78 research outputs found
Nonautonomous control of stable and unstable manifolds in two-dimensional flows
We outline a method for controlling the location of stable and unstable
manifolds in the following sense. From a known location of the stable and
unstable manifolds in a steady two-dimensional flow, the primary segments of
the manifolds are to be moved to a user-specified time-varying location which
is near the steady location. We determine the nonautonomous perturbation to the
vector field required to achieve this control, and give a theoretical bound for
the error in the manifolds resulting from applying this control. The efficacy
of the control strategy is illustrated via a numerical example
Probing turbulent superstructures in Rayleigh-B\'{e}nard convection by Lagrangian trajectory clusters
We analyze large-scale patterns in three-dimensional turbulent convection in
a horizontally extended square convection cell by Lagrangian particle
trajectories calculated in direct numerical simulations. A simulation run at a
Prandtl number Pr , a Rayleigh number Ra , and an aspect ratio
is therefore considered. These large-scale structures, which are
denoted as turbulent superstructures of convection, are detected by the
spectrum of the graph Laplacian matrix. Our investigation, which follows
Hadjighasem {\it et al.}, Phys. Rev. E {\bf 93}, 063107 (2016), builds a
weighted and undirected graph from the trajectory points of Lagrangian
particles. Weights at the edges of the graph are determined by a mean dynamical
distance between different particle trajectories. It is demonstrated that the
resulting trajectory clusters, which are obtained by a subsequent -means
clustering, coincide with the superstructures in the Eulerian frame of
reference. Furthermore, the characteristic times and lengths
of the superstructures in the Lagrangian frame of reference agree
very well with their Eulerian counterparts, and ,
respectively. This trajectory-based clustering is found to work for times
. Longer time periods require a
change of the analysis method to a density-based trajectory clustering by means
of time-averaged Lagrangian pseudo-trajectories, which is applied in this
context for the first time. A small coherent subset of the pseudo-trajectories
is obtained in this way consisting of those Lagrangian particles that are
trapped for long times in the core of the superstructure circulation rolls and
are thus not subject to ongoing turbulent dispersion.Comment: 12 pages, 7 downsized figures, to appear in Phys. Rev. Fluid
Role of critical points of the skin friction field in formation of plumes in thermal convection
The dynamics in the thin boundary layers of temperature and velocity is the
key to a deeper understanding of turbulent transport of heat and momentum in
thermal convection. The velocity gradient at the hot and cold plates of a
Rayleigh-B\'{e}nard convection cell forms the two-dimensional skin friction
field and is related to the formation of thermal plumes in the respective
boundary layers. Our analysis is based on a direct numerical simulation of
Rayleigh-B\'{e}nard convection in a closed cylindrical cell of aspect ratio
and focused on the critical points of the skin friction field. We
identify triplets of critical points, which are composed of two unstable nodes
and a saddle between them, as the characteristic building block of the skin
friction field. Isolated triplets as well as networks of triplets are detected.
The majority of the ridges of line-like thermal plumes coincide with the
unstable manifolds of the saddles. From a dynamical Lagrangian perspective,
thermal plumes are formed together with an attractive hyperbolic Lagrangian
Coherent Structure of the skin friction field. We also discuss the differences
from the skin friction field in turbulent channel flows from the perspective of
the Poincar\'{e}-Hopf index theorem for two-dimensional vector fields
Numerical analysis of transport in dynamical systems
Transport processes play an important role in many natural phenomena. Prominent examples are the chaotic advection of fluid particles in geophysical flows or the transport of asteroids and comets in the solar system. Similar transport mechanisms are also at work in chemical physics explaining for example the transition between different conformations of molecules or the kinematics of chemical reactions. Therefore, in the numerical analysis of such dynamical systems one is interested in the identification of those regions in phase space that are involved in the transport process. In this context, invariant manifolds of hyperbolic objects play a crucial role as these structures are known to form natural barriers to transport ...thesi
Layered Architecture Consistency for MANETs: Introducing New Team Members
In this paper we extend our results concerning the layered architecture for modeling workflows in Mobile Ad-Hoc networks (MANETs) using algebraic higher order nets. MANETs are networks of mobile devices that communicate with each other via wireless links without relying on an underlying infrastructure. Workflows in \manets can be adequately modeled using a layered architecture, where the overall workflow, the team members' activities and the mobility issues are separated into three different layers, namely the workflow layer, the mobility layer and the team layer. In fromer papers a formal notion of layer consistency was suggested, that we now extend to allow changes of the interfaces of the gluing of the workflow and the mobility layer
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