Congratulations to Arkopal Dutt for successfully clearing the MIT Mechanical Engineering Ph.D Qualifying Exams. Arkopal now begins his journey towards an outstanding Ph.D thesis. All the best!

The talk will present the integrated data-driven modeling and forecasting system that we have developed to study and understand the physical and biological variability of the Red Sea. I will first describe the modeling system and summarize our key findings on the Red Sea general circulation, including the striking seasonally overturning circulation, the dominant eddy activity, and the occasional northern deep water formation events, and discuss their impact on the Red Sea ecosystem. I will then focus on our efforts to develop an efficient ensemble data assimilation and forecasting system for the Red Sea, presenting recent algorithmic developments and results, and discussing our future plans. 

Autonomous underwater vehicles (AUVs) are a valuable resource in several oceanic applications such as security, surveillance and data collection for ocean prediction. These vehicles typically travel at speeds comparable to ocean currents, and their movement is significantly affected by these dynamic currents. Further, the speed of currents may vary greatly with depth. Hence, path planning to generate safe and fast vehicle trajectories in such a three-dimensional environment becomes crucial for the successful operation of these vehicles. In addition, many marine vehicles can only move in specific directions and with a speed that is dependent on the direction of travel. Such constraints must be respected in order to plan safe and optimal paths.

Thus, our motivation in this thesis is to study path planning for vehicles with and without motion constraints in three-dimensional dynamic flow-fields. We utilize the time-optimal path planning methodology given by Lolla et al. (2012) for this purpose.

In this thesis, we first review some existing path planning methods (both in two and three-dimensional settings). Then, we discuss the theoretical basis of the rigorous partial differential equation based methodology that is utilized in order to plan safe and optimal paths. This is followed by an elaborate discussion about the application of this methodology to the various types of marine vehicles. We then look at the robust and accurate numerical methods developed in order to solve the governing equations for the path planning methodology with high accuracy in real ocean domains. We illustrate the working and capabilities of our path planning algorithm by means of a number of applications. First we study some benchmark examples with known analytical solutions. Second, we look at more complex flow-fields that analytically model different oceanic flows. Finally, we look at the path planning for different types of marine vehicles in a realistic ocean domain to illustrate the capabilities of the path planning methodology and the developed numerical framework.

Arkopal Dutt secured the second place award for his project in the 18.335 Introduction to Numerical Methods course at MIT. His project was titled “Algorithms for Low Rank Approximations: Contest Between Deterministic and Randomized”. Congratulations Arkopal!

Graduate student Chinmay Kulkarni and Prof. Pierre Lermusiaux presented some of the recent results from our MSEAS group on Lagrangian Coherent Structures at the SIAM Conference on Applications of Dynamical Systems at Snowbird, Utah between May 21 and 25, 2017.