The dynamics of Lagrangian particles in a complex geometry is studied, both experimentally and through a full numerical simulation of the Navier–Stokes equations. The geometry is an annulus whose walls can be rotated independently. Stationary cylindrical rods can be positioned within the annulus in several arrangements. A variety of heteroclinic orbits are found at low Reynolds numbers, where the fluid flow is steady. As the flow becomes unsteady to a time‐periodic (two‐dimensional) state, it spontaneously gives rise to heteroclinic tangles that provide the organizing structure for the chaotic motion of fluid particles.
REFERENCES
1.
J. M. Ottino, The Kinematics of Mixing: Stretching, Chaos, and Transport (Cambridge U. P., Cambridge, 1989).
2.
3.
4.
5.
J.
Chaiken
, R.
Chevray
, M.
Tabor
, and Q. M.
Tan
, Proc. R. Soc. London Ser. A
408
, 165
(1986
).6.
7.
8.
9.
10.
11.
T.
Dombre
, U.
Frisch
, J. M.
Greene
, M.
Henon
, A.
Mehr
, and A. M.
Soward
, J. Fluid Mech.
167
, 353
(1986
).12.
13.
14.
15.
M. F.
Schatz
, R. P.
Tagg
, H. L.
Swinney
, P. F.
Fischer
, and A. T.
Patera
, Phys. Rev. Lett.
66
, 1579
(1991
).16.
Handbook of Chemistry and Physics, 54th ed. (CRC, Cleveland, 1974).
17.
18.
G. E. Karniadakis, E. T. Bullister, and A. T. Patera, in Finite Element Methods for Nonlinear Problems (Springer-Verlag, New York, 1985), p. 803.
19.
20.
21.
22.
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© 1991 American Institute of Physics.
1991
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