[Soft-matter] Soft Matter & Complex Systems Seminar on 22 Nov 2024

[Maciej Lisicki]

Dear Soft Matter & Complex Systems Colleagues and Friends,

On Friday 22 November 2024 at 9:30 AM at the UW Faculty of Physics (Pasteura 5, Warsaw; room 1.40) we are hosting a seminar during which 

Stanisław Gepner (Warsaw University of Technology)

will give a talk
Is the Laminar-Turbulent Edge Crowded? Exploring Multiple Local Attractors in the Edge of Square-Duct Flow

Abstract

In this work, we present the first streamwise-localized invariant
solution for turbulent square duct flow in the moderate Reynolds number
range. Through heuristic analysis, we demonstrate that during specific
periods within the turbulent time evolution, the flow state approaches
the identified localized solution. This finding indicates that the
localized solution is embedded within the turbulent attractor, making it
the first localized solution identified for square duct flow and a
the potential building block of turbulence in this configuration.

We obtain this solution through a bisection process applied within the
symmetric subspace of the full state space, which enables the tracking
of edge state solutions. Edge states are characterized by a single
unstable direction, or a co-dimension one stable manifold, within the
symmetric subspace. In the context of the full state space, these
solutions are embedded within the turbulent attractor. As relative
attractors on the edge of the laminar and turbulent basins, edge states
play a significant role in governing the laminar-turbulent transition
process. This characteristic makes them particularly interesting for
turbulence control applications. In addition to the bisection method, we
use Newton-Krylov GMRES-based iterations to converge to invariant
solutions. To analyze stability, we apply an Arnoldi-based eigenvalue
solver, and an arc-length continuation to track bifurcations. Stability
analysis reveals that both branches of our localized solution are
unstable in at least one direction. This instability suggests the
presence of additional structures that may connect to the branches of
the identified solution, indicating that the edge subspace (a
co-dimension one subspace of the full space) contains multiple local
attractors. Each of these local edge states would have stable manifolds
that locally separate initial conditions, leading either toward the
laminar attractor, a transient non-laminar excursion or, if it exists,
a turbulent attractor. In our ongoing work, we identify and analyze a
series of solutions on the edge. We study the positions and potential
connections between the lower and upper branches of the identified
solutions. By disturbing either the lower or upper branch in the
unstable direction, we observe that the system tends either to
laminarize smoothly or to experience a transient turbulent excursion.
This behavior confirms that both solution branches reside on the edge
and that the bifurcation responsible for their creation also lies on the
edge. Additionally, we identify a potential heteroclinic connection
between these states, which further enriches our understanding of the
dynamics governing laminar-turbulent transition in square duct flow.

We warmly welcome everyone to attend the talk and the Soft Matter Coffee Break after the seminar, held in room 2.63 (2nd floor).

Maria Ekiel-Jeżewska
Maciej Lisicki
Piotr Szymczak
Panagiotis Theodorakis
Marek Trippenbach

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