Inertial Oscillations and Frontal Processes in an Alboran Sea Jet: Effects on Divergence and Vertical Transport

Abstract

Vertical transport pathways in the ocean are still only partially understood despite their importance for biogeochemical, pollutant, and climate applications. Detailed measurements of a submesoscale frontal jet in the Alboran Sea (Mediterranean Sea) during a period of highly variable winds were made using cross-frontal velocity, density sections and dense arrays of surface drifters deployed across the front. The measurements show divergences as large as ±f implying vertical velocities of order 100 m/day for a ≈ 20 m thick surface layer. Over the 20 hr of measurement, the divergences made nearly one complete oscillation, suggesting an important role for near-inertial oscillations. A wind-forced slab model modified by the observed background frontal structure and with initial conditions matched to the data produces divergence oscillations and pattern compatible with that observed. Significant differences, though, are found in terms of mean divergence, with the data showing a prevalence of negative, convergent values. Despite the limitations in data sampling and model uncertainties, this suggests the contribution of other dynamical processes. Turbulent boundary layer processes are discussed, as a contributor to enhance the observed convergent phase. Water mass properties suggest that symmetric instabilities might also be present but do not play a crucial role, while downward stirring along displaced isopycnals is observed.

Key Points

• Divergence and vertical velocity oscillations are observed at a submesoscale front on the edge of an anticyclone in the Alboran Sea

• Near-inertial oscillations play a major role in the observed divergence oscillatory pattern as suggested by a modified slab model of a wind-forced frontal jet

• Turbulent boundary layer processes and symmetric instabilities can contribute to differences between modeled and observed vertical dynamics

Plain Language Summary

Vertical transport pathways are essential for the exchange of properties between the surface and the deeper layers of the ocean. Despite the recognized role of vertical dynamics in biogeochemical and climate applications, it is still only partially understood. This is principally due to observational challenges. Vertical transport pathways are generally very localized processes and are associated with vertical velocities comparable to instrumental uncertainty. In this work, we focus on vertical processes occurring along a front at the edge of an eddy in the Mediterranean Sea. The paper combines the analysis of multiple observations with the use of an idealized numerical model to isolate and study surface divergence patterns. These analyses allow the investigation of the role of the wind forcing and of small-scale ocean processes in vertical transport.

1 Introduction

Understanding vertical transport between the ocean surface and the interior is still an open and challenging question, despite its importance for several ecological and climatic issues such as exchange of heat, biogeochemical tracers and pollutants (Lévy, 2003; Lévy et al., 2001). Vertical velocity (w) is typically several order of magnitude smaller than horizontal velocity in the ocean, reaching significant values up to only during sporadic events occurring at short time and space scales (typically of the order of a day or hours and less than 10 km [Capó et al., 2021]). From an observational point of view, identifying and measuring these processes is therefore quite complex. Frontal regions are especially prone to the occurrence of large w (D’Asaro et al., 2018; Tarry et al., 2021), even though the transport is often oscillatory and confined to near surface layers. Irreversible subduction, which implies crossing the base of the mixed layer along outcropping isopycnals is a rare event and its dynamics, occurrence, and consequences in terms of large scale budgets are still under investigation (M. Freilich & Mahadevan, 2021; Mahadevan et al., 2020; Qu et al., 2022).

Different processes are likely to be involved in the occurrence of high w at fronts. Near inertial oscillations (NIOs) are expected to be present within frontal areas (Weller, 1982), and their vertical velocity is expected to be oscillatory in the surface mixed layer (ML). NIOs are mostly generated by intermittent wind pulses (Kunze, 1985; Mooers, 1975) and while they are non divergent for large scale winds in absence of background velocity structure, in case of strong mesoscale or submesoscale frontal jets (Jing et al., 2017; Weller, 1982), when lateral velocity gradients are comparable to the Coriolis frequency f, the NIO frequency f_eff can be strongly affected and modulated, leading to inertial pumping within the jet, with significant divergence and w.

The effects of winds can also play a role in modulating divergence at a front through turbulent boundary layer processes (McWilliams et al., 2015). Wind induced turbulence causes vertical mixing of momentum in the geostrophic along-front shear, generating ageostrophic cross-frontal velocities that induce surface convergence and frontogenesis, with associated vertical velocities (Barkan et al., 2019). In presence of daily fluctuations in vertical mixing due to varying winds or to diurnal heating and cooling, these processes can lead to significant fluctuations in divergence and w (Qu et al., 2022; Sun et al., 2020), as described by the so-called Transient Turbulent Thermal Wind balance (TTTW, Dauhajre and McWilliams, 2018).

Also submesoscale instability processes at fronts can provide a mechanism for the occurrence of high divergence and w. Submesoscale instabilities occur in flows with high Rossby and Richardson numbers of , with typical horizontal space scales 1–10 km and time scales of 1 day (McWilliams, 2016), and can be seen as an intermediate regime between the mesoscale and three-dimensional turbulence (Klein et al., 2019; McWilliams, 2016) playing a significant role in the horizontal and vertical transport in the upper ocean (Huntley et al., 2019; Mahadevan & Tandon, 2006; Poje et al., 2014). Areas with high horizontal gradients of buoyancy are especially conducive to submesoscale instabilities, leading to ageostrophic secondary circulations and overturning cells. Frontal jets in particular have elongated gradients, allowing for many types of instabilities, such as symmetric instabilities (SI) and ageostrophic baroclinic instabilities (Boccaletti et al., 2007; Capet et al., 2008; Fox-Kemper et al., 2008; J. R. Taylor & Ferrari, 2010; L. N. Thomas et al., 2013)

All these processes interact in several ways. NIOs are likely to influence instability processes at fronts (L. N. Thomas et al., 2016) such as SI (L. N. Thomas & Lee, 2005; L. N. Thomas et al., 2013), since they influence stratification. Results from a Gulf Stream front campaign suggest that SI more efficiently extracts energy on the phase of the NIOs when stratification is reduced (L. N. Thomas et al., 2016). Also, at fronts NIOs can be subinertial, so that the interaction between balanced currents and NIOs is stronger than in other regions and can lead to energy exchange between both motions and small scale turbulence, with important consequences for energy cascading to small scales (L. N. Thomas, 2017). Energy exchanges between NIOs, near inertial waves and balanced mean flows and eddies have been investigated by Whitt and Thomas (2013), S. Taylor and Straub (2016); S. Taylor and Straub (2020), Rocha et al. (2018), J. Thomas and Arun (2020), Xie and Vanneste (2015), and Barkan et al. (2021).

Unraveling the various processes responsible for high divergence and w is critical to an understanding of vertical transport in frontal regions. But this is challenging given that these processes occur on similar time and space scales. Recent results (Torres et al., 2022) in the framework of vertical fluxes and from a modeling point of view, suggest that it is possible to discriminate between internal waves (such as near inertial waves) and submesoscale frontal dynamics looking at the vertical scales, which are different for each mechanism. However, as described in L. N. Thomas (2017), these mechanisms inherently interact with one-another, which makes the problem of process separation even more complex especially when based on observational information that is necessarily limited in both space and time.

