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Layered structures, or staircases, in passive-scalar advection are resilient to disturbances. These structures form when diffusion time is much longer than turnover time, and remain stable across various conditions.

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Area of Science:

  • Plasma physics
  • Fluid dynamics
  • Turbulence theory

Background:

  • Layered profile structures, or staircases, are observed in systems like drift-wave turbulence within magnetic confinement devices.
  • These staircases arise from passive-scalar advection, driven by the interplay of cell turnover time (τH) and cell diffusion time (τD).

Purpose of the Study:

  • Investigate the resilience of staircase structures under global transverse shear and weak vortex scattering.
  • Generalize findings from fixed cellular arrays to fluctuating vortex arrays in numerical experiments.
  • Focus on low-to-modest effective Reynolds numbers relevant to magnetic fusion devices.

Main Methods:

  • Numerical experiments simulating passive-scalar advection with stationary and fluctuating vortex arrays.
  • Systematic perturbation of vortex array elements to assess staircase stability.
  • Analysis of scalar concentration transport along shear regions and homogenization within vortices.

Main Results:

  • Staircases form and exhibit resilience across a broad range of Reynolds numbers, though steps become less regular due to cell mergers.
  • Key criteria for staircase resiliency include τD ≫ τH and profile curvature κ ≥ 1.5.
  • Scalar concentration propagates along shear regions, forming staircase barriers before homogenizing in vortices; vortex scattering reduces front propagation speed.

Conclusions:

  • Staircase structures in passive-scalar advection are robust to shear and vortex scattering under specific conditions (τD ≫ τH, κ ≥ 1.5).
  • Cell geometric properties can approximate effective scalar diffusivity in fluctuating vortex arrays.
  • Effective diffusivity in fluctuating vortex arrays is comparable to that in fixed cellular arrays.