Title: Stochastic Switching and Optimal Vehicle Navigation in Flows

Noise plays a fundamental role in a wide variety of physical systems. In recent years, researchers have identied situations where noise can induce a large fluctuation that leads to switching between metastable states of the system. After providing an overview of the theory needed to understand the dynamics of rare events for stochastic ODEs, I will demonstrate how large fluctuation theory may be applied for controlling autonomous agents in a stochastic ocean-like ow. In particular, it is shown that a controller can effectively manipulate the probability of a large fluctuation in order to modify the stochastic escape times from one gyre to another.

Title: Learning Uncertainty in Ocean Current Predictions for Safe and Reliable Navigation of Underwater Vehicles

Operating autonomous underwater vehicles (AUVs) near shore is challeng- ingheavy shipping traffic and other hazards threaten AUV safety at the sur- face, and strong ocean currents impede navigation when underwater. Pre- dictive models of ocean currents have been shown to improve navigation accuracy, but these forecasts are typically noisy, making it challenging to use them effectively. Prior work has explored the use of probabilistic planners, such as Markov decision processes (MDPs), for planning in these scenarios, but prior methods have lacked a principled way of modeling the uncertainty in ocean model predictions, which limits applicability to cases in which high delity models are available. To overcome this limitation, we propose using Gaussian processes (GPs) augmented with interpolation variance to provide condence measures on predictions. This paper describes two novel plan- ners that incorporate these confidence measures: (1) a stationary risk-aware GPMDP (for low-variability currents), and (2) a nonstationary risk-aware NS-GPMDP (for faster and high-variability currents). Extensive simulations indicate that the learned confidence measures allow for safe and reliable op- eration with uncertain ocean current models. Field tests of the planners on Slocum gliders over several weeks in the ocean demonstrate the practical efficacy of our approach.

Title: Optimal Deployment for Persistent Autonomy in Geophysical Flows

Marine vehicles are increasingly deployed for persistent monitoring of various oceanic processes. These vehicles are often deployed for long periods of time and must operate with limited energy budgets, exert control in a high inertia environment, rely solely on near field perception, all with little to no direct human supervision. In this talk, I will present our recent developments in planning energy effcient trajectories for these vehicles that leverage the dynamics of the surround flow field. Our approach is a graph based method that can be used to plan energy as well as time optimal paths while accounting for the vehicle's kinematic actuation constraints. I will also show how tools from topological path planning can be used to generate optimal paths in different homotopy classes to facilitate simultaneous exploration of the environment by multiple vehicles. I will also discuss our vision towards incorporating coherent structures and other topological information of the flow field to develop highly eective and computationally efficient path and motion planning strategy for autonomous vehicles operating in large scale, dynamic, and uncertain environments.

Title: Transient Transport Boundaries

Classical methods for delineating ocean transport boundaries assume the flow is essentially two dimensional and dominated by slowly varying dynamical processes. Submesoscale dynamics must allow for vertical motions and transient velocity fields. However, recent experiments have confirmed that sub- mesoscale processes, i.e. those operating on time scales of hours to a few days and horizontal scales of 100 meters, have significant impact on oceanic transport. Thus the question arises whether classical methods such as finite time Lyapunov exponents (FTLE) are an appropriate tool for studying submesoscale transport boundaries. Using an internal-wave-like solution to the linear Euler equations, we show here that time dependent FTLE, calculated at submesoscale intervals, do indeed delineate transport boundaries, provided information on the vertical velocities is available. AUVs are particularly sensitive to submesoscale processes, thus these results may be of some interest to operators. Since transport boundaries organize the flow into different regimes, knowledge of their characteristics impact AUV operations. One example would be to use information about these boundaries to minimize power consumption during navigation, thus extending mission lifetimes.

Title: Lagrangian Coherent Structures for Stochastic Ocean Flow Transports

We discuss recent progress towards the computation and utilization of Lagrangian Coherent Structures (LCS) for the analysis and prediction of multi-scale ocean flow transports. Specic emphases include Eulerian approaches, stochastic advection, probabilistic LCS, mutual information, and fully three-dimensional flows. Examples are provided for idealized incompressible fluid and geophysical flows, as well as for realistic data-assimilative multi-resolution ocean simulations.

Title: Capturing Diffusive and "Ballistic" Transport from Lagrangian Observations

Inferring physical properties of complex flows from Lagrangian, i.e. freely-drifting, observations is one of the main challenges of observational oceanography. Here progress is reported on two aspects of this problem: (i) a stochastic model for the unstructured "background" flow that drives diffusive dispersion, and (ii) a mathematical approach to detecting and analyzing coherent eddies, the propagation of which is a primary contributor to non-diffusive transport and has been called the "ballistic" component. The first of these involves modeling Lagrangian velocities as a *damped* version of fractional Brownian model. The second exploits a powerful tool from signal analysis, the method of instantaneous moments, and can be shown to exactly recover coherent eddy properties subject to a slow variation condition. Application to numerical models as well as to a global dataset are presented.

