Chaotic streamlines in steady bounded three-dimensional Stokes flows

Physica D: Nonlinear Phenomena

Volumn 130, Issue 1-2, 1999, Pages 105-132

  Kroujiline, Dimitri ^a   Stone, H A ^a  

^a HARVARD UNIVERSITY   (United States)

Author keywords

Chaotic streamlines; Kinematics; Stokes flows

Indexed keywords

EID: 0346965756     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-2789(99)00003-2     Document Type: Article

References (23)

1. J.M. Ottino, The Kinematics of Mixing: Stretching, Chaos, and Transport, Cambridge University Press, Cambridge, 1989.
2. A. Gilbert, Magnetic field evolution in steady chaotic flows, Phil. Trans. R. Soc. Lond. 339 (1992) 627.
3. V.I. Arnold, Sur la topologie des écoulements stationnaires des fluides parfaits, C.R. Acad. Sci. Paris. 261 (1965) 17.
4. M. Hénon, Sur la topologie des lignes de courant dans un cas particulier, C.R. Acad. Sci. Paris. 262 (1966) 312.
5. T. Dombre, U. Frisch, J.M. Greene, M. Hénon, A. Mehr, A.M. Soward, Chaotic streamlines in the ABC flows, J. Fluid Mech. 167 (1986) 353.
6. K. Bajer, H.K. Moffatt, On a class of steady confined Stokes flows with chaotic streamlines, J. Fluid Mech. 212 (1990) 337.
7. K. Bajer, Hamiltonian formulation of the equations of streamlines in three-dimensional steady flows, Chaos Solitons Fractals 4 (1994) 895.
8. V. Toussaint, P. Carriere, F. Raynal, A numerical Eulerian approach to mixing by chaotic advection, Phys. Fluids 7 (1995) 2587.
9. D.L. Vainstein, A.A. Vasiliev, A.I. Neishtadt, Changes in the adiabatic invariant and streamline chaos in confined incompressible Stokes flow, Chaos 6 (1996) 67.
10. H.A. Stone, A. Nadim, S.H. Strogatz, Chaotic streamlines inside drops immersed in steady Stokes flows, J. Fluid Mech. 232 (1991) 629.
11. A.I. Neishtadt, D.L. Vainstein, A.A. Vasiliev, Chaotic advection in a cubic Stokes flow, Physica D 3 (1998) 227.
12. B.V. Chirikov, A universal instability of many-dimensional oscillator system, Phys. Rep. 52 (1979) 263.
13. R.Z. Sagdeev, D.A. Usikov, G.M. Zaslavsky, Nonlinear Physics: from the Pendulum to Turbulence and Chaos, Harwood, New York, 1988.
14. L.E. Reichl, The Transition to Chaos in Conservative Classical Systems: Quantum Manifestations, Springer, Berlin, 1992.
15. I. Mezić, S. Wiggins, On the integrability and perturbation of three-dimensional fluid flows with symmetry, Nonlinear Sci. 4 (1994) 157.
16. G.K. Batchelor, An Introduction to Fluid Dynamics, Cambridge University Press, Cambridge, 1967.
17. I.S. Gradshteyn, I.M. Ryzhik, Table of Integrals, Series and Products, Academic Press, New York, 1980.
18. N.N. Filonenko, R.Z. Sagdeev, G.M. Zaslavsky, Destruction of magnetic surfaces by magnetic field irregularities: part II, Nucl. Fusion 7 (1967) 253.
19. J. Guckenheimer, P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, Springer, Berlin, 1983.
20. S. Wiggins, Global Bifurcations and Chaos: Analytical Methods, Springer, Berlin, 1988.
21. M. Bryden, H. Brenner, Mass-transfer enhancement via chaotic laminar flow within a droplet, J. Fluid Mech. 379 (1999) 319.
22. J. Villermaux, Presentation at the Alpha Chi Sigma Symposium of the 1995 AIChE Annual Meeting.
23. S.I. Braginsky, Kinematic models of the Earth's hydromagnetic dynamo, Geomagn. Aeron. 4 (1964) 572.