On the Finite-Time Scope for Computing Lagrangian Coherent Structures from Lyapunov Exponents

Abstract Two sea surface height (SSH) anomaly fields distributed by Archiving, Validation, and Interpretation of Satellite Oceanographic (AVISO) Altimetry are evaluated in terms of the effects that they produce on mixing. One SSH anomaly field, tagged REF, is constructed using measurements made by two satellite altimeters; the other SSH anomaly field, tagged UPD, is constructed using measurements made by up to four satellite altimeters. Advection is supplied by surface geostrophic currents derived from the total SSH fields resulting from the addition of these SSH anomaly fields to a mean SSH field. Emphasis is placed on the extraction from the currents of Lagrangian coherent structures (LCSs), which, acting as skeletons for patterns formed by passively advected tracers, entirely control mixing. The diagnostic tool employed to detect LCSs is provided by the computation of finite-time Lyapunov exponents. It is found that currents inferred using UPD SSH anomalies support mixing with characteristics similar to those of mixing produced by currents inferred using REF SSH anomalies. This result mainly follows from the fact that, being more easily characterized as chaotic than turbulent, mixing as sustained by currents derived using UPD SSH anomalies is quite insensitive to spatiotemporal truncations of the advection field.

Download Full-text

An Alternative Formulation of Lyapunov Exponents for Computing Lagrangian Coherent Structures

2014 IEEE Pacific Visualization Symposium ◽

10.1109/pacificvis.2014.27 ◽

2014 ◽

Cited By ~ 2

Author(s):

Allen R. Sanderson

Keyword(s):

Lyapunov Exponents ◽

Coherent Structures ◽

Lagrangian Coherent Structures ◽

Alternative Formulation

Download Full-text

Lagrangian coherent structures in tropical cyclone intensification

Atmospheric Chemistry and Physics ◽

10.5194/acp-12-5483-2012 ◽

2012 ◽

Vol 12 (12) ◽

pp. 5483-5507 ◽

Cited By ~ 11

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.

Download Full-text

Supergranular turbulence in the quiet Sun: Lagrangian coherent structures

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/stz1909 ◽

2019 ◽

Vol 488 (3) ◽

pp. 3076-3088 ◽

Cited By ~ 4

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.

Download Full-text

Finite-time statistics of scalar diffusion in Lagrangian coherent structures

Physical Review E ◽

10.1103/physreve.86.045201 ◽

2012 ◽

Vol 86 (4) ◽

Cited By ~ 6

Author(s):

Wenbo Tang ◽

Phillip Walker

Keyword(s):

Coherent Structures ◽

Finite Time ◽

Lagrangian Coherent Structures ◽

Scalar Diffusion

Download Full-text

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.

10.5194/egusphere-egu21-6710 ◽

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

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.[1] G. Froyland. Dynamic isoperimetry and the geometry of Lagrangian coherent structures. Nonlinearity, 28:3587-3622, 2015[2] G. Froyland and E. Kwok. A dynamic Laplacian for identifying Lagrangian coherent structures on weighted Riemannian manifolds. Journal of Nonlinear Science, 30:1889&#8211;1971, 2020.[3] Gary Froyland and Oliver Junge. Robust FEM-based extraction of finite-time coherent sets using scattered, sparse, and incomplete trajectories. SIAM J. Applied Dynamical Systems, 17:1891&#8211;1924, 2018.

Download Full-text