scholarly journals Detecting invariant manifolds as stationary Lagrangian coherent structures in autonomous dynamical systems

2013 ◽  
Vol 23 (4) ◽  
pp. 043107 ◽  
Author(s):  
Hiroshi Teramoto ◽  
George Haller ◽  
Tamiki Komatsuzaki
Keyword(s):  
Dynamical Systems ◽  
Coherent Structures ◽  
Invariant Manifolds ◽  
Lagrangian Coherent Structures ◽  
Autonomous Dynamical Systems

scholarly journals From manifolds to Lagrangian coherent structures in galactic bar models

2018 ◽  
Vol 618 ◽  
pp. A72 ◽  
Author(s):  
P. Sánchez-Martín ◽  
J. J. Masdemont ◽  
M. Romero-Gómez
Keyword(s):  
Dynamical System ◽  
Fluid Dynamics ◽  
Coherent Structures ◽  
Invariant Manifolds ◽  
Lagrangian Coherent Structures ◽  
Galactic Dynamics ◽  
Secular Evolution ◽  
Autonomous Case ◽  
The Galaxy ◽  
Pattern Speed

We study the dynamics near the unstable Lagrangian points in galactic bar models using dynamical system tools in order to determine the global morphology of a barred galaxy. We aim at the case of non-autonomous models, in particular with secular evolution, by allowing the bar pattern speed to decrease with time. We have extended the concept of manifolds widely used in the autonomous problem to the Lagrangian coherent structures (LCS), widely used in fluid dynamics, which behave similar to the invariant manifolds driving the motion. After adapting the LCS computation code to the galactic dynamics problem, we apply it to both the autonomous and non-autonomous problems, relating the results with the manifolds and identifying the objects that best describe the motion in the non-autonomous case. We see that the strainlines coincide with the first intersection of the stable manifold when applied to the autonomous case, while, when the secular model is used, the strainlines still show the regions of maximal repulsion associated to both the corresponding stable manifolds and regions with a steep change of energy. The global morphology of the galaxy predicted by the autonomous problem remains unchanged.

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

2021 ◽  
Author(s):  
Muhammad Hashir ◽  
◽  
Tauseef -ur-Rehman ◽  
Aamir Sohail ◽  
Muhammad Yasar Javaid ◽  
...  
Keyword(s):  
Dynamical System ◽  
Vortex Shedding ◽  
Coherent Structures ◽  
Invariant Manifolds ◽  
Saddle Points ◽  
Lagrangian Coherent Structures ◽  
Speed Ratio ◽  
Cylinder Wall ◽  
Steady Rotation ◽  
Autonomous Dynamical System

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.

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

2021 ◽  
Author(s):  
◽  
Timothy Getscher
Keyword(s):  
Dynamical Systems ◽  
Coherent Structures ◽  
Vertical Structure ◽  
Transport Processes ◽  
Lagrangian Coherent Structures ◽  
New Techniques ◽  
The Real ◽  
Ocean Flows ◽  
Surface Drifters ◽  
Future Work

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.

Lagrangian coherent structures in the planar parabolic/hyperbolic restricted three-body problem

2020 ◽  
Vol 493 (2) ◽  
pp. 1574-1586
Author(s):  
Qingyu Qu ◽  
Mingpei Lin ◽  
Ming Xu
Keyword(s):  
Phase Space ◽  
Coherent Structures ◽  
Body Problem ◽  
Invariant Manifolds ◽  
Lagrangian Coherent Structures ◽  
Time Dependent ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Three Body ◽  
Capture Trajectories

ABSTRACT It is clarified that the parabolic/hyperbolic restricted three-body problem (PRTBP/HRTBP) can be adopted to provide a simple description of the dynamics of fly-by asteroids or the close encounters between different galaxies. For these reasons, PRTBP and HRTBP have been investigated for long intervals of time. However, they are quite different from the circular restricted three-body problem due to the time-dependent and non-periodic dynamics. The Lagrangian coherent structures (LCSs), as a useful tool to analyse the time-dependent dynamical system, could be applied to explain some mechanics of the PRTBP and HRTBP. In this paper, we verify the invariant manifolds on the boundary manifolds of PRTBP by analysing the LCSs in proper Poincaré sections, which shows that it works in such a non-periodic problem. One of the contributions is to investigate the LCSs in the complete phase space of PRTBP, and then some natural escape and capture trajectories from or to the two main bodies can be obtained in this way. Another contribution is to establish and study the dynamics of HRTBP and its boundary. The LCSs can be introduced into this system, reasonably, to work as the analogues of the invariant manifolds, and the similar natural escape and capture trajectories corresponding to the two main bodies can also be obtained in the complete phase space of HRTBP. As a typical technique applied to fluid, flows to identify transport barriers in the time-dependent system, the LCSs provide an effective way to determine the time-dependent analogues of invariant manifolds for the PRTBP/HRTBP.

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