Title: Temporal Variability in Ocean Mesoscale and Submesoscale Turbulence
Description: Turbulence in the Ocean is characterized by a highly nonlinear interaction of waves, eddies and jets drawing energy from instabilities of the large-scale flow and spans a wide range of scales. Turbulent mesoscale eddies are well known as the dominant reservoir of kinetic energy in the ocean and are suspected to contribute significantly to the transport of heat, momentum, and chemical tracers, thereby playing an important role in the global climate system. The intermediate-scale flow structures (i.e. the submesoscale), often manifest as fronts, filaments, wakes and coherent vortices and pose considerable theoretical challenges due to the breakdown of balanced dynamics and the overlapping of scales with inertia-gravity waves. The full role of these submesoscale motions in transport and mixing, therefore remains unknown. This thesis is divided into three chapters focusing on different aspects of turbulence in the mesoscale and submesoscale range. In Chapter 1, we develop an analytical framework for understanding the time dependent mesoscale eddy equilibration process in the Southern Ocean using theory and idealized numerical simulations.

In the Southern Ocean, conventional wisdom dictates that the equilibrium stratification is determined by a competition between westerly-wind-driven Ekman upwelling and baroclinic eddy restratification. The transient picture however, is not well established. To study the time dependent response of the stratification in the Southern Ocean to changing winds, we derive a simple theoretical framework describing the energetic pathways between wind input, available potential energy (APE), eddy kinetic energy (EKE), and dissipation. By characterizing the phase and amplitude of the APE and EKE response to oscillating wind stress, with a transfer function, we show that the transient ocean response lies between - a high frequency (Ekman) limit, characterized by the isopycnal slopes responding directly to wind stress, and a low frequency ("eddy saturation") limit, wherein a large fraction of the anomalous wind work goes into mesoscale eddies. Both the phase and amplitude responses of EKE and APE predicted by the linear theory agrees with results from numerical simulations using an eddy resolving isopycnal-coordinate model.

Furthermore, this theory can be used to explain certain features, like the lagged EKE response to winds, observed in previous modeling studies and observations. In Chapter 2, we investigate the role of submesoscale flows and inertia-gravity waves (IGW) on lateral transport, and lagrangian coherence, using velocity fields and particle trajectories from a high resolution ocean general circulation model (MITgcm llc4320). We use a temporal filter to partially filter the fast timescale processes, which results in a largely rotational/geostrophic flow, with a rapid drop off in energy at scales away from the mesoscales. We calculate and compare various Lagrangian diagnostics from particle advection simulations with these filtered/unfiltered velocities.At large length/time scales, dispersion by filtered and unfiltered velocities is comparable, while at short scales, unfiltered velocities disperse particles much faster. For the temporally filtered velocity fields, we observe strong material coherence similar to previous studies with altimetry derived velocities.

When temporal filtering is reduced/removed, this material coherence breaks down with the particles experiencing enhanced vertical motion, which indicates that vertical advection is mainly associated with small scale, high frequency motions embedded within the larger scale flows. This study suggests that Lagrangian diagnostics based on satellite-derived surface geostrophic velocity fields, even with improved spatial resolution, as in the upcoming SWOT mission, may overestimate the presence of coherent structures and underestimate small scale dispersion. These high-frequency unbalanced motions are likely to alias the estimation of surface currents from low temporal resolution satellite altimetry, and the high-wavenumber sea surface height (SSH) variability may represent a dynamically different ageostrophic regime, where geostrophy might not be the best route to infer velocities. In Chapter 3, we explore statistical models based on machine learning (ML) algorithms, as an alternate route to infer surface currents from satellite observable quantities like SSH, wind and temperature.

Our model is simply a regression problem with sea surface height, sea surface temperature, windstress (quantities that are directly observable by satellites) as input (regressors) and the surface currents (which are typically inferred by physical models like geostrophy, Ekman etc.) as the output (regressands). To help the model learn physical principles like geostrophy (which relies on taking spatial gradients), we also provide the spatial coordinates and information in the neighboring gridpoints as additional features. Using output from an ocean general circulation model (CESM POP) simulation as data, we first train a linear rigression model on small domains and show that linear models only work up to a certain extent in small localized regions far from the equator (no large variation in the Coriolis parameter f). We then train a deep neural network on the whole globe for a relatively short period of time and use it to make predictions. Even with a short training period, the NN can make fairly accurate predictions of surface currents over most of the global ocean just as well as the physical models themselves.

At its present state the NN fails to pick up on some mesoscale and submesoscale turbulent flow features. We discuss some possible ways to address these present problems in future studies.