In the last decade there has been a growing interest in estimating surface ocean divergence as an indicator for areas of high w, especially using large drifter clusters (tens to hundreds), that are relatively cheap and easy to deploy (D’Asaro et al., 2020). Areas of enhanced convergence can be identified from drifter clusters, and then targeted with further dedicated ship based measurements (D’Asaro et al., 2018). Also, drifter results have provided very valuable information on divergence statistics in the upper ocean, quantifying its scale dependence and linking it to boundary layer dynamics in the upper ocean (Berta et al., 2020; Esposito et al., 2021; Tarry et al., 2021). Oscillations with periods qualitatively consistent with NIOs have also been observed from drifter based divergence since early studies (Molinari & Kirwan, 1975).

In this paper, we investigate the dynamics behind the occurrence of divergence and w as estimated by drifter arrays and other measurements in an Alboran Sea front in the western Mediterranean Sea. The Alboran Sea is characterized by frontal structures, mesoscale eddies and filaments due to the inflow of the fresher and colder Atlantic water encountering the warmer and saltier Mediterranean waters (Allen et al., 2001; Pascual et al., 2017; Ruiz et al., 2019; Tintore et al., 1988; Tintoré et al., 1991). The front has been sampled in the framework of the CALYPSO project (Mahadevan et al., 2020). Previous analysis of drifter data at the surface and 15 m (Tarry et al., 2022), have provided estimates of divergence and w in the near surface, showing the presence of strong w variability (reaching 100 m/day) occurring at scales of less than 1 day. The dynamical nature of these oscillations is still unclear, and provides the main motivation of the present paper.

The data focus on an intense 1-day survey (Section 2) sampling a submesoscale jet in the eastern side of an anticyclone, under the effect of variable winds with a significant across front component (Poulain et al., 2022). We start from the analysis of near surface divergence observations (Section 3) from drifters following the front for approximately 20 hr, complemented by divergence from currents measured along three cross-front transects. Ship measurements along the transects are also used to compute water column gradient properties (Section 4). We then proceed to investigate possible dynamical processes responsible for the observations (Section 5). We start considering the effects of NIOs, given the significant presence of inertial oscillations (with local period of ≈20 hr) in the CALYPSO drifters and given the significant background velocity structure. Horizontal shear within the jet varies of order f in ≈5 km, therefore providing a suitable mechanism for inertial pumping and for divergence and w fluctuations. In order to isolate and illustrate the NIO mechanisms, we use a simple reduced-physics model, that is, a slab layer model modified by the frontal shear. Divergence results from the model are compared with the observations in terms of magnitude, duration and patterns. We then discuss the contribution of TTTW processes in addition to NIOs, and possible interactions with submesoscale instabilities. A summary and discussion are provided in Section 6.

2 Material and Methods

2.1 Data Collection

From 28 March to 29 April, a comprehensive set of oceanographic data were taken in the Alboran Sea using the R.V. Pourquoi Pas? and R.V SOCIB (Figure 1a). The data collected include a number of vessel-based observations such as continuous vessel-mounted Acoustic Doppler Current Profiler (ADCP), Underway Conductivity, Temperature and Depth (UCTD (Rudnick & Klinke, 2007)) and EcoCTD (Dever et al., 2020), sea-surface temperature and salinity (flow-through CTD), wind (speed and direction) as well as discrete CTD profiles and water bottle samples and include the deployment of various freely drifting platforms (surface and sub-surface). Two types of near surface drifters were launched, CARTHEs (Consortium for Advanced Research on Transport of Hydrocarbon in the Environment [Novelli et al., 2017]), sampling the surface layer down to 0.6 m, and SVPs (Surface Velocity Programs [Centurioni, 2018]), sampling around 15 m.

Figure 1

Study area. Top panel illustrates the entire CALYPSO survey made between 28 March and 11 April with the ship and between 4 and 29 April by the Consortium for Advanced Research on Transport of Hydrocarbon in the Environment drifters (CARTHEs). Black box is the insert presented in the bottom panel. The latter illustrates the surveys done between 1 and 5 April. The surface currents were calculated using altimeter data and the colored dots represent the water surface density as measured by the Underway Conductivity, Temperature and Depth. Black dots represent the origin of the transect reference system used in the calculation (i.e., km 0). N_t, C_t and S_t stand for Northern transect, Central transect and Southern transect, respectively. The purple and red dots represent the Acoustic Doppler Current Profiler surveys performed during 1–3 and 5 April, respectively. The drifter trajectories presented are those collected on 5 April.

In this study, we focus on the data collected around 5 April from CARTHEs, SVPs, ADCP, and UCTD (Donnet et al., 2022). The target of the observations was the eastern flank of the anticyclonic eddy in Figure 1, characterized by a southwestward frontal jet. ERA-5 wind data (Hersbach et al., 2018) provides forcing conditions in the area (Figures 2a and 2b) showing light winds from 1 to 3 April (<5 m/s), oscillating from SW to NW, followed by strong near-diurnal variations from 3 to 6 April (less than 5 m/s to more than 10 m/s) and then by a period of strong, sustained winds (6 and 7 April). During peak periods, winds were blowing consistently from the west (thus with an important across-front component) while periods of light winds were from either the NW or the SW (across and along front, respectively).

Figure 2

Top panels (a and b) show 10 m wind speed and direction time series, averaged over the area in Figure 1b (data on land were disregarded). Wind data source is the European Centre for Medium-Range Weather Forecasts ERA-5 (https://doi.org/10.24381/cds.adbb2d47), providing global atmospheric reanalysis, which includes hourly wind maps at 30 km resolution. Vertical dashed lines in magenta represent our main period of interest (5 April). Bottom panels (c–e) are potential density sections of transects N_t, C_t, and S_t, as determined by Underway Conductivity, Temperature and Depth surveys in 5 April, indicated in Figure 1b.

The analyses performed here use 19 CARTHE and 17 SVP drifters launched in arrays in the northern part of the anticyclonic jet (Figure 1b) starting from 4 April at 21:00. The drifters traveled southwestward during the following hours, following the jet for a distance of approximately 36 km. While moving along the jet, the drifters were also influenced by inertial oscillations, as shown by the trajectories obtained subtracting the mean velocity along each trajectory (corresponding to the frontal jet advection component). Examples are shown in Figure 3 for three CARTHE sample trajectories taken in the western, center and eastern part of the drifter coverage in Figure 1b. A cycloidal pattern, that is, a tendency for the drifters to turn around in circle, was already visible in the full trajectories, but after the mean removal a clear anticyclonic looping emerges with a period of about 20 hr, that is, corresponding to the inertial period, and a space excursion of approximately 5 km. The relevance of inertial oscillations during the CALYPSO experiment is also shown by the rotary spectrum (Figure 3), calculated over the whole CALYPSO 2019 drifter data set which shows a clear, clockwise, peak around the inertial frequency (∼0.05 cph). Semi-diurnal tidal contribution (∼0.08 cph) are also visible.

