Chaotic advection and transport in helical Beltrami flows: A Hamiltonian system with anomalous diffusion
- Institut de Recherche sur les Phenomenes Hors Equilibre, 12, avenue General Leclerc, F-13003 Marseille Cedex (France)
- Courant Institute of Mathematical Sciences and Department of Physics, New York University, New York, New York 10012 (United States)
The chaotic advection of a passive scalar in a three-dimensional flow is investigated. The stationary velocity field of the incompressible fluid possesses a helical symmetry and satisfies the Beltrami property, and is then an exact solution to the Euler equations. The streamlines of the fluid form a stochastic web which determines the transport properties. In this cylindrical geometry the origin plays a special role. For pure 2{pi}/n symmetry (n is an integer) the particles can return to the origin in finite time, as can be demonstrated analytically. The statistical behavior of the passive scalar is studied by using numerical integrations of the motion equations. Subdiffusive behavior is found, the radial variance growing in time with a characteristic exponent of {approx}0.52 (this exponent is 1 for normal Brownian diffusion). The return probability is also computed. A random walk model, assuming absorption and waiting times proportional to the distance from the origin, appropriately describes the observed features of the particle statistics. In the continuous limit this model gives a diffusion equation with memory effects, highlighting the non-Markovian character of the dynamical system. {copyright} {ital 1997} {ital The American Physical Society}
- OSTI ID:
- 503667
- Journal Information:
- Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, Vol. 55, Issue 5; Other Information: PBD: May 1997
- Country of Publication:
- United States
- Language:
- English
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