. Much more precise criteria than (1) could be used to locate the regions of formation of strong gradients (Lapeyre et al. 1999), but they require a higher-resolution streamfunction field.

The most important result revealed by the analysis of this high-resolution experiment is that, outside mesoscale eddies, a significant horizontal deformation field can trigger an energetic vertical pump characterized by small-scale structures, elongated in one direction, with alternately positive and negative signs. This strongly emphasizes the potential dynamical importance of these stirring regions for the dispersion of any tracer. Indeed any upwelled or downwelled tracer, whose vertical structure differs from that of density, is instantaneously horizontally dispersed over long distance, a scenario that leads to enhance the 3D dispersion of such tracers (Martin et al. 2002) in these stirring regions. It should be also noted that, as found in other studies (Giordani et al. 2006; Lapeyre and Klein 2006; Shearman et al. 1999), the small-scale elongated structures revealed by the present analysis appear to be trapped within the upper layers and therefore have a only a weak signature below 300 m.

One potential importance of these small-scale vertical motions within stirring regions has been highlighted by recent theoretical and numerical studies (Lapeyre and Klein 2006; Lévy and Klein 2004; Lévy et al. 2001; Martin et al. 2002). These studies have shown that these motions can have a significant impact on the vertical injection of any tracer characterized by a strong vertical gradient. This is the case for nutrients in the upper layers that are depleted because of phytoplankton consumption and that have large values in the deeper layers. In that case these numerical studies indicate that the contribution of these small-scale vertical motions in stirring regions can increase by a factor of 2 the total injection of such tracers. Another potential importance is the effect of these vertical motions on the restratification of the upper layers of the ocean (Lapeyre et al. 2006). Thus the present experimental results reinforce the conclusions and perspectives of these different numerical studies and in particular the necessity to explicitly include the effects of the filamentation process in the ocean models.