Transport in a slowly perturbed convective cell flow.

@article{Itin2002TransportIA,
  title={Transport in a slowly perturbed convective cell flow.},
  author={Alexander P. Itin and Rafael de la Llave and Anatoly I. Neishtadt and Alexei Vasiliev},
  journal={Chaos},
  year={2002},
  volume={12 4},
  pages={
          1043-1053
        }
}
We study transport properties in a simple model of two-dimensional roll convection under a slow periodic (period of order 1/ varepsilon >>1) perturbation. The problem is considered in terms of conservation of the adiabatic invariant. It is shown that the adiabatic invariant is well conserved in the system. It results in almost regular dynamics on large time scales (of order approximately varepsilon (-3) ln varepsilon ) and hence, fast transport. We study both generic systems and an example… 
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References

SHOWING 1-10 OF 23 REFERENCES
Different transport regimes in a spatially-extended recirculating background
Transport of a passive tracer in time-dependent Rayleigh-Be´nard convection
Transport of a passive scalar and Lagrangian chaos in a Hamiltonian hydrodynamic system
An experimental and numerical study is made of the chaotic behavior of Lagrangian trajectories and transport of a passive tracer in a quasi-two-dimensional four-vortex flow with a periodic time…
Chaotic advection in a Rayleigh-Bénard flow.
  • Camassa, Wiggins
  • Physics
    Physical review. A, Atomic, molecular, and optical physics
  • 1991
TLDR
By modeling the flow with a stream function, it is shown how to construct and identify invariant structures in the flow that act as a ‘‘template’’ for the motion of fluid particles, in the absence of molecular diffusivity.
An analytical study of transport in Stokes flows exhibiting large-scale chaos in the eccentric journal bearing
In the present work, we apply new tools from the field of adiabatic dynamical systems theory to make quantitative predictions of various important mixing quantities in quasi-steady Stokes flows which…
An analytical study of transport, mixing and chaos in an unsteady vortical flow
We examine the transport properties of a particular two-dimensional, inviscid incompressible flow using dynamical systems techniques. The velocity field is time periodic and consists of the field…
Resonant flights and transient superdiffusion in a time-periodic, two-dimensional flow
Chaotic mixing of immiscible impurities in a two-dimensional flow
Experiments compare the chaotic mixing of miscible and immiscible impurities in a two-dimensional flow composed of a chain of alternating vortices. Periodic time dependence is imposed on the system…
Stirring by chaotic advection
In the Lagrangian representation, the problem of advection of a passive marker particle by a prescribed flow defines a dynamical system. For two-dimensional incompressible flow this system is…
Lagrangian turbulence in nonstationary 2-D flows.
Lagrangian particle transport in nonstationary 2-D flows is studied both analytically and numerically. Analytic expressions for the diffusion coefficients are obtained for the adiabatic regime.…
...
1
2
3
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