Lagrangian coherent structures and inertial particle dynamics

Finite-horizon, energy-efficient trajectories in unsteady flows

Intelligent mobile sensors, such as uninhabited aerial or underwater vehicles, are becoming prevalent in environmental sensing and monitoring applications. These active sensing platforms operate in unsteady fluid flows, including windy urban environments, hurricanes and ocean currents. Often constrained in their actuation capabilities, the dynamics of these mobile sensors depend strongly on the background flow, making their deployment and control particularly challenging. Therefore, efficient trajectory planning with partial knowledge about the background flow is essential for teams of mobile sensors to adaptively sense and monitor their environments. In this work, we investigate the use of finite-horizon model predictive control (MPC) for the energy-efficient trajectory planning of an active mobile sensor in an unsteady fluid flow field. We uncover connections between trajectories optimized over a finite-time horizon and finite-time Lyapunov exponents of the background flow, confirming that energy-efficient trajectories exploit invariant coherent structures in the flow. We demonstrate our findings on the unsteady double gyre vector field, which is a canonical model for chaotic mixing in the ocean. We present an exhaustive search through critical MPC parameters including the prediction horizon, maximum sensor actuation, and relative penalty on the accumulated state error and actuation effort. We find that even relatively short prediction horizons can often yield energy-efficient trajectories. We also explore these connections on a three-dimensional flow and ocean flow data from the Gulf of Mexico. These results are promising for the adaptive planning of energy-efficient trajectories for swarms of mobile sensors in distributed sensing and monitoring.

Feature identification in time-indexed model output

We present a method for identifying features (time periods of interest) in data sets consisting of time-indexed model output. The method is used as a diagnostic to quickly focus the attention on a subset of the data before further analysis methods are applied. Mathematically, the infinity norm errors of empirical orthogonal function (EOF) reconstructions are calculated for each time output. The result is an EOF reconstruction error map which clearly identifies features as changes in the error structure over time. The ubiquity of EOF-type methods in a wide range of disciplines reduces barriers to comprehension and implementation of the method. We apply the error map method to three different Computational Fluid Dynamics (CFD) data sets as examples: the development of a spontaneous instability in a large amplitude internal solitary wave, an internal wave interacting with a density profile change, and the collision of two waves of different vertical mode. In all cases the EOF error map method identifies relevant features which are worthy of further study.

Particle slip velocity influences inertial focusing of particles in curved microchannels

Size based separation and identification of particles in microfluidics through purely hydrodynamic means has gained significant interest due to a number of possible biomedical applications. Curved micro-channels, particularly spiral micro-channels with rectangular cross-section and the dynamics of particles in such channels have been extensively researched to achieve size based separation of particles. In this paper we present evidence that sheds new light on the dynamics of particles in such curved channels; that a unique particle slip velocity is associated with the focusing positions in the cross sections, which leads to a balance of forces. Our experiments therefore imply that the forces acting on the particle lead to convergence to an attractor in both the physical space (the cross section of the channel) and the slip velocity space.

Topological Analysis of Inertial Dynamics

Traditional vector field visualization has a close focus on velocity, and is typically constrained to the dynamics of massless particles. In this paper, we present a novel approach to the analysis of the force-induced dynamics of inertial particles. These forces can arise from acceleration fields such as gravitation, but also be dependent on the particle dynamics itself, as in the case of magnetism. Compared to massless particles, the velocity of an inertial particle is not determined solely by its position and time in a vector field. In contrast, its initial velocity can be arbitrary and impacts the dynamics over its entire lifetime. This leads to a four-dimensional problem for 2D setups, and a six-dimensional problem for the 3D case. Our approach avoids this increase in dimensionality and tackles the visualization by an integrated topological analysis approach. We demonstrate the utility of our approach using a synthetic time-dependent acceleration field, a system of magnetic dipoles, and N-body systems both in 2D and 3D.