Chaotic Advection by Two-Dimensional Stokes Flow in a Semicircle

2004 ◽  
Vol 31 (4) ◽  
pp. 344-357
Author(s):  
T. A. Dunaeva ◽  
A. A. Gourjii ◽  
V. V. Meleshko
Keyword(s):  
Stokes Flow ◽  
Chaotic Advection ◽  
Two Dimensional

Chaotic Advection by Two-Dimensional Stokes Flow in Circle

2002 ◽  
Vol 29 (5) ◽  
pp. 9
Author(s):  
T. A. Dunaeva ◽  
H. Aref ◽  
V. V. Meleshko
Keyword(s):  
Stokes Flow ◽  
Chaotic Advection ◽  
Two Dimensional

Cellular flow in a partially filled rotating drum: regular and chaotic advection

2017 ◽  
Vol 825 ◽  
pp. 631-650 ◽  
Author(s):  
Francesco Romanò ◽  
Arash Hajisharifi ◽  
Hendrik C. Kuhlmann
Keyword(s):  
Three Dimensional ◽  
Reynolds Numbers ◽  
Chaotic Advection ◽  
Two Dimensional ◽  
Rotating Drum ◽  
Three Dimensional Flow ◽  
Dimensional Flow ◽  
Heteroclinic Connection ◽  
Two Dimensional Flow ◽  
Chaotic Streamlines

The topology of the incompressible steady three-dimensional flow in a partially filled cylindrical rotating drum, infinitely extended along its axis, is investigated numerically for a ratio of pool depth to radius of 0.2. In the limit of vanishing Froude and capillary numbers, the liquid–gas interface remains flat and the two-dimensional flow becomes unstable to steady three-dimensional convection cells. The Lagrangian transport in the cellular flow is organised by periodic spiralling-in and spiralling-out saddle foci, and by saddle limit cycles. Chaotic advection is caused by a breakup of a degenerate heteroclinic connection between the two saddle foci when the flow becomes three-dimensional. On increasing the Reynolds number, chaotic streamlines invade the cells from the cell boundary and from the interior along the broken heteroclinic connection. This trend is made evident by computing the Kolmogorov–Arnold–Moser tori for five supercritical Reynolds numbers.

Experiments on mixing due to chaotic advection in a cavity

1989 ◽  
Vol 209 ◽  
pp. 463-499 ◽  
Author(s):  
C. W. Leong ◽  
J. M. Ottino
Keyword(s):  
Large Scale ◽  
Spatial Arrangement ◽  
Periodic Points ◽  
Chaotic Advection ◽  
Two Dimensional ◽  
Complex Behaviour ◽  
Chaotic Flows ◽  
Regular Time ◽  
Slow Flows ◽  
Time Periodic

Chaotic mixing of fluids in slow flows is ubiquitous but incompletely understood. However, relatively simple experiments provide a wealth of information regarding mixing mechanisms and indicate the need for complementary theoretical developments in dynamical systems. In this work we presnt a versatile cavity flow apparatus, capable of producing a variety of two-dimensional velocity fields, and use it to conduct a detailed experimental study of mixing in low-Reynolds-number flows. Since the goal is detailed understanding, only two time-periodic co-rotating flows induced by wall motions are considered: one continuous and the other discontinuous. Both types of flows produce exponential growth of intermaterial area, as expected from chaotic flows, and a mixture of islands and chaotic regions. A procedure for identifying periodic points and determining their movements is presented as well as how to make meaningful comparisons between periodic flows. We observe that periodic points move very much as a planetary system; planets (hyperbolic points) have moons (elliptic points) with twice the period of the planets; furthermore the spatial arrangement of periodic points becomes symmetric at regular time intervals. Detailed analyses reveal complex behaviour: birth, bifurcation, and collapse of islands; formation and periodic motion of coherent structures, such as islands and large-scale folds. However, the richness and complexity of the results obtained indicate that these two-dimensional time-periodic systems are far from completely understood and that other wall motions might deserve a similar level of scrutiny.

The boundary contour method for two-dimensional Stokes flow and incompressible elastic materials

2002 ◽  
Vol 28 (5) ◽  
pp. 425-433 ◽  
Author(s):  
A.-V. Phan ◽  
L. J. Gray ◽  
T. Kaplan ◽  
T.-N. Phan
Keyword(s):  
Stokes Flow ◽  
Contour Method ◽  
Two Dimensional ◽  
Boundary Contour ◽  
Elastic Materials ◽  
Boundary Contour Method

scholarly journals Stokes flow singularities in a two-dimensional channel: a novel transform approach with application to microswimming

2013 ◽  
Vol 469 (2157) ◽  
pp. 20130198 ◽  
Author(s):  
Darren G. Crowdy ◽  
Anthony M. J. Davis
Keyword(s):  
Spectral Analysis ◽  
Fourier Transform ◽  
Boundary Value Problems ◽  
Stokes Flow ◽  
Evolution Equations ◽  
Two Dimensional ◽  
Third Order ◽  
Transform Method ◽  
Independent Variables ◽  
Simply Connected

A transform method for determining the flow generated by the singularities of Stokes flow in a two-dimensional channel is presented. The analysis is based on a general approach to biharmonic boundary value problems in a simply connected polygon formulated by Crowdy & Fokas in this journal. The method differs from a traditional Fourier transform approach in entailing a simultaneous spectral analysis in the independent variables both along and across the channel. As an example application, we find the evolution equations for a circular treadmilling microswimmer in the channel correct to third order in the swimmer radius. Significantly, the new transform method is extendible to the analysis of Stokes flows in more complicated polygonal microchannel geometries.

A remark on two-dimensional stokes flow solutions

1975 ◽  
Vol 26 (2) ◽  
pp. 245-247
Author(s):  
Jean-Yves Parlange
Keyword(s):  
Stokes Flow ◽  
Two Dimensional
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