Turbulent “Dynamo” in the Passive Scalar Problem Academic Article uri icon


  • A turbulent magnetic dynamo can be considered as the evolution of a vector field in a turbulent fluid flow. The problem of evolution of scalar fields (e.g., number density of small particles) in a turbulent fluid flow is similar to the turbulent magnetic dynamo. The dynamo instability results in generation of magnetic field. The most important effect which can cause a generation of mean magnetic field in a turbulent fluid flow is the α-effect: α = − (1/3)〈 τu · (∇ × u)〉, whereuis the turbulent velocity field with the correlation time τ. A similar instability in the passive scalar problem results in formation of large-scale inhomogeneous structures in a spatial distribution of particles due to the β-effect: β= 〈 τ up (∇ · up)〉, whereu p is the random velocity field of the particles which they acquire in a turbulent fluid velocity field. The effect is caused by inertia of particles which results in divergent velocity field of the particles. This results in additional turbulent nondiffusive flux of particles.

publication date

  • January 1, 1998