Session 6

Thursday, 19 May 2016, 9:00 AM to 10:30 AM

20 minutes per talk, 10 minutes for questions and speaker change

From	To	Name	Affiliation	Title
9:00am	9:30am	Michel Speetjens	Eindhoven University of Technology	Lagrangian transport in three-dimensional unsteady flows with (perturbed) periodic lines
9:30am	10:00am	Wenbo Tang	Arizona State University	Scalar density evolution with Lagrangian measures
10:00am	10:30am	Daniel Karrasch	Technische Universität München	Properties of coherent structure detection methods

 

Session 6 Abstracts

Lagrangian transport in three-dimensional unsteady flows with (perturbed) periodic lines

Michel Speetjens (Eindhoven University of Technology)
Periodic lines and their response to perturbations are key to the Lagrangian dynamics of many threedimensional
(3D) time-periodic flows. However, studies on this subject in general concern highly idealized
flows and/or investigate dynamics in terms of a canonical representation based on linearization in the
direct proximity of periodic lines. An important question in the light of applications is to what extent such
approaches connect with realistic flow situations. This is addressed by investigating (perturbed) periodic
lines in experimentally realizable 3D time-periodic flows.
Analyses reveal that each periodic line has a "zone of influence" in which it exclusively governs the
dynamics. Here Lagrangian motion is, irrespective of the existence of a global invariant, restricted to local
invariant surfaces in which essentially 2D Hamiltonian dynamics occurs. Moreover, the dynamics in (almost)
the entire zone of influence admits reconciliation with the beforementioned canonical form through a
linearizing transformation. This extends the link between physical and canonical space from the direct
proximity of the periodic line to (almost) the entire zone of influence.
The canonical form facilitates systematic exploration of the impact of weak perturbation on the dynamics
throughout (almost) the entire zone of influence. Thus various response scenarios and mechanisms can
be identified as a function of the nature of the perturbation and the properties of the periodic lines. This
encompasses several (in part ill-understood) phenomena studied in literature, demonstrating that the
canonical form adequately captures the full richness of the dynamics.
Key findings on (perturbed) periodic lines are supported by laboratory studies on 3D Lagrangian dynamics
of tracer particles. This experimentally demonstrates the existence of periodic lines. Moreover, this
provides first direct experimental evidence of the existence and universality of a certain response scenario
to weak perturbations.

Scalar density evolution with Lagrangian measures

Wenbo Tang (Arizona State University)
In integrable shear flows, the second order moments of a passively advected and diffusive scalar can be
computed analytically to obtain the spatial- and temporal-dependent effective diffusivity. In nonintegrable
flows, such analytical results are not accessible. In this talk, we discuss a semi-analytic
framework, which reconstructs scalar density evolution from finite-time Lagrangian measures. We pay
close attention to the stretching and shearing components of the deformation tensor, both playing
important roles in shaping scalar patches. With proper choice of time-scale for mapping the scalar density
forward, we show that the scalar density field can be resolved without having to solve the transport
equation.

Properties of coherent structure detection methods

Daniel Karrasch (Technische Universität München)
In my talk I critically review the common use of terminology related to coherent structure detection
methods. This includes terms like "Eulerian", "Lagrangian", and "objectivity". The aim of the talk is to
propose a slightly different use of that terminology for the benefit of conceptual clarity and consistency
with continuum mechanics.