Invariant manifold templates for chaotic advection

Chaos, Solitons and Fractals

Volumn 4, Issue 6, 1994, Pages 749-868

  Beigie, Darin ^a   Leonard, Anthony ^b   Wiggins, Stephen ^b  

^a Center for Applied Mathematics Theory Center Cornell University ^*  (United States)

^b CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CHAOS THEORY; EQUATIONS OF MOTION; FRACTALS; INVARIANCE; LYAPUNOV METHODS; MIXING; SET THEORY; SYSTEM STABILITY; TOPOLOGY; VELOCITY;

CHAOTIC ADVECTION; CHAOTIC TANGLES; FLUID STRETCHING; HYPERBOLIC SETS; INVARIANT MANIFOLD TEMPLATES; LOBE BOUNDARIES; LOBE DYNAMICS;

FLUID DYNAMICS;

EID: 0028443749     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/0960-0779(94)90128-7     Document Type: Article

References (108)

1. Stirring by chaotic advection
2. Chaotic advection in a Stokes flow
3. Enhanced separation of diffusing particles by chaotic advection
4. Probability distribution functions in turbulent convection
5. Small-scale variation of convected quantities like temperature in turbulent fluid
6. Chaos and mixing in a geostrophic flow
7. A global study of enhanced stretching and diffusion in chaotic tangles
8. Chaotic transport in the homoclinic and heteroclinic tangle regions of quasiperiodically forced two-dimensional dynamical systems
9. The dynamics associated with the chaotic tangles of two-dimensional quasiperiodic vector fields: theory and applications
10. Dynamics associated with a quasiperiodically forced Morse oscillator: Application to molecular dissociation
11. Transport, Stretching, and Mixing in Classes of Chaotic Tangles
12. Statistical relaxation under nonturbulent chaotic flows: Non-Gaussian high-stretch tails of finite-time Lyapunov exponent distributions
13. Extended Chaos and Disappearance of KAM Trajectories
14. Multifractality in the statistics of the velocity gradients in turbulence
15. Regular and irregular motion
16. Chaotic advection in a Rayleigh-Bénard flow
17. The effect of strain rate on diffusion flames
18. Experimental study of Lagrangian turbulence in a Stokes flow
19. Laminar and chaotic mixing in cavity flows
20. Probabilities for temperature differences in Rayleigh-Bénard convection
21. Direct high resolution measurements of the fine scale structure of SC 〉〉1 molecular mixing in turbulent flows
22. Turbulent shear layer mixing with fast chemical reactions
23. Turbulent free shear layer mixing and combustion
24. Chaotic streamlines in the ABC flows
25. The persistence of strain in dynamical systems
26. The kinematics of stretching and alignment of material elements in general flow fiels
27. Trellises formed by stable and unstable manifolds in the plane
28. Transport through chaos
29. Observations of the flow produced in a cylindrical container by a rotating endwall
30. Passive scalars, three-dimensional volume-preserving maps, and chaos
31. Persistence and Smoothness of Invariant Manifolds for Flows
32. Chaotic flows and fast magnetic dynamos
33. Complex particle trajectories and transport in stationary and periodic convective flows
34. Fluctuations and transport in a stirred fluid with a mean gradient
35. Scaling laws for invariant measures on hyperbolic and nonhyperbolic attractors
36. Some remarks on chaotic particle paths in time-periodic three-dimensional swirling flows
37. Long-time correlations and expansion-rate spectra of chaos in Hamiltonian systems
38. The bifurcation of homoclinic tori in the quasiperiodically forced Duffing oscillator
39. Chaotic advection by laminar flow in a twisted pipe
40. Probability Density of Velocity Increments in Turbulent Flows
41. Bubble dynamics in time-periodic straining flows
42. Lobe area in adiabatic Hamiltonian systems
43. Analysis of chaotic mixing in two model systems
44. Dynamics of a three-dimensional incompressible flow with stagnation points
45. The form and dynamics of Langmuir circulations
46. Fluid Mixing and Dynamical Systems
47. Experiments on mixing due to chaotic advection in a cavity
48. Axisymmetric vortex breakdown—Part 3: Onset of periodic flow and chaotic advection
49. Transport in Hamiltonian Systems
50. Flux and differences in action for continuous time Hamiltonian systems
51. Resonances in area-preserving maps
52. Relation between quantum and classical thresholds for multiphoton ionization of excited atoms
53. Growth of a diffusion flame in the field of a vortex
54. Particle dynamics and mixing in a viscously decaying shear layer
55. Markov tree model of transport in area-preserving maps
56. Symplectic maps, variational principles, and transport
57. Advection of a vortex pair atmosphere in a velocity field of point vortices
58. On the stability of the center for time periodic perturbations
59. Melnikov transforms, Bernoulli bundles, and almost periodic perturbations
60. Stochastic geometric properties of scalar interfaces in turbulent jets
61. Double Poincaré sections of a quasi-periodically forced, chaotic attractor
62. The statistics of stretching and stirring in chaotic flows
63. Scaling and multifractal properties of mixing in chaotic flows
64. Mixing distributions produced by multiplicative stretching in chaotic flows
65. Fractal measures of passively convected vector fields and scalar gradients in chaotic fluid flows
66. Description of mixing with diffusion and reaction in terms of the concept of material surfaces
67. Mixing, Chaotic Advection, and Turbulence
68. Unity and diversity in mixing: Stretching, diffusion, breakup, and aggregation in chaotic flows
69. Large-scale horizontal mixing in planetary atmosphere
70. The measurement and interpretation of fractal dimensions of the scalar interface in turbulent flows
71. Transport by Capillary Waves—1: Particle Trajectories
72. Sustained resonance for a nonlinear system with slowly varying coefficients
73. An analytical study of transport, mixing and chaos in an unsteady vortical flow
74. Transport in two-dimensional maps
75. Transport Rates of a Class of Two-Dimensional Maps and Flows
76. Chaotic solutions of systems with almost periodic forcing
77. Spectral Analysis of Conservative Dynamical Systems
78. Acoustics and dynamics of coaxial interacting vortex rings
79. Dynamics of a class of vortex rings
80. A dynamical systems analysis of kinematics in the time-periodic wake of a circular cylinder
81. Vortex rings
82. Physical model of intermittency in turbulence—inertial-range non-Gaussian statistics
83. Chaotic particle transport in time-dependent Rayleigh-Bénard convection
84. The fractal facets of turbulence
85. Fractals and multifractals in fluid turbulence
86. Transversal homoclinic points and hyperbolic sets for non-autonomous maps—I
87. Transversal homoclinic points and hyperbolic sets for non-autonomous maps—II
88. Random perturbations of heteroclinic attractors
89. Unstable fixed points, heteroclinic cycles and exponential tails in turbulence production
90. Spectrum of fractal dimensions of passively convected scalar gradients in chaotic fluid flows
91. The spatial structure and statistical properties of homogeneous turbulence
92. Mass transport and mixing by modulated traveling waves
93. Chaos in the quasiperiodically forced Duffing oscillator
94. On the geometry of transport in phase space—I: Transport in k-degree-of-freedom Hamiltonian systems, 2 ⪕k<∞
95. Preliminary study of mutual slip-through of a pair of vortices