scholarly journals Finite-time statistics of scalar diffusion in Lagrangian coherent structures

2012 ◽  
Vol 86 (4) ◽  
Author(s):  
Wenbo Tang ◽  
Phillip Walker
Keyword(s):  
Coherent Structures ◽  
Finite Time ◽  
Lagrangian Coherent Structures ◽  
Scalar Diffusion

scholarly journals Lagrangian coherent structures in tropical cyclone intensification

2012 ◽  
Vol 12 (12) ◽  
pp. 5483-5507 ◽  
Author(s):  
B. Rutherford ◽  
G. Dangelmayr ◽  
M. T. Montgomery
Keyword(s):  
Boundary Layer ◽  
Tropical Cyclone ◽  
Flow Field ◽  
Coherent Structures ◽  
Finite Time ◽  
Potential Temperature ◽  
Three Dimensional ◽  
Lagrangian Coherent Structures ◽  
Moist Convection ◽  
Hyperbolic Structures

Abstract. Recent work has suggested that tropical cyclones intensify via a pathway of rotating deep moist convection in the presence of enhanced fluxes of moisture from the ocean. The rotating deep convective structures possessing enhanced cyclonic vorticity within their cores have been dubbed Vortical Hot Towers (VHTs). In general, the interaction between VHTs and the system-scale vortex, as well as the corresponding evolution of equivalent potential temperature (θe) that modulates the VHT activity, is a complex problem in moist helical turbulence. To better understand the structural aspects of the three-dimensional intensification process, a Lagrangian perspective is explored that focuses on the coherent structures seen in the flow field associated with VHTs and their vortical remnants, as well as the evolution and localized stirring of θe. Recently developed finite-time Lagrangian methods are limited in the three-dimensional turbulence and shear associated with the VHTs. In this paper, new Lagrangian techniques developed for three-dimensional velocity fields are summarized and we apply these techniques to study VHT and θe phenomenology in a high-resolution numerical tropical cyclone simulation. The usefulness of these methods is demonstrated by an analysis of particle trajectories. We find that VHTs create a locally turbulent mixing environment. However, associated with the VHTs are hyperbolic structures that span between adjacent VHTs or adjacent vortical remnants and represent coherent finite-time transport barriers in the flow field. Although the azimuthally-averaged inflow is responsible for the inward advection of boundary layer θe, attracting Lagrangian coherent structures are coincident with pools of high boundary layer θe. Extensions of boundary layer coherent structures grow above the boundary layer during episodes of convection and remain with the convective vortices. These hyperbolic structures form initially as boundaries between VHTs. As vorticity aggregates into a ring-like eyewall feature, the Lagrangian boundaries merge into a ring outside of the region of maximal vorticity.

scholarly journals Supergranular turbulence in the quiet Sun: Lagrangian coherent structures

2019 ◽  
Vol 488 (3) ◽  
pp. 3076-3088 ◽  
Author(s):  
Abraham C-L Chian ◽  
Suzana S A Silva ◽  
Erico L Rempel ◽  
Milan Gošić ◽  
Luis R Bellot Rubio ◽  
...  
Keyword(s):  
Coherent Structures ◽  
Finite Time ◽  
Local Maximum ◽  
Lagrangian Coherent Structures ◽  
Quiet Sun ◽  
Finite Time Lyapunov Exponent ◽  
Magnetic Elements ◽  
Disc Centre ◽  
Transport Barriers ◽  
Intensity Images

ABSTRACT The quiet Sun exhibits a wealth of magnetic activities that are fundamental for our understanding of solar magnetism. The magnetic fields in the quiet Sun are observed to evolve coherently, interacting with each other to form prominent structures as they are advected by photospheric flows. The aim of this paper is to study supergranular turbulence by detecting Lagrangian coherent structures (LCS) based on the horizontal velocity fields derived from Hinode intensity images at disc centre of the quiet Sun on 2010 November 2. LCS act as transport barriers and are responsible for attracting/repelling the fluid elements and swirling motions in a finite time. Repelling/attracting LCS are found by computing the forward/backward finite-time Lyapunov exponent (FTLE), and vortices are found by the Lagrangian-averaged vorticity deviation method. We show that the Lagrangian centres and boundaries of supergranular cells are given by the local maximum of the forward and backward FTLE, respectively. The attracting LCS expose the location of the sinks of photospheric flows at supergranular junctions, whereas the repelling LCS interconnect the Lagrangian centres of neighbouring supergranular cells. Lagrangian transport barriers are found within a supergranular cell and from one cell to other cells, which play a key role in the dynamics of internetwork and network magnetic elements. Such barriers favour the formation of vortices in supergranular junctions. In particular, we show that the magnetic field distribution in the quiet Sun is determined by the combined action of attracting/repelling LCS and vortices.

Surface and deep ocean connectivity inferred from robust extraction of coherent sets in ocean flow using models and sparse, scattered, and incomplete float data with transfer operator and dynamic Laplacian methods.