Figure 3

Left panel shows the rotary spectrum (clockwise, in black, and counterclockwise, in gray, components) over the whole CALYPSO 2019 drifter data set, from 28 March to 30 April, in the Alboran Sea. Right panels show the inertial oscillation in three Consortium for Advanced Research on Transport of Hydrocarbon in the Environment sample trajectories, obtained subtracting the mean velocity (corresponding to the jet advection) along each trajectory.

While the drifters traveled along the jet, the vessel crossed the front along several transects. Here we consider the three main transects shown in Figure 1b, performed from 4 April 23:40 to 5 April 20:10 (Table 1) and separated by about 18 km with horizontal resolutions varying from 1 km (UCTD) to 2 km (ADCP). Transects are 14 km (Northern, N_t) to 36 km (Southern, S_t) long, increasing southward, and took 1.8 hr (Northern and Central, C_t) to 5.7 hr to survey at cruising speed of 1.4 m/s (Northern) to 3.3 m/s (Central) (Table 1). While the Central and Southern transects run parallel (111° from North), the Northern transect runs more southward (126° from North). Prior to 5 April, between 1 and 3 April, a larger scale survey was conducted to identify the geographical extent of the eddy (Figure 1b). The ADCP data collected along 2 April line (running parallel and slightly north from 5 April central transect) are also used in this study as input for the model (details in Section 2.2). Results are presented herein as along-transect distances calculated using the westernmost ADCP point of each transect as the origin (i.e., km 0) (see black dots in Figure 1b). They approximately correspond to cross-frontal distances, given the transects orientation.

Table 1. Transects Surveyed From the End of 4 April to the Eve of 5 April

Transect name	Survey time (UTC)	Length (km)	Speed (m/s)	Orientation (°N)	Resolution (km)
Nt	23:40–02:30	14.2	1.4	126	1.4 (ADCP) 1.4 (UCTD)
Ct	07:55–09:50	21.9	3.3	111	2.2 (ADCP) 1.2 (UCTD)
St	14:30–20:10	35.6	1.7	111	1.6 (ADCP) 1.1 (UCTD)

• Note. N_t, C_t, and S_t stand for Northern transect, Central transect, and Southern transect, respectively. The orientation is calculated clockwise from North.

The geostrophic circulation of the area and of the anticyclonic eddy in particular are illustrated in Figures 1a and 1b, respectively. These geostrophic currents were calculated using altimetry data provided by the Copernicus Marine Environment Monitoring Service (CMEMS). The data used are the daily, 0.125 × 0.125° horizontal resolution, European Seas Gridded SSALTO/DUACS Sea Surface Height L4 product (Taburet et al., 2019). The gridded data were averaged over the period 1–5 April and show the presence of a fairly strong anticyclonic eddy of about 80 km in diameter and currents on the order of 0.5 m/s along its edges (Figure 1b). The frontal zone studied, located on the eastern side, is characterized by surface density variability of a few tenths of kg/m³ per transect length (Figure 1b). It is dominated by changes of salinity, varying from 36.5 to the east to more than 37.1 to the west, a 0.6 change (not shown). In contrast, near-surface temperature does not vary by more than 0.2°C along the same transects. Surface frontal lines can be defined as being between the isopycnal 27.2 and 27.4 kg/m³ (36.9–37.1 salinity range). The front was only partially covered by the Northern transect, in its most eastern part.

In the vertical, the transect density structure (Figure 2) is characterized by a main thermocline ≈50 m deep in the dense side of the front and ≈75 m deep in the light side. The thermocline is characterized by the strongest density gradient corresponding to a temperature change of about 2°C (15.8°C–13.8°C) and to a salinity change of about 2 (36.5–38.5), and is stronger and slightly shallower in the Central and Southern transects than in the Northern one. The density stratification has been further quantified computing the Brunt-Vaisala frequency N², as discussed in more details in Section 4. N²(z) shows the presence of a surface mixed layer in addition to the thermocline, with MLD (ML Depth) ≈ 20–25 m in all the sections (Figure 8c and Figures S2c and S3c in Supporting Information S1). This corresponds to an early summer mixed layer mostly temperature driven, emerging in the area at the time of the measurements (see Figure 4 in Esposito et al. (2021)).

In the following we provide a brief technical description of the in-situ platforms involved in this study.

CARTHE drifters are composed of a toroidal float and GPS at the center linked to a small drogue panel and flexible rubber tether to measure the surface drift from the sea surface down to 60 cm (maximum depth of the drogue). CARTHEs are 85% biodegradable, low-cost drifters designed to obtain high accuracy observations of horizontal dynamics by reducing the rectification wave and slip velocity due to wind (<0.5% with respect to wind speed as quantified in Novelli et al. (2017)). SVPs are standard drifters of the Global Drifter Program (Centurioni, 2018), they comprise a surface float linked to a drogue spanning the layer from 12 to 18 m depth with observed water-following capabilities centered around 15 m depth. While CARTHEs sample near-surface dynamics, including direct atmospheric forcing, wind-waves interaction, surface Ekman currents, Stokes drift and Langmuir circulation, SVPs are less influenced by near-surface processes (Poulain et al., 2022).

The ADCP unit, a 150 kHz Teledyne RD Instruments (T-RDI) Ocean Surveyor, was setup to sample as quickly as possible, typically reaching 30–75 pings per minute, over 65 water cells of 4 m thick and averaged over 10 min (Long-Term Average, LTA) leading to an accuracy of 0.5–1 cm/s. With a vessel draft of 7 m and blanking distance set to 4 m; the first sampled cell was at a depth of 15 m but good data started at 19 m. Earth referenced velocities (u and v) were converted into along-transect and across-transect velocities using transects' angles (Table 1). Maximum sampling depth was on the order of 200 m but only the first 120 m were retained due to poorer data quality below that depth (typically due to a lack of scatters in the water column). The UCTD unit was mounted on the ship tail and measured conductivity, temperature and pressure at a sampling rate of 16 Hz with a typical free-fall rate of 1.5–3.5 m/s along the ship track. Data were calibrated using the discrete CTD profiles and were processed to correct for high frequency noise and sensors alignment before being eventually gridded using a spline interpolation to obtain a vertical resolution of 1 m over a 0–300 m depth range (see details in Dever et al. (2019); Mahadevan et al. (2020)). The top 3 m of all the casts were also removed for this study due to vessel's wake interference.

To homogenize the data set, both UCTD and ADCP data were re-sampled at 1 km horizontal and 1 m vertical resolutions and filtered (in the vertical) using 5 m moving average to smooth the profiles; similarly to Ramachandran et al. (2018). Derived quantities such as absolute salinity, conservative temperature and in-situ density were calculated using the Gibbs-SeaWater relations (McDougall & Barker, 2011). In addition to temperature, salinity and density fields, we also used the UCTD data in conjunction with ADCP data to calculate the Brunt-Vaisala frequency, the horizontal gradient of buoyancy, the balanced Richardson number and the Ertel Potential Vorticity (ErtelPV) (details provided in Section 4).