Title: Data-driven Methods for Modal Decomposition and Model Reduction of Fluid Flows

In this presentation we will review some data-driven methods for modal analysis and model reduction of fluid flows. In particular, we will focus on the following variations that are often used in the fluid dynamics community: Proper Orthogonal Decomposition (POD), Dynamic Mode Decomposition (DMD), Balanced Proper Orthogonal Decomposition (BPOD) and the Eigensystem Realization algorithm (ERA). We provide an overview of these methods, describe how they are related, and illustrate with some example applications.

Title: Nearshore Sticky Waters

Wind- and current-driven flotsam, oil spills, pollutants, and nutrients, approaching the nearshore will frequently appear to park just beyond the break zone, where waves break. Furthermore, the portion of these tracers that beach, if it does, will do so only after a long time. We refer to the parking phenomenon as nearshore sticky waters.

In the process of developing a comprehensive oil-fate model for oceanic oil spills we came upon an explanation for nearshore sticky waters. In this talk I will describe the mechanism of nearshore sticky waters using the oil-fate model in its simplest form. Our understanding of the phenomenon allows us to draw several consequences on how oil spills are arrested in nearshore envi- ronments, and further, suggests how circulation models need to be modied in order to simulate important dynamics at the very large spatio-temporal scales demanded by environmental studies.

Title: Geophysical Transport Structure, Forecasting, and Connections with Field Experiments

Lagrangian techniques for revealing the most influential transport structures in geophysical flows are poised to make a significant impact on the prediction of material transport, with application to the assessment of hazards which spread in the ocean and atmosphere. However, we have a ways to go to bridge the gap between powerful theoretical concepts and practical field experiments. Here we discuss some results relevant for real-time analysis and prediction of geophysical transport structures which have arisen from field applications. We discuss challenges involved in forecasting atmospheric Lagrangian coherent structures, including the effect of subgrid turbulence and ensemble averaging. We also consider the local approximation of the most influential material surfaces using tracer release (or collection) or the monitoring of meteorological gradients. If time permits, we will comment on the incorporation of transport structure into reduced order modeling of geophysical flows and extensions of the coherent structure concept to non-passive tracers.

Title: Teacup in a Tempest: Closing Gaps between Experiment and Theory of Lagrangian Transport in Fluids

Since Aref first showed how fluid kinematics and chaos in dynamical systems were linked, a variety of mathematical tools have been introduced and applied to increasingly complex flows. Being kinematic, this approach does not distinguish a large scale ocean circulation from the flow made by a swimming micro-organism, although the fluid dynamics of these two examples is very different. Kinematic similarity is a boon in the laboratory, allowing high fidelity GFD experiments to be performed using a small apparatus, but it is also a severe hindrance when the transport of tracers must be predicted or even described.

One tool in particular, the finite time Lyapunov exponent, or FTLE (like finite strain in continuum mechanics or geodesic deviation in relativity) has been useful in diagnosing transport features of passive tracers. But FTLE is generally computationally intensive and has been applied mostly to model flows, primarily the model of Rayleigh-Benard convection rolls of Solomon and Gollub, better known as the double gyre. In other words, true flow dynamics, such as intrinsic variability or Coriolis effects on particles, to name just a few, are missing from FTLE analyses.

In this talk, results of laboratory and numerical experiments on time dependent multi-gyre flows are presented. In the lab, a time-dependent effectively two-dimensional low Reynolds number flow is used to distinguish transport properties of passive tracer (dye) from that of small dense paramagnetic (i.e. controllable) spheres. In conjunction, results of FTLE calculations for inertial particles in a time-dependent multi-gyre flow are presented, illustrating the role of density and Stokes number on their transport. The role of a Coriolis force and stochastic forces acting on inertial particles are explored, as is the influence of simple magnetic control. To conclude, the potential value of three dimensional direct numerical simulations of transport of a small number of particles is examined.

Title: Motion Tomography and Collective Mobile Sensing in the Ocean

Modeling and predicting ocean currents are great challenges for physical oceanography due to the lack of direct measurements. Mobile sensor net- works have been proven to be an eective tool to answer this challenge, providing estimated flow information along the Lagrangian trajectories. To incorporate these flow estimates into ocean models, existing approaches based on Lagrangian data assimilation usually require significant amount of com- puting power. We develop generic environmental models (GEMs) to combine computational ocean models with real-time data streams collected by mobile sensing platforms to provide high-resolution predictions of ocean current in a small spatial area around the mobile platforms. Motion tomography (MT) can be viewed as a novel way to construct GEMs. The method fuses the data collected by multiple mobile platforms along their paths to formulate an inverse problem that has been the core problem underlying medical CT imaging. By solving this inverse problem, a high-resolution spatial map of ocean flow in the volume traversed by the mobile platforms can be recon- structed. While a similar inverse problem has been formulated and solved in ocean acoustic tomography to reconstruct spatial maps of sound speed, mo- tion tomography provides a directly measured Eulerian map of ocean current, which has never been achieved by other means before. MT may significantly increase the spatial accuracy of GEMs. More accurate GEMs also feed high quality data to data assimilation algorithms, hence eventually improve ocean circulation models.