Dynamics of passively advected impurities in simple two-dimensional flow models

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Abstract
The motion of passively advected impurities with density ρ p different from the fluid density ρ f in simple models of two‐dimensional velocity fields is studied. The impurity dynamics strongly depends on the parameter δ=ρ f /ρ p . For a stationary streamfunction, impurities that are lighter than the fluid undergo regular motions and converge to the centers of the advection cells. Particles denser than the fluid exhibit chaotic trajectories and standard diffusion at large times. For isotropic velocity fields, the diffusion coefficients display a scaling dependence upon the parameter ε=1−δ. For heavy impurities in weakly anisotropic velocity fields, the diffusion coefficients in the x and y directions may be different by several orders of magnitude. These features bear several resemblances to the motion of fluid particles in the presence of additive noise. For a time‐periodic streamfunction, the heavy particles undergo chaotic trajectories and standard diffusion; light particles may either display chaotic behavior and diffusion or regular motions ending with periodic trajectories, depending upon the values of the control parameters of the Eulerian flow. At intermediate times, the particle distribution displays complex caustic structures. Except that at very short times, the distribution of advected impurities trace neither the density nor the velocity of the advecting flow, even for δ only slightly different from one.