2.2 Frontal Slab-Layer Model

Here we introduce a reduced-physics model that will be used in Section 5 to illustrate how NIOs can induce oscillating divergence through the mechanism of inertial pumping at the front. The chosen model is purposely very simple, since its goal is to isolate a specific physical process.

Excitation of NIOs by the wind was illustrated using the simplified slab-layer analytical model, originally developed by Pollard and Millard (1970). The reduced physics of the model includes wind forcing, acceleration, Coriolis force and a simple bulk friction term. Here we use a version originally introduced by Weller (1982) that takes into account the modification of the response by a background velocity associated to a flow in geostrophic balance. For our application, we consider a simple background flow, that is, a unidirectional laterally sheared frontal jet, with a velocity structure suggested by observations.

In the cross-front coordinate system, aligned so that the background flow V_g(x) is along the y axis and varies only along x, the evolution of the slab layer velocity is described as

(1)

(2)

where (u, v) is the slab layer velocity, f is the Coriolis frequency, V_g(x) is the background geostrophic velocity, (τ_x, τ_y) is the surface wind stress, ρ₀ is the characteristic water density, H is the slab layer thickness, and r is the friction parameter (D’Asaro, 1985; Weller, 1982; Whitt & Thomas, 2015). Because of the presence of the background flow shear, ∂V_g/∂x, the effective inertial frequency varies across the front. As a result, emerging NIOs are expected to grow out of phase with time and produce quasi-periodic near-inertial divergence δ = ∂u/∂x and the associated vertical velocity “pumping.” In this configuration of the slab model, NIO pumping occurs in bands parallel to the front and can be expected to develop predominantly in areas where ∂²V_g/∂x² is large, that is, near the background velocity extrema. Note that the lateral background flow shear ∂V_g/∂x can also be interpreted as vertical vorticity ζ or shear strain rate. Both interpretations offer an added benefit of being invariant of the coordinate system. Vorticity interpretation tends to be more popular in the literature, possibly owing to the pioneering work on the NIO dispersion by vorticity-dominated mesoscale eddies (Kunze, 1985; Mooers, 1975). In this interpretation, the expression for the effective NIO frequency becomes (Kunze, 1985). We will also follow the vorticity interpretation below. It should be emphasized that the above expressions for f_eff are only valid for the chosen approximations of the background flow. In a more general flow configuration, NIO response would depend on other velocity gradient components, or, equivalently, on vorticity, strain rate, and the vertical shear (Jing et al., 2017; Kunze, 1985).

For this study, we used realistic parameter values of H = 20 m (consistent with the surface MLD), ρ₀ = 1027 kg/m³, f = 8.572 × 10⁻⁵/s (at 36° N, reference latitude), and r = 0.15f = 1.3 × 10⁻⁵/s, corresponding to damping time scale 1/r = 21 hr. Since the slab model is used for illustration, no attempt was made to optimize these parameters further. Background flow V_g(x) for the slab model was derived from the ADCP observations during the 2 April 2019 crossing of the eastern flank of the anticyclonic eddy prior to the strong wind episode. The transect was approximately perpendicular to the eddy front (Figure 1b), therefore the transect direction (toward 113° true) was adopted as the x-axis. Observed velocities were averaged over the top 20 m and only the cross-transect component of the flow was retained to produce the background flow transect V_g(x). The resulting background velocities spanned the range between −0.7 and −0.2 m/s, with the cyclonic vorticity up to 1.5f at the eastern flank of the jet (Figure 4). Since the wind forcing was weak during this time (Figure 2a), the flow was assumed to be geostrophically balanced to the extent necessary for the validity of the slab model. The effects potentially arising from the eddy flow curvature, as discussed in Wenegrat and Thomas (2017), were not included in the model for simplicity. The wind stress forcing (τ_x, τ_y) for the slab model was calculated from R/V Pourquoi Pas? underway wind observations using the neutral drag coefficient following Large and Pond (1981) and rotated into the along-front coordinate system. The model is initialized at rest (u = v = 0) on 00:00 UTC 3 April 2019 and ran through 10 April.

Figure 4

Background flow for the slab-layer model derived from the 2 April Acoustic Doppler Current Profiler transect: (a) Background cross-section velocity and (b) Normalized relative vorticity.

3 Near Surface Divergence From Drifters and ADCP

In this section we present results on near surface divergence δ, estimated from drifters and ADCP, defined as:

(3)

where u, v are the components of zonal (x) and meridional (y) velocity.

Drifters transmit their position as they drift along the front (Figures 1 and 2) at two depths, that is, down to 0.6 m for CARTHE and around 15 m for SVP. Many methods are available for δ estimates based on drifter trajectories, and more specifically on the deformation of drifter clusters with a minimum number of three drifters (e.g., Berta et al., 2020; Lodise et al., 2020; Ohlmann et al., 2017). The two main classes of methods, going back to the seminal paper of Molinari and Kirwan (1975), are based on (a) velocity least squares fits to linearizations around the cluster centroid (Okubo et al., 1976), and (b) estimates of the area A change in time,

(4)

where A is approximated considering a simple, closed curve connecting the positions of the drifters within the cluster (Kawai, 1985), and Dt is the time step over which δ is estimated.

Here we use the area based method (Berta et al., 2016; Huntley et al., 2022; Molinari & Kirwan, 1975) with the smallest cluster configuration of three drifters. The use of triplets allows to uniquely determine the perimeter of the triangle (while ordering is needed for bigger clusters) and maximizes the number of samples also for relatively small scale of a few kilometers. Even though the use of bigger clusters is expected to increase estimate reliability (Ohlmann et al., 2017), the use of triplets have been thoroughly investigated with positive results. Berta et al. (2020) compared divergence results from area based triplets with estimates from least squares methods using bigger clusters (at least five drifters) and with independent Eulerian estimates based on currents from X-band radar. A recent model based study (Huntley et al., 2022) has allowed quantification of error sources. An important aspect, common to all methods and cluster sizes, is that estimates deteriorate when the aspect ratio of the drifter cluster is too small (Berta et al., 2016; Essink, 2019; Ohlmann et al., 2017). Clusters with small aspect ratio are therefore typically discarded. Huntley et al. (2022) performed an extensive study to identify an appropriate cut off value for the aspect ratio, that guarantees reliable estimates without penalizing the sample size. For the simple, triplet specific deformation metric λ (Berta et al., 2016, 2020):

(5)

where P is the triangle perimeter, a suitable cut off corresponds to λ > 0.2.