2021 ◽  
Author(s):  
Gary Froyland ◽  
Ryan Abernathey ◽  
Michael Denes ◽  
Shane Keating
Keyword(s):  
Coherent Structures ◽  
Finite Time ◽  
Transfer Operator ◽  
Deep Ocean ◽  
Difficult Problem ◽  
Lagrangian Coherent Structures ◽  
Diffusion Limit ◽  
Small Diffusion ◽  
Transport And Mixing ◽  
Atmospheric Vortices

<p>Transport and mixing properties of the ocean's circulation is crucial to dynamical analyses, and often have to be carried out with limited observed information. Finite-time coherent sets are regions of the ocean that minimally mix (in the presence of small diffusion) with the rest of the ocean domain over the finite period of time considered. In the purely advective setting (in the zero diffusion limit) this is equivalent to identifying regions whose boundary interfaces remain small throughout their finite-time evolution. Finite-time coherent sets thus provide a skeleton of distinct regions around which more turbulent flow occurs. Well known manifestations of finite-time coherent sets in geophysical systems include rotational objects like ocean eddies, ocean gyres, and atmospheric vortices. In real-world settings, often observational data is scattered and sparse, which makes the difficult problem of coherent set identification and tracking challenging. I will describe mesh-based numerical methods [3] to efficiently approximate the recently defined dynamic Laplace operator [1,2], and rapidly and reliably extract finite-time coherent sets from models or scattered, possibly sparse, and possibly incomplete observed data. From these results we can infer new chemical and physical ocean connectivities at global and intra-basin scales (at the surface and at depth), track series of eddies, and determine new oceanic barriers.</p><p>[1] G. Froyland. Dynamic isoperimetry and the geometry of Lagrangian coherent structures. <em>Nonlinearity</em>, 28:3587-3622, 2015</p><p>[2] G. Froyland and E. Kwok. A dynamic Laplacian for identifying Lagrangian coherent structures on weighted Riemannian manifolds. <em>Journal of Nonlinear Science</em>, 30:1889–1971, 2020.</p><p>[3] Gary Froyland and Oliver Junge. Robust FEM-based extraction of finite-time coherent sets using scattered, sparse, and incomplete trajectories. <em>SIAM J. Applied Dynamical Systems</em>, 17:1891–1924, 2018.</p>

scholarly journals Chaotic Manifold Analysis of Four-Screw Extruders Based on Lagrangian Coherent Structures

Materials ◽  
2018 ◽  
Vol 11 (11) ◽  
pp. 2272 ◽  
Author(s):  
Xiang Zhu ◽  
Ying Tong ◽  
Yue Hu
Keyword(s):  
Coherent Structures ◽  
Finite Time ◽  
Fluid Transport ◽  
Polymer Processing ◽  
Lagrangian Coherent Structures ◽  
Initial Time ◽  
Chaotic Mixing ◽  
Mixing Efficiency ◽  
Mixing Performance ◽  
Screw Extruders

The four-screw extruder (FSE) is a novel equipment for polymer processing. In this paper, from a new viewpoint of Lagrangian coherent structures (LCS), two-dimensional fluid transport and chaotic mixing characteristics within three kinds of novel industrial FSEs are explored based on LCS to better understand the flow and mixing natures in the FSEs. Firstly, based on the finite-time invariant manifold theory, the finite-time Lyapunov exponent (FTLE) and LCS of FSEs are calculated by considering the different initial time. Hyperbolic LCSs from the FTLE maps are adopted to identify chaotic mixing manifolds in FSEs. Moreover, particle tracking and Poincaré sections are used to illustrate the different fluid motions in the above three isolated regions. Finally, the effects of relative rotating directions and layout of four screws on the chaotic manifolds in FESs are discussed in order to enhance local mixing performance. Furthermore, quantitative mixing measures, such as the segregation scale, logarithmic of stretching, and mean-time mixing efficiency are employed to compare the mixing efficiencies in three kinds of FSEs. The results show that the relative rotating directions and positions of four screws can change the chaotic manifolds and increase mixing performance in local poor mixing regions. FTLE and LCS analysis are helpful to better understand the chaotic mixing nature in the novel screw extruders.

scholarly journals Investigating the connection between complexity of isolated trajectories and Lagrangian coherent structures

2011 ◽  
Vol 18 (6) ◽  
pp. 977-987 ◽  
Author(s):  
I. I. Rypina ◽  
S. E. Scott ◽  
L. J. Pratt ◽  
M. G. Brown
Keyword(s):  
Coherent Structures ◽  
Finite Time ◽  
Correlation Dimension ◽  
Reference Frames ◽  
Lagrangian Coherent Structures ◽  
New Method ◽  
Data Sets ◽  
Time Intervals ◽  
Basic Principles ◽  
Two Measures

Abstract. It is argued that the complexity of fluid particle trajectories provides the basis for a new method, referred to as the Complexity Method (CM), for estimation of Lagrangian coherent structures in aperiodic flows that are measured over finite time intervals. The basic principles of the CM are explained and the CM is tested in a variety of examples, both idealized and realistic, and in different reference frames. Two measures of complexity are explored in detail: the correlation dimension of trajectory, and a new measure – the ergodicity defect. Both measures yield structures that strongly resemble Lagrangian coherent structures in all of the examples considered. Since the CM uses properties of individual trajectories, and not separation rates between closely spaced trajectories, it may have advantages for the analysis of ocean float and drifter data sets in which trajectories are typically widely and non-uniformly spaced.

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