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 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 Pollution Transport Patterns Obtained Through Generalized Lagrangian Coherent Structures

Atmosphere ◽  
2020 ◽  
Vol 11 (2) ◽  
pp. 168
Author(s):  
Peter J. Nolan ◽  
Hosein Foroutan ◽  
Shane D. Ross
Keyword(s):  
Velocity Field ◽  
Coherent Structures ◽  
Initial Conditions ◽  
Saddle Points ◽  
Chemical Species ◽  
Lagrangian Coherent Structures ◽  
Time Interval ◽  
Pollution Transport ◽  
Material Transport ◽  
Material Surfaces

Identifying atmospheric transport pathways is important to understand the effects of pollutants on weather, climate, and human health. The atmospheric wind field is variable in space and time and contains complex patterns due to turbulent mixing. In such a highly unsteady flow field, it can be challenging to predict material transport over a finite-time interval. Particle trajectories are often used to study how pollutants evolve in the atmosphere. Nevertheless, individual trajectories are sensitive to their initial conditions. Lagrangian Coherent Structures (LCSs) have been shown to form the template of fluid parcel motion in a fluid flow. LCSs can be characterized by special material surfaces that organize the parcel motion into ordered patterns. These key material surfaces form the core of fluid deformation patterns, such as saddle points, tangles, filaments, barriers, and pathways. Traditionally, the study of LCSs has looked at coherent structures derived from integrating the wind velocity field. It has been assumed that particles in the atmosphere will generally evolve with the wind. Recent work has begun to look at the motion of chemical species, such as water vapor, within atmospheric flows. By calculating the flux associated with each species, a new effective flux-based velocity field can be obtained for each species. This work analyzes generalized species-weighted coherent structures associated with various chemical species to find their patterns and pathways in the atmosphere, providing a new tool and language for the assessment of pollutant transport and patterns.

scholarly journals Lagrangian coherent structures and plasma transport processes

2015 ◽  
Vol 81 (5) ◽  
Author(s):  
M. V. Falessi ◽  
F. Pegoraro ◽  
T. J. Schep
Keyword(s):  
Dynamical System ◽  
Phase Space ◽  
Coherent Structures ◽  
Transport Processes ◽  
Lagrangian Coherent Structures ◽  
Plasma Transport ◽  
Periodic Systems ◽  
Transport Barriers ◽  
Definition Of ◽  
General Time

A dynamical system framework is used to describe transport processes in plasmas embedded in a magnetic field. For periodic systems with one degree of freedom, the Poincaré map provides a splitting of the phase space into regions where particles have different kinds of motion: periodic, quasi-periodic or chaotic. The boundaries of these regions are transport barriers, i.e. a trajectory cannot cross such boundaries throughout the evolution of the system. Lagrangian coherent structures generalize this method to systems with the most general time dependence, splitting the phase space into regions with different qualitative behaviours. This leads to the definition of finite-time transport barriers, i.e. trajectories cannot cross the barrier for a finite amount of time. This methodology can be used to identify fast recirculating regions in the dynamical system and to characterize the transport between them.

DYNAMICS OF A SIMPLE ENDOGENOUS GROWTH MODEL WITH FINANCIAL INTERMEDIATION

2019 ◽  
pp. 1-15
Author(s):  
Dominika Byrska ◽  
Adam Krawiec ◽  
Marek Szydłowski
Keyword(s):  
Dynamical System ◽  
Economic Growth ◽  
Invariant Manifolds ◽  
Financial Intermediation ◽  
Three Dimensional ◽  
Mathematical Methods ◽  
Endogenous Growth Model ◽  
Dimensional Dynamical System ◽  
Insight Into ◽  
Autonomous Dynamical System

We study an impact of the financial intermediation on economic growth. We assume the simple model of the economic growth in the form of an autonomous dynamical system with a financial sector represented by banks and real sector represented by households and firms. We assume that financial intermediation services are described by financial intermediation technology which is a function depending on the share of labor employed by banks. Investments realized by firms depend not only on savings accumulated by banks but also on financial intermediation technology. We obtain a three-dimensional dynamical system and analyze the existence of a saddle equilibrium in the growth process associated with financial intermediation. Using mathematical methods of dynamical systems, we analyze growth paths, and we study the stationary states of the system and their stability. We found that equilibrium is reached only by trajectories located on two submanifolds. The resulting analysis provides an insight into the saddle solution with a stable incoming separatrix lying on one of the invariant manifolds.

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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