The most robust representations of flow trajectories are Lagrangian coherent structures

What is the most robust way to communicate flow trajectories? To answer this question, we employ two neural networks to respectively deconstruct (the encoder) and reconstruct (the decoder) trajectories, where information is passed between the two networks through a low-dimensional latent space in a set-up known as an autoencoder. To ensure that their communications are robust, we add noise to the coded information passed through this latent space. In the low-noise limit the latent space structures are non-spatial in nature, resembling modes of a principle component analysis (PCA). However, as the signal-to-noise ratio is decreased, we uncover Lagrangian coherent structures (LCS) as the most compact representations which still allow the decoder to accurately reconstruct trajectories. This relationship offers increased interpretability to both PCA and LCS analysis, and helps to bridge the gap between two methods of flow analysis.

Numerical investigation of lagrangian coherent structures in steady rotation vortex shedding control

In this paper, vortex shedding and suppression are numerically investigated as autonomous and non-autonomous dynamical systems respectively. Lagrangian coherent structures (LCSs) are used as a numerical tool to analyze these systems. These structures are ridges of Finite time Lyapunov exponent (FTLE) which act as material surfaces that are transport barriers within the flow. Initially, the utility of LCSs is explored for revealing the coherent structures of these systems. Finally, an active flow control method, steady rotation is applied to the non-autonomous dynamical system with different speed ratios to mitigate vortex shedding magnitude. This will eventually turn the system into an autonomous system. Fixed saddle points, separation profiles essentially as unstable time variant manifolds attached to cylinder wall and evolution of other unstable manifolds with variant speed ratios are analyzed with reference to LCSs. It is revealed that speed ratio of 2.1 fully suppresses the von Karman vortex street at Reynolds number of 100 and system turns into an autonomous dynamical system with fixed saddle points and time-invariant manifolds.

Observing and quantifying kinematic properties and lagrangian coherent structures of ocean flows using drifter experiments

This thesis analyzes data from two types of unique drifter experiments in order to characterize two aspects of ocean flows that are often difficult to study. First, vertical velocities and their associated transport processes are often challenging to observe in the real ocean since vertical velocities are typically orders of magnitude smaller than horizontal velocities in mesoscale and submesoscale flows. Second, Lagrangian coherent structures (LCS) are features which categorize ocean flows into regimes of distinct behavior. These structures are also difficult to quantify in the real ocean, since sets of gridded trajectories from real ocean data (rather than model fields) are rarely available. The first experiment uses drifters drogued at multiple depths in the Alboran Sea to observe and characterize the ocean’s vertical structure, particularly near a strong front where vertical velocities are expected to be much stronger than other regions of the Ocean. The second experiment uses a roughly gridded pattern of surface drifters in the Gulf of Mexico to study LCSs as quantified by methods from dynamical systems such as finitetime Lyapunov exponents (FTLEs), trajectory arc-length, correlation dimension, dilation, Lagrangian-averaged vorticity deviation (LAVD), and spectral clustering. This thesis includes the first attempt to apply these dynamical systems techniques to real drifters for LCS detection. Overall, these experiments and the methods used in this paper are shown to be promising new techniques for quantifying both the vertical structure of ocean flows and Lagrangian Coherent Structures of flows using real drifter data. Future work may involve modified versions of the experiments, with denser sets of ocean drifters in the horizontal and/or vertical directions.

Experimental Investigation of Lagrangian Coherent Structures and Lobe Dynamics in Perturbed Rayleigh-Benard Convection

It is well known that Rayleigh-Benard convection with perturbations yields Lagrangian chaotic transport, and the mechanism of inducing chaotic transport has been numerically clarified by lobe dynamics [2]. On the other hand, the mechanism of such Lagrangian transport has not been enough studied by experiments. In our previous work [16], we made an experimental study to investigate the Lagrangian transport appeared in the two-dimensional Rayleigh-Benard convection by giving oscillation on the velocity fields and showed that there exist Lagrangian Coherent Structures (LCSs) which correspond to invariant manifolds of non-autonomous systems. We also showed that the LCSs entangle with each other around cell boundaries. In this paper, we further explore the global invariant structures of the perturbed Rayleigh-Benard convection by clarifying the details on the LCSs and explain how the fluid transport obeys lobe dynamics. Finally, we propose a novel Hamiltonian model for the two-dimensional perturbed Rayleigh-Benard convection that enables to elucidate the global structures detected by experiments.