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Self-consistent chaotic transport in fluids and plasmas.

Diego Del-Castillo-Negrete1

  • 1Theoretical Division, Los Alamos National Laboratory, T-15 MS-K717, Los Alamos, New Mexico 87545.

Chaos (Woodbury, N.Y.)
|June 5, 2003
PubMed
Summary

This study explores self-consistent chaotic transport in fluid dynamics and plasma physics. New simplified models capture key phenomena like shear flow instability and vortex dynamics.

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Area of Science:

  • Fluid Dynamics
  • Plasma Physics
  • Dynamical Systems

Background:

  • Self-consistent chaotic transport involves field transport governed by advection-diffusion equations with dynamical constraints.
  • Lagrangian trajectories in these systems exhibit sensitive dependence on initial conditions.
  • This study focuses on two-dimensional incompressible shear flows, relating vorticity (F) and velocity (v) via nabla x v = zeta.

Purpose of the Study:

  • To investigate self-consistent chaotic transport in 2D incompressible shear flows.
  • To develop intermediate-complexity models bridging kinematic chaos and direct Navier-Stokes simulations.
  • To explore analogies with Vlasov-Poisson systems in plasma physics and coupled oscillator models.

Main Methods:

  • Developed three self-consistent models: vorticity defect, single wave, and a space-time discretized map.
  • Models simplify the vorticity-velocity coupling for dynamical systems analysis.
  • Used numerical simulations to validate model phenomenology against Navier-Stokes results.

Main Results:

  • The models successfully capture shear flow instability, vortex formation, and relaxation.
  • The vorticity defect model is analogous to Vlasov-Poisson plasma models.
  • The single wave model and map are applicable to both fluids and plasmas.

Conclusions:

  • Simplified models offer insights into complex self-consistent chaotic transport phenomena.
  • These models provide tractable Hamiltonians for Lagrangian advection studies.
  • The findings have implications for both fluid dynamics and plasma physics research.

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