In this study, we consider triplets at scales of 0.1–10 km, specifically targeting submesoscale processes, with aspect ratio 0.2–1. Resampling is performed every 15 min. A total of 839 CARTHE and 559 SVP triplets are used. Results are expressed in terms of the divergence normalized by the Coriolis frequency, f.

The triplet divergence estimates have been averaged in 2 km bins to make divergence maps (Section 3.1). The binned estimates have also been used to compute time series of δ following the drifters (Section 3.2), averaging bin values occurring at the same time (within an hour). In order to provide a meaningful time series, some criteria were introduced to guarantee that the bins were representative. First of all, bins with <2 triplets were discarded as well as “geographically isolated” bins, defined as having only 1 or less neighboring bins. A third criterion was also introduced relative to the variability of the triplet sizes within a bin, since δ is known to be scale dependent (Berta et al., 2016, 2020; Esposito et al., 2021). Bins with standard deviation of triplet size larger than 3 km (approximately a third of the considered range) were discarded. Overall, approximately 15% of the total number of bins were eliminated according to the criteria.

When the divergence estimates from CARTHE and SVP drifters are horizontally co-located in space and time, it is also possible to evaluate vertical velocity w making use of the continuity equation , that relates the horizontal divergence with the rate of vertical displacement of the water parcel (Tarry et al., 2021). Tarry et al. (2022) used this method to obtain a time series of w along the front studied in this work, although they used a different method from the one used here to computed divergence from drifters, that is, a linear least squares method (Molinari & Kirwan, 1975). Here we use an approach similar to Tarry et al. (2021), using our triplet based divergence estimates and computing w in all the bins where CARTHE and SVP values are available within 3 hr (sensitivity tests using 1 and 2 hr windows show consistent results). The binned w values are then used to compute a time series by performing a running mean over a 30 min time window.

Divergence estimates from the ADCP were calculated from the along-transect velocities using a method originally proposed by Rudnick (2001) and subsequently called the “one-ship method” by Shcherbina et al. (2013) which makes the following approximation: , where u* is the along transect velocity and dx is the along transect horizontal sampling resolution. The approximation implies that the velocity is independent of the across transect component, as for instance in the case of a one dimensional jet. This is of course not strictly valid in our case, even though the transects are indeed approximately perpendicular to the frontal jet. As noted in Section 2, ADCP observations are sub-surface, sampling from 19 m down to about 120 m.

3.1 Space and Time Distribution of Divergence

The spatial distribution of divergence δ for co-located CARTHE and SVP drifters is shown in Figure 5, together with the divergence estimates from ADCP along the three transects. The corresponding time for each bin (computed as the average of triplet times) and for each ADCP estimate are also shown.

Figure 5

Binned maps of time distribution (left) and divergence (right) for drifters Consortium for Advanced Research on Transport of Hydrocarbon in the Environment (a and b) and Surface Velocity Program (c and d). In all panels divergence from Acoustic Doppler Current Profiler measurements are shown at 19 m depth along the transects on 5 April 2019.

Since the drifters move following the jet, they mostly provide information on divergence variability along the front, while the ADCP transects mostly illustrate the cross front variability. Northern and central transects data were collected at similar times than the drifters sampling but the southern transect was started approximately 4–5 hr before drifters arrived to this location (Figures 5a and 5c, and Table 1).

The normalized divergence values (Figures 5b and 5d) range between −f and f, and are similar for CARTHE and SVP. During the first few hours after deployment, divergence is mostly positive, indicating that the drifters are sampling an upwelling area. Later, when the drifters sample the area around the central transect from 8 to 16 hr, the values are negative, indicating downwelling. After that, there is again a positive upwelling area, and then a suggestion of a negative area but the coverage is reduced. The ADCP transects are in qualitative agreement with the drifters, but also show additional across front variability.

In order to better understand similarities and differences between results from the different data sets, we focus on the central transect (Figure 6). CARTHE and SVP drifters are concentrated to the east of maximum vorticity, in an area of predominantly positive vorticity on the dense side of the front, where convergent flow and downwelling are found. In the range between ≈8 and 15 km, divergence is negative for all the data sets, with minimum values <− f around 10 km for CARTHE drifters, and barely reaching −f for SVP and ADCP. East of 15 km, CARTHE divergence remains negative, while ADCP values become positive. The SVP values appear more consistent with ADCP showing an increase east of 10 km, and reaching slightly positive values east of 15 km. The difference is likely due to the fact that ADCP and SVP observations are made at similar depths (ADCP samples at 19 m and SVPs are centered around 15 m), while CARTHEs sample the surface down to 0.6 m.

Figure 6

Divergence from binned drifters (square) and Acoustic Doppler Current Profiler (circle) for Consortium for Advanced Research on Transport of Hydrocarbon in the Environment (a) and Surface Velocity Program (b), along the central transect, together with background vorticity (magenta line).

In summary, a convergence signal is consistently observed in all the three data sets around 10 km, extending from the upper 0.6–19 m. On the eastern side, the pattern is more complex, suggesting that near surface processes tend to maintain convergence in the upper 0.6 m sampled by the CARTHE.

3.2 Time Series of Divergence and Vertical Velocity

Divergence time series are shown in Figures 7a and 7b for CARTHE and SVP. With the application of the criteria described in Section 3, CARTHE time series starts at 02:30, while SVP starts at 01:27. The variability appears characterized by the presence of a low frequency fluctuation of large amplitude as well as by higher frequency signals (of smaller amplitude). As already suggested by Figure 5, the dominant low frequency oscillation starts with positive values, followed by a negative period of approximately 10 hr between 6 and 16 hr, and then again positive values followed by a negative oscillation with decreasing coverage. Overall, there is a good consistency between CARTHE and SVP results.

Figure 7

In color, time series of divergence for Consortium for Advanced Research on Transport of Hydrocarbon in the Environment (a), Surface Velocity Program (b) and vertical velocity integrated down to 15 m (c) from drifter triplets. The errorbar indicates the 95% confidence interval. The black solid line indicates the wind magnitude time series over the area of interest.

The w time series results (Figure 7c) shows a strong oscillation consistent with the δ fluctuation, with initial upwelling followed by downwelling reaching 100 m/day at approximately 8:00–10:00 and lasting until approximately 14:30, followed again by upwelling. The results are compared with the ones by Tarry et al. (2022) (Figure S1 in Supporting Information S1), obtained using a similar approach but with a different implementation as detailed in Supporting Information S1. The two time series are qualitatively consistent, providing further confirmation of the robustness of results.

Overall, divergence and vertical velocity show alternating patterns in space and time along the front, with an oscillation period of ≈20 hr, compatible with the inertial period in the area, and this result provide motivation to further investigate NIO signature.

4 Water Column Dynamical Properties Along the Transects

In this section, potential density profiles and velocity profiles obtained from UCTD and ADCP data respectively are used to describe the flow properties in the water column along the transects, complementing the near surface results of Section 3. We focus first on the central transect (Figure 2d), which is co-located with the drifter convergence maximum registered around 9 hr (Table 1, Figure 7), while the results for the North and South sections are shown in Supporting Information (Figures S2 and S3 in Supporting Information S1).

