In frontal zones, water masses that are tens of kilometers in extent with origins in the mixed layer can be identified in the pycnocline for days to months. Here, we explore the pathways and mechanisms of subduction, the process by which water from the surface mixed layer makes its way into the pycnocline, using a submesoscale-resolving numerical model of a mesoscale front. By identifying Lagrangian trajectories of water parcels that exit the mixed layer, we study the evolution of dynamical properties from a statistical standpoint. Velocity and buoyancy gradients increase as water parcels experience both mesoscale (geostrophic) and submesoscale (ageostrophic) frontogenesis and subduct beneath the mixed layer into the stratified pycnocline along isopycnals that outcrop in the mixed layer. Subduction is transient and occurs in coherent regions along the front, the spatial and temporal scales of which set the scales of the subducted water masses in the pycnocline. As a result, the tracer-derived vertical transport rate spectrum is flatter than the vertical velocity spectrum. An examination of specific subduction events reveals a range of submesoscale features that support subduction. Contrary to the forced submesoscale processes that sequester low potential vorticity (PV) anomalies in the interior, we find that PV can be elevated in subducting water masses. The rate of subduction is of similar magnitude to previous studies (~100 m/year), but the pathways that are unraveled in this study along with the Lagrangian evolution of properties on water parcels, emphasize the role of submesoscale dynamics coupled with mesoscale frontogenesis.

Kinematic properties, such as the vorticity, divergence, and rate of strain, describe the evolution of velocity and encapsulate the rate of deformation and rotation of a fluid parcel. Kinematic properties are particularly important in submesoscale flows, where the Rossby number $Ro$ becomes $\mathcal{O}$(1). However, since submesoscale flows are typically highly anisotropic, evolving over timescales of hours to days and over length scales of $\mathcal{O}$(0.1-20) km, their velocity and velocity gradients are challenging to observe from contemporary measurement platforms. With increasing quantity and quality of Lagrangian drifter observations, we here study the velocity gradient estimation from swarms of drifters. First, by simulating drifter swarms, we quantify the sources of uncertainty in the velocity gradient calculation associated with the deformation of drifter swarms using a bootstrap approach and determine the ideal parameter space for the application to observed trajectories. We then apply the most robust method - a two-dimensional, linear least-squares fit of the swarm velocity field - to a drifter dataset from the Bay of Bengal. The drifter-estimated vorticity, divergence, and lateral strain rate reflect the presence of a cyclonic mesoscale eddy, frontal circulation as well as banded patterns that are likely generated by turbulent thermal wind. The distributions and magnitudes of the kinematic properties suggest the presence of submesoscale flows associated with a strong freshwater-dominated density front. Understanding and improving methods for multi-drifter observations are timely challenges which will help design future drifter experiments with the goal of observing two-dimensional divergence and vorticity in submesoscale flows.

Wind-driven coastal upwelling is an important process that transports nutrients from the deep ocean to the surface, fueling biological productivity. To better understand what affects the upward transport of nutrients (and many other properties such as temperature, salinity, oxygen, and carbon), it is necessary to know the depth of source waters (i.e. “source depth’) or the density of source waters (“source density’). Here, we focus on the upwelling driven by offshore Ekman transport and present a scaling relation for the source depth and density by considering a balance between the wind-driven upwelling and eddy-driven restratification processes. The scaling suggests that the source depth varies as $(\tau/N)^{1/2}$, while the source density goes as $(\tau^{1/2} N^{3/2})$. We test these relations using numerical simulations of an idealized coastal upwelling front with varying constant wind forcing and initial vertically-uniform stratification, and we find good agreement between the theory and numerical experiments. This highlights the importance of considering stratification in wind-driven upwelling dynamics, especially when thinking about how nutrient transport and primary production of coastal upwelling regions might change with increased ocean warming and stratification.