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.

A Characterization of Harmonic $$L^r$$-Vector Fields in Two-Dimensional Exterior Domains

2019 ◽  
Vol 30 (4) ◽  
pp. 3742-3759 ◽  
Author(s):  
Matthias Hieber ◽  
Hideo Kozono ◽  
Anton Seyfert ◽  
Senjo Shimizu ◽  
Taku Yanagisawa
Keyword(s):  
Vector Fields ◽  
Two Dimensional ◽  
Exterior Domains

scholarly journals Two-dimensional global manifolds of vector fields

1999 ◽  
Vol 9 (3) ◽  
pp. 768-774 ◽  
Author(s):  
Bernd Krauskopf ◽  
Hinke Osinga
Keyword(s):  
Vector Fields ◽  
Two Dimensional
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