The δ values computed from ADCP data in the water column are shown in Figure 8b, with superimposed isopycnals indicating the structure of the jet. We recall that ADCP values are retrieved from 19 m depth, while the UCTD data are available from 4 m. We notice the presence of a sharp deepening of the isopycnals around 10 km, suggesting possible subduction. The near surface convergence is evident between 10 and 15 km, corresponding to the frontal expression of the isopycnals. δ is predominantly negative also in the water column below, down to approximately 100 m depth.

Figure 8

Results for central transect, indicated in panel (a): divergence δ with superimposed isopycnals (b), N² (c), M² (d), Ri_B superimposed to δ (e), Ertel q (f).

In order to characterize the stability properties of the flow, we then compute a number of parameters. The Brunt-Vaisala frequency , where is the buoyancy, ρ is the potential density, g = 9.81 m/s² is the gravitational acceleration, and ρ₀ = 1,027 kg/m³ is the reference density, is shown in (Figure 8c). N² is maximum at the thermocline, around 50 and 75 m in the dense and light side of the front respectively, but also shows the presence of a surface ML around 20–25 m, as already discussed in Section 2. The horizontal buoyancy gradients, (where x is the across gradient direction) is maximum at the front around 10 km (Figure 8d).

From M² and N², the balanced Richardson number is computed (Figure 8e), showing an extended area of Ri_B <= 1 at the front around 10 km. This signals an area prone to submesoscale instabilities (Fox-Kemper et al., 2008; Tandon & Garrett, 1994), as it can be expected in a surface frontal region where large horizontal gradients overcome vertical stability induced by stratification.

Another important stability indicator is also computed, that is, Ertel potential vorticity.

where k is the unit vector in the vertical direction. For SI to occur, q must be negative (in the Northern hemisphere) (Hoskins, 1974). (Figure 8f) shows that q is positive almost everywhere along the transect, but there are some negative values in the frontal area, even though restricted to the upper 30–50 m.

A further discussion on the implications of the results for submesoscale instabilities is provided in Section 5, including also the other two sections.

5 NIOS and Frontal Processes

In this section, we investigate the physical processes behind the observed fluctuations in divergence and w. We start by considering the NIO mechanism, since the high velocity gradients observed in the background frontal jet and the presence of inertial oscillations in the trajectories make it a likely candidate to contribute to the observed fluctuations. This is investigated comparing results of the slab model in Section 2.2 with the observed divergence. The contribution of other mechanisms, such as TTTW processes and submesoscale instabilities, is then discussed.

5.1 Comparison Between Slab-Layer Model and Observations

Results from the slab-layer model for the day of 5 April (Figure 9a) are used to investigate divergence induced by NIOs. Distinctive bands of divergence and convergence can be seen (red and blue, respectively), varying both with time (vertical axis) and in space (horizontal axis). If we focus on the sector east of the vorticity maximum, that corresponds to the location of most drifter data in Figure 5, we can see an alternation of red-blue-red colors occurring from top to bottom, that is, ranging in time from 0 to 24 hr. The model pattern is indeed reminiscent of the red-blue-red pattern in Figure 5 observed by the drifters as they sample the dense part of the front from North to South during a similar time window (0–21 hr).

Figure 9

Slab-layer model divergence results of 5 April (colors, both panels). Dashed lines of panel a illustrate the places where data were extracted to be compared with the observations and analyzed via cross-correlation (Figure 10). Panel b represents the model data shifted in both space (x-axis) and time (y-axis) based on the cross-correlation results. Drifters and Acoustic Doppler Current Profiler (ADCP) divergence observations are also overlaid on panel b as colored dots and squares, respectively. Data of both panels are geo-referenced on the central transect coordinates as for the ADCP and Underway Conductivity, Temperature and Depth (UCTD) data (i.e., along distance from first available ADCP point). Background vorticity is overlaid on both panels as a black line with corresponding y-axis on the right.

Quantitative comparisons between model output and observations were performed considering the time and space distribution of δ independently and using drifters and ADCP observations also independently. That is, we used the drifter data to make comparisons in the time domain considering the time series in Figures 7a and 7b and ADCP data to make comparisons with respect to space along the central transect represented in Figure 5.

Noting that the drifters sample the eastern side of the vorticity maximum, model data at 10 km (vertical dashed line in Figure 9a) were extracted and compared with the drifters time series of divergence (Figure 7). The 10 km distance is expected to be representative of the drifter sampling since it is located about 4 km eastward from the vorticity peak used by the model; a comparable distance to the bulk of drifters' observations measured on Apr 5 from the vorticity peak observed that day (Figure 6). We then calculated lagged cross-correlations between the series and found a maximum R of 0.54 and 0.61 at lags of 4 and 3 hr (observations leading) with the CARTHEs and SVPs, respectively (Figure 10).

Figure 10

Model versus observations cross-correlation results. Top panel (a) illustrates the comparison with Consortium for Advanced Research on Transport of Hydrocarbon in the Environment drifters (time domain) and bottom panel (b) with Acoustic Doppler Current Profiler (space domain). Blue dashed lines represent 95% confidence interval.

Taking a 4 hr time-lag into consideration, we extracted the model divergence results at 13:00 on 5 April, corresponding to the sampling time of the ADCP (9:00 + 4 hr; illustrated by the horizontal dashed line on Figure 9) and found best correlation (R = 0.62) at a lag of 1.5 km. A space lag could be expected, considering that the maximum peak used by the model (2 April survey) is located about 3.5 km westward from the peak measured on 5 April, however, our estimate is a little smaller than what could be expected. Poorer results were obtained using a 3 hr lag. Additional sensitivity tests were done by adjusting the model extracted point ±1 km from 10 km (i.e., 9 and 11 km marks) and they led to comparable results although with a phase shift either decreased (9 km) or increased (11 km) by 1 hr and a somewhat less good of a fit in amplitude.

These shifts are not surprising given the uncertainties of the model, due primarily to the uncertainties in the initial conditions, that are assumed to be fully geostrophic with zero slab velocities at initial time on 3 April. Indeed, the shifting can be seen as a simple way to fit model results to the data, matching the initial conditions to produce an oscillation similar to the observed one in terms of phase and amplitude. Other uncertainty factors still remain, including the evolution of the background velocity and its advection effects, non linearity and flow curvature (Wenegrat & Thomas, 2017), as well as forcing details.

The shifted model results are then used to refine the comparison with observation in terms of space and time patterns of divergence. This is shown in Figure 9b where divergence estimates of drifters (vertical line) and ADCP (horizontal line) are overlaid to the shifted model. The blue and red patterns of the model appear visually consistent with the patterns of the drifters and ADCP. Starting from the initial time of the analysis (top boundary) and progressing downward in time both model and data show an alternation of positive (red) divergence, followed by negative (blue) convergence and then red again. Along the space line sampled by ADCP, going from east to west, a similar alternation of red, blue and red again is shown by both model and observations. The only visually obvious difference occurs in the most western sector, past the maximum vorticity, in an area located at the western boundary of the frontal jet, outside of the drifter coverage.

