We illustrate the use of our Lagrangian flow map analyses to quantify submesoscale transports and non-advective dynamics. We utilize our flow map predictions to extract dynamical regions and coherent structures, classify submesoscale processes, and inform classical analyses. Our emphasis is on the use of spatiotemporal flow maps to help differentiate the advective transports from time-integrated non-advective transformations of water masses and submesoscale features. Results are presented for real-time sea experiments with autonomous sensing platforms and probabilistic modeling systems in diverse ocean regions and dynamical regimes. They include the Nova Scotia Shelf-Slope and New England Seamount Chain regions, the Gulf of Mexico, the Balearic and Alboran Seas, and the Southern California Bight. Our analyses highlight regions of higher shear and mixing, Lagrangian energy and buoyancy dissipation rates, frontogenesis and frontolysis zones, and strong vertical and helical-spiral motions, including filaments and internal waves.

In the winter 2022, a multidisciplinary experiment in the Balearic Sea (northwestern Mediterranean Sea) combined multiplatform in-situ observations with high-resolution numerical simulations to investigate the evolution of a mesoscale oceanic front. The study focuses on analyzing the energy transfer from the mesoscale front to submesoscale cyclonic eddies (SCEs) and understanding their impact on subduction processes from the ocean surface to the interior, using a numerical simulation with 650 m horizontal resolution. The frontal evolution exhibited two distinct phases: (i) an intensification phase driven by strain-induced frontogenesis, and (ii) a subsequent decay phase occurring under conditions favorable to overturning instabilities, triggered by a down-front wind event. These processes enhanced vertical velocities through an ageostrophic secondary circulation across the front, contributing to upper-ocean restratification. Following the wind event, the front decayed and fragmented into smaller-scale structures, leading to the formation of SCEs along its edges. The formation of SCEs was associated with the frontal decay, as well as with centrifugal and gravitational instabilities, which transferred energy from the mesoscale front to the SCEs. These eddies exhibited a three-dimensional helical-spiral recirculation pattern that facilitated the vertical transport of water parcels. Submesoscale eddy-induced frontogenesis drove subduction into the mixed layer, intensified by submesoscale instabilities and guided by downward-sloping isopycnal surfaces at the eddy periphery.

A four-dimensional, three-month-long survey by eight gliders at the Balearic Sea in the western Mediterranean Sea was used to examine the evolution and variability of mesoscale eddies and related physical processes, including frontogenesis, and subduction. The combined glider fleet covered nearly 15978 km over the ground, performing 704 glider days while doing over 4837 dives to as deep as 700 m, measuring temperature, salinity, velocity, chlorophyll fluorescence, oxygen, and acoustic backscatter. The data was objectively mapped on 10 m vertical levels in space and time. Vertical and ageostrophic horizontal velocities were estimated using the omega equation. Uplift of the isopycnal surface, 28.9 kg/m³, ~70 m in 10 km, was observed in an asymmetric cyclonic eddy (CE) on April 29, 2022, with ~25 km width and ~35 km length. Downward velocities of ~20 m/day developed, with the CE axis shifted westward. After the first CE decay, the 28.9 isopycnal shoaled again in the east as another CE formed, where relative vorticity reached ~0.5f. The eddy axis shifted westward during CE growth, and the downward velocities were ~25 m/day during the eddy intensification. Then, the new cyclonic feature spread over before splitting again into two 15 km CEs on May 2. The two smaller CEs proceeded north and west until they vanished. An anticyclonic structure (20 km) developed within their separation. The glider observations reveal horizontal density gradients up to 0.5 kg/m³ over ~10 km. Both upwelling and downwelling were observed near the frontal interface by biochemical tracers.

Mesoscale and submesoscale features with Rossby and Richardson numbers near unity indicate a breakdown of geostrophic balance. This gives rise to ageostrophic flows that drive circulation across density gradients and produce vertical motions, transporting heat and biogeochemical tracers below the mixed layer. During winter 2022, high resolution multiplatform in situ observations and realistic numerical simulations captured the evolution of mesoscale and submesoscale features in the northwestern Mediterranean Sea. A mesoscale front in the Balearic Sea was observed progressing from intensification to decay, culminating in the formation of two submesoscale cyclonic frontal eddies (SCEs). These formed as the front elongated and interacted with a mesoscale ridge, illustrating the dynamic interplay between mesoscale and submesoscale processes. The front intensified due to strain-induced frontogenesis. A strong down-front wind event triggered submesoscale instabilities and the nonlinear Ekman effect, enhancing vertical motions through an ageostrophic secondary circulation and contributing to restratification. As the front weakened, isopycnal slopes flattened, and energy cascaded toward smaller scales, forming the SCEs. This energy transfer was primarily driven by submesoscale instabilities, with additional contributions from centrifugal and gravitational instabilities. A Lagrangian analysis revealed that horizontal parcel transport was dominated by mesoscale circulation, while vertical displacements were controlled by submesoscale processes. The evolving SCEs exhibited a three-dimensional helical-spiral recirculation pattern, promoting vertical transport. Submesoscale eddy-induced frontogenesis drove subduction into the mixed layer, intensified by submesoscale instabilities and guided by downward-sloping isopycnal surfaces at the eddy periphery.