In order to further compare the values obtained from model and observations, we consider the probability distribution function of δ values (Figure 11) obtained from CARTHE and SVP drifters during the period of observation and from the model during a comparable time (shifted of 4 hr) and within the sector east of the vorticity maximum that is most heavily sampled by the drifters. Drifters and model show comparable positive values, with model tails slightly higher than the observations, likely because of the lower resolution of the drifter based divergence, controlled by triplet size. Negative values, on the other hand, significantly differ, with the drifters sampling more heavily the convergent zones and providing higher negative values than the model. The most important difference occurs from −0.5f to −f, where drifter values (for both CARTHE and SVP) have much higher probability with respect to model data. This corresponds to the enhanced convergence sampled by the drifters around 9 hr in the area of the central transect (Figure 5). We notice that the differences between model and data are statistically significant in terms of mean convergence of the distribution in Figure 11, especially for CARTHE, and in terms of time series in Figure 10a (exceeding the 95% CI). These differences, could be at least partially influenced by drifter sampling that tends to favor convergent areas (Garraffo et al., 2001; Pearson et al., 2019) especially at the surface and by the inherent model uncertainties as discussed above.

Figure 11

Probability distribution function of δ from model and drifters observation.

Overall the results show that model results can be matched to the data in terms of period of the main oscillation and in terms of space and time pattern of divergence, suggesting a relevant role played by NIOs. Significant differences, though, are found in terms of mean divergence, with the data showing a prevalence of negative, convergent values. Despite the limitations in data sampling and model uncertainties, this likely indicates the contribution of other dynamical processes.

5.2 TTTW Processes and Submesoscale Instabilities

Turbulent boundary layer processes in the presence of variable winds are also expected to lead to fluctuations in divergence and w in a frontal submesoscale jet. Wind amplitude modulates turbulence and therefore vertical mixing of momentum. Strong vertical mixing modifies the thermal wind geostrophic shear of the jet, leading to a surface cross front velocity and inducing front sharpening (frontogenesis), surface convergence and associated ageostrophic secondary circulation with significant vertical velocity, as described by the Turbulent Thermal Wind equation (TTW) (Barkan et al., 2019; McWilliams, 2016). When turbulent mixing varies on short (diurnal) time scales, either because of wind fluctuations or because of diurnal cooling and heating, inertial effects and vertical diffusive mechanisms lead to fluctuations on divergence and associated frontogenesis that lag the vertical diffusivity fluctuations (Transient Turbulent Thermal Wind, TTTW, Dauhajre and McWilliams, 2018). As shown by model and data results for the case of diurnal heating and cooling (Dauhajre & McWilliams, 2018; Sun et al., 2020), maximum convergence indeed tends to occur when vertical mixing is at its minimum.

In our case, almost diurnal wind oscillations are observed during 4 and 5 April (Figure 2a) with amplitude changes of ≈8 m/s, that are likely to induce significant oscillations in the turbulent boundary layer mixing. Zooming on the period of our analysis on 5 April, we overlay time series of wind amplitude to divergence and vertical velocity w from the drifters (Figure 7). Maximum convergence and downwelling occur around 9 hr, that is, very close to the minimum on wind amplitude occurring around 9–10 hr. It is therefore very plausible that the observed convergent episode is influenced by TTTW mechanisms.

We notice though that the maximum in wind amplitude occurring around 2 hr (expected to be associated with maximum turbulent mixing) corresponds to a maximum in upwelling as sampled by the drifters on the dense side of the front. This is not easily explained in terms of TTTW only. Indeed, previous studies based on cooling and heating rather than wind forcing (Dauhajre & McWilliams, 2018; Sun et al., 2020), showed only one maximum in RMS δ roughly corresponding to minimum turbulent mixing, while in our case we have two maxima in |δ|, associated to both minimum and maximum wind. A possible hypothesis is that the alternating pattern of high positive/negative δ and upwelling/downwelling is mostly due to the NIO response to oscillating winds as analyzed in Section 5.1, while the interaction between NIO and TTTW is responsible for the enhanced convergent episode around 9 hr. The interaction between inertial oscillations and TTTW processes has been recently investigated also to explain rapid vertical exchanges occurring at fronts in the Northern Gulf of Mexico (Qu et al., 2022).

Submesoscale instabilities are also likely to play a role in vertical motion in an upper-ocean front (Verma & Sarkar, 2021). The water column gradient properties presented in Section 4 show that the balanced Richardson number Ri_B is smaller or close to 1 in the frontal area, as expected given the high horizontal buoyancy gradients and the relatively weak stratification. Restratification due to geostrophic adjustments can lead to Ri_B of order 1 (Fox-Kemper et al., 2008; Tandon & Garrett, 1994), while SI (J. R. Taylor and Ferrari, 2010) are permitted for Ri_B < 1, provided that Ertel potential vorticity is negative, q < 0 (Hoskins, 1974; L. N. Thomas et al., 2013). In order to better understand and characterize q, we consider the 2-dimensional approximation obtained neglecting gradients in the along front direction:

(6)

where u(x), v(y) are the velocity components (coordinates) in the reference system oriented across the front (Rudnick & Luyten, 1996). Equation 6 suggests that low PV anomalies can be generated through two different mechanisms. “Baroclinic” low PV is attained when the second term prevails, that is, in presence of large geostrophic shears at fronts, with large M² and relatively small N². “Vortical” low PV, on the other hand, can be attained when the first term dominates, and is negative that is, for large negative vorticity , in presence of weak M² and N².

Figure 8f shows that q attains some negative values in the frontal area in the upper 30–50 m, and an analysis of the two q components (not shown) indicates that the negative q values are of baroclinic origin, that is, mostly due to shear and large M² values. This indicates that SI instabilities can actually occur in the area, but their relevance is questionable given that the region of negative q is limited. Also, it should be considered that the horizontal scale of SIs (Dong et al., 2021) is typically smaller than the 1 km maximum resolution allowed by the drifter estimates, and the wind forcing during the analysis period has a significant across component, which is not SI favorable (L. N. Thomas & Lee, 2005). On the other hand, SI have been shown to be reinforced by vertical mixing and TTTW process (Verma et al., 2022) that are expected to occur at the time of the measurements, and NIO convergent phase could facilitate the onset of SI (L. N. Thomas et al., 2016).

The other two transects to the North and South show even more reduced sign of instabilities at the front. The northern transect has no negative q values and also the Ri_B values of order 1 are restricted to the very surface (Figure S2 in Supporting Information S1). The southern transect, sampled from 14:30 to 20:10, is more extended (Table 1 and Figure S3 in Supporting Information S1) and encompasses not only the front (west of 15 km), but also an area with flatter isopycnals to the east The frontal area shows a very small area of negative q with Ri_B < 1 in the upper 50 m. The eastern area has more extended surface instability signals, possibly related to wind processes.

In addition to the downward displacement of isopycnal surfaces, stirring of water masses downward along the sloping isopycnal surfaces provides another route for subduction. Along-isopycnal transport is enhanced at the submesoscale (M. A. Freilich & Mahadevan, 2019) and both symmetric instability, also known as slantwise convection, and NIOs stir along isopycnal surfaces. We use the distribution of the water mass tracer spice, the anomaly of temperature and salinity on a constant density surface from a reference profile (McDougall & Krzysik, 2015) as evidence of along isopycnal stirring. Positive anomalies are relatively warm and salty while negative anomalies are relatively fresh and cool. In the isopycnal range affected by the low Ertel PV and low balanced Richardson number the water from the dense side of the front (the relatively spicy Mediterranean water) is drawn downwards along the isopycnal surface (Figure 12). This observation suggests that the vertical velocity induced by submesoscale frontal dynamics is partially along-isopycnal.

Figure 12

Spice anomaly from a regional reference profile on the central transect. Spiciness is defined as in McDougall and Krzysik (2015) and anomalies are computed along isopycnal surfaces. Black lines are density contours.

6 Summary and Conclusions

Divergence patterns observed by drifters in a frontal jet in the Alboran Sea are analyzed, with the goal of identifying their main dynamical processes and their consequences in terms of vertical transport. The drifters, launched in the northern part of a jet flanking an anticyclone, follow the front for approximately 20 hr, showing fluctuations of near surface divergence (order f) and vertical velocity (order 100 m/day). Divergence and upwelling are sampled during the first few hours, followed by convergence and downwelling lasting approximately 10 hr, followed by weaker upwelling. The wind is highly variable during the observation period and the previous few days, and is expected to play a role in the observed variability through various mechanisms.

We first investigate NIOs as main candidate process that can be responsible for divergence variability, through the interaction with the background velocity gradients of the submesoscale jet. NIOs have periods of 20 hr in the region, which is consistent with the observed trajectories and with the divergence fluctuation. Indeed, divergence oscillations consistent with NIOs periods have been observed in early drifter based observations (Molinari & Kirwan, 1975). In order to isolate and illustrate the NIO process we run a reduced-physics model, that is, a vorticity-modified slab model where the background vorticity in the jet is provided by ADCP measurements during a period of low winds a few days earlier. Despite being very simple and idealized, the model generates complex space and time patterns of divergence variability. For initial conditions matched to the data, corresponding to a lag of approximately 4 hr and 1.5 km between data and model, comparison with observations shows compatible results in terms of oscillation and δ patterns. Mean divergence values, though, are significantly different, and the data show more prevalent and higher negative values occurring during the convergence phase with respect to the model. Despite the many uncertainties in the model and in the data sampling, the results suggest that NIOs play an important part in the observed fluctuations, but other dynamical processes are likely to contribute to the observed convergent phase.

Variable winds can also induce convergence fluctuations at submesoscale fronts through turbulent boundary layer processes, since high wind amplitude generates high vertical mixing of momentum, which induces cross frontal ageostrophic velocities and frontogenesis. TTTW balance suggests that maximum convergence lags vertical mixing (and therefore maximum wind amplitude), and indeed the present results show maximum convergence occurring approximately at minimum wind amplitude. It is therefore likely that the observed convergent episode is influenced by TTTW processes and their interaction with NIOs.

To further investigate other mechanisms that can influence the observed fluctuations, we computed water column gradients and instability indicators using ADCP and UCTD data collected along a transect surveyed approximately at the same time as the drifter passage during the convergent phase. Balanced Richardson number Ri_B is close or less than 1 in the frontal area, but Ertel potential vorticity q is negative only in a restricted region, suggesting a possible but limited occurrence of SIs. The distribution of water mass tracer spice also indicates stirring along downward displaced isopycnal surfaces. Northern and southern transects, performed by the ship during upwelling and at the end of the downwelling phase, do not show indications of submesoscale instabilities.

In summary, the results suggest that the observed near surface divergence pattern is consistent with NIOs and with TTTW processes likely contributing to enhance the observed convergent phase. Water mass properties suggest that submesoscale SIs might be present but do not play a crucial role, while downward stirring along displaced isopycnals is observed.

The study highlights the importance of time variability in submesoscale frontal dynamics and indicates a number of interesting open points that need further investigation. A crucial question is related to the interaction between the various processes, that is likely to play a key role in the observed patterns. The interaction between TTTW and NIOs has been considered in Qu et al. (2022) for the case of non-divergent NIO oscillations, showing that it can led to inertially modulated convergence and rapid vertical exchanges at fronts. Here we propose an interaction between NIO induced divergent oscillations and TTTW modulated convergence. In order to quantitatively unravel the processes and identify their influence on vertical transport, further studies are needed involving, for instance, a realistic model combined with reduced physics process models. Also, we recall that our study period is characterized by winds with significant cross-front components, which are not expected to be favorable to the onset of SIs. An interesting question is whether and how SIs could be supported by TTTW (Verma et al., 2022) or by NIO phases, for instance through shear enhancement and stratification modification.

Acknowledgments

This work has been supported and co-financed by the CALYPSO project, within the Office of Naval Research Departmental Research Initiative, under the following grants: N00014-18-1-2782 and N00014-22-1-2039 (GE,SD,MB,AG), N00014-18-1-2139 (AYS,EAD), N00014-18-1-2138 (TO), N00014-18-1-2418 and N00014-20-1-2754 (PMP), N00014-19-1-2692 and N00014-19-1-2380 (LC and part of the drifter data collection/analysis), N00014-18-1-2431 (JTF), N00014-18-1-2416 (TMSJ), N00014-16-1-3130 (AP,DRT,SR), N00014-21-1-2702 (AM). MF was supported by the Scripps Institutional Postdoctoral Fellowship (MAF). Investigation of front dynamics in the Mediterranean Sea from multiplatform observations is supported as well by the European Union's JERICO-S3 project through Grant 871153. Open Access Funding provided by Consiglio Nazionale delle Ricerche within the CRUI-CARE Agreement.

Open Research

Data Availability Statement

Remotely sensed geostrophic currents, derived from satellite altimetry, are available from the Copernicus Marine Environment Monitoring Service (CMEMS) at the following link https://doi.org/10.48670/moi-00141 (Taburet et al., 2019). Wind data is provided by the European Centre for Medium-Range Weather Forecasts (ECMWF) ERA-5 (https://doi.org/10.24381/cds.adbb2d47, Hersbach et al., 2018). The subsets of drifter, Underway Conductivity, Temperature and Depth and Acoustic Doppler Current Profiler data collected in CALYPSO 2019 and used for the analysis, together with the slab-layer model output, are made public at the link https://doi.org/10.6084/m9.figshare.21432558 (Donnet et al